Flight control systems: practical issues in design and implementation

FLIGHT CONTROL SYSTE,,MS practical"

" issues In

design and implementation Edited by Roger W. Pratt

The Institution of Electrical Engineers

Copublished by: The Institution of Electrical Engineers, Michael Faraday House, Six Hills Way, Stevenage, Herts. SG1 2AY, United Kingdom and The American Institute of Aeronautics and Astronautics 1801 Alexander Bell Drive Suite 500 Reston VA 20191-4344 USA © 2000 Editorial selection and presentation: The Institution of Electrical Engineers For copyright ownership details see final page of each chapter. This publication is copyright under the Berne Convention and the Universal Copyright Convention. All rights reserved. Apart from any fair dealing for the purposes of research or private study, or criticism or review, as permitted under the Copyright, Designs and Patents Act, 1988, this publication may be reproduced, stored or transmitted, in any forms or by any means, only with the prior permission in writing of the Institution of Electrical Engineers (lEE) or in the case of reprographic reproduction in accordance with the terms of licences issued by the Copyright Licensing Agency or Copyright Clearance Centre Inc. Inquiries concerning reproduction outside those terms should be sent to the lEE at the address above. While the authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgment when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence or any other cause. Any and all such liability is disclaimed. The moral right of the authors to be identified as authors of this work has been asserted by them in accordance with the Copyright, Designs and Patents Act 1988.

British Library Cataloguing in Publication Data A CIP catalogue record for this book is available from the British Library ISBN 0 85296 766 7

Printed in England by TJ International, Padstow, Cornwall

To Gill, Joanne, Ian and Sara

Contributors

B.D. Caldwell Aerodynamics (W310C) British Aerospace Warton Aerodrome Preston PR4 lAX UK M.V° Cook Flight Test and Dynamics Group College of Aeronautics Cranfield University Cranfield, Bedfordshire MK43 0AL UK L.F. Faleiro Control Design Engineering Institute for Robotics and Mechatronics German Aerospace Center DLR Oberpfaffenhofen Postfach 1116 82234 Wessling Germany R,D. Felton 14 Cromwell Court Eynesbury St Neots, Cambs. PE19 2NZ UK J. Fenton Smiths Industries Aerospace Bishops Cleeve Cheltenham, Glos. GL52 4SF UK

C. Fielding Aerodynamics (W427D) British Aerospace Warton Aerodrome Preston PR4 lAX UK J. Hodgkinson 7022 Starstone Drive Rancho Palos Verdes, CA 90275 USA R.A. Hyde Cambridge Control Ltd Matrix House Cowley Park Cambridge CB4 0HH UK R. Luckner DaimlerChrysler Aerospace Airbus GmbH Flight Mechanics Flight Guidance and Control PO Box 95 01 09 D-21111 Hamburg Germany D.G. Mitchell Hoh Aeronautics Inc. Vista Verde Center 217 2075 Palos Verdes Drive North Lomita, CA 90717 USA

xiv

Contributors

R.W. Pratt Formerly: Department of Aeronautical and Automotive Engineering Loughborough University Loughborough UK Now with: Ricardo MTC Ltd. Midlands Technical Centre Southam Road Radford Semele Leamington Spa Warwicks CV31 1FQ UK S.P. Ravenscroft

Flight Systems (W354C) British Aerospace Warton Aerodrome Preston PR4 lAX UK

T,D. Smith Flight Test (W27K) British Aerospace Warton Aerodrome Preston PR4 lAX UK R. Taylor Ricardo MTC Ltd. Midlands Technical Centre Southam Road Radford Semele Leamington Spa Warwicks CV31 1FQ UK

Preface

If you belong to the school of thought that says 'give me a model and I'll give you a controller' then this book is not for you. If, however, you believe that using linear-control design methodologies to develop flight control laws requires a fuller understanding of the dynamics of the plant (aircraft), the problems associated with implementation and the n e e d to satisfy the requirements of a highly trained h u m a n operator (pilot) then the chapters in this b o o k should help you to develop that understanding. In essence, m u c h of this b o o k is a message to the academic researcher which says: ' I f your work is to be useful to practising engineers in industry, then you n e e d to understand, or at least appreciate, the issues dealt with in this book'. Additionally, young engineers who are beginning their careers in the aerospace industry should find it useful to have a coverage of the key aspects of flight control in a single volume T h e authors were chosen because of their depth of experience and mix of backgrounds, which I believe are reflected in their individual contributions. Additionally, in a n u m b e r of cases the chapters were reviewed by senior managers who have spent their entire careers in the aerospace industry. Hopefully, the experience which lies behind the individual contributions will encourage a new generation of engineers, mathematicians and scientists to b e c o m e involved in this exciting branch of e n g i n e e r i n g - - f l i g h t control systems. In the late seventies and eighties very few texts were p r o d u c e d on flight control. T h e n in the nineties a n u m b e r of books appeared. For readers who are new to flight control it might be useful to attempt to assign a place for this text in the total grouping. Fundamentals of the subject with varying degrees o f emphasis on aircraft dynamics and flight control are covered by a n u m b e r of texts [1-7]. All of these texts should be of use to u n d e r g r a d u a t e students in the final year or years of their courses, as well as to postgraduate students who are in the process of strengthening their knowledge of f u n d a m e n t a l concepts before immersing themselves in their specific topic. The texts by McLean [4] and Stevens and Lewis [7] will extend the r e a d e r ' s knowledge into the realms of research work. The contribution edited by Tischler [8] is significantly different from the other texts in that experienced practitioners, some of whom have contributed to this book, give a strong account of the state of the art, for rotorcraft, combat aircraft and fixed-wing transport

xvi

Preface

aircraft. Our text is seen as bridging the gap between the work on fundamental principles and Tischler's excellent collection of research reviews. The aim of this text is to build on the fundamentals of flight dynamics and flight control as described in References [ 1-7] and embellish these principles by assigning their relevance to the development of flight control systems in the aircraft industry. The first seven chapters cover most of the key areas within the discipline of flight control systems with explicit reference to recent development programmes written by engineers who were closely involved in the work. The last two chapters look at just two of the multitude of m o d e r n control methods which have been the subject of research studies. The text is largely restricted to military and civil fixed-wing aircraft. Only the constraint of space has prevented equivalent material for rotorcraft and missiles from being included. The book comprises nine chapters: Chapter 1 'Industrial considerations for flight control', Chris Fielding and Robert Luckner: the authors set the scene for the whole book by explaining the industry's perspective on flight control systems, giving a comprehensive overview of the subject with more detailed discussions of some particular topics being given in later chapters. The authors have carried through their chapter the parallel themes of military combat aircraft and civil aircraft, an interesting feature which strongly reflects their backgrounds. The Chapter begins by examining the general objectives of flight control and the role of the flight control system (FCS). This is followed by the operational requirements for both types of aircraft and a discussion of the benefits of fly-by-wire (FBW) in the pilot-vehicle system. The systems issues are explored, as are reliability and integrity, the twin versus--verification and validation. The Chapter is rounded off by a discussion of the state-of-the-art and a look at some exciting future developments. Chapter 2 'Aircraft modelling', Mike Cook: the author summarises from his own text [3] the main elements of axis systems and the equations of motion for the longitudinal and lateral dynamics of fixed-wing aircraft. Aircraftresponse transfer functions and state-space representations are then developed from the equations of motion. Any reader who requires a fuller treatment than can be given within the confines of this book is strongly r e c o m m e n d e d to refer to Mike's own text. Chapter 3 'Actuation systems', Steven Ravenscroft: since the advent of powered control surfaces without manual reversion, in the era of the Lightning, actuation systems have assumed great importance. The significance of actuation systems has been further enhanced by the drive to develop highly agile combat aircraft in which a safety-critical flight control system is required to stabilise the unstable open-loop dynamics of the aircraft. This comprehensive chapter begins with an overview of primary and secondary control surfaces and their operation and leads on to a discussion of performance criteria and modelling. The latter sections discuss more

Preface

xvii

advanced topics: nonlinear frequency response, saturation analysis, j u m p resonance and failure transients. Chapter 4 'Handling qualities', J o h n Hodgkinson and Dave Mitchell: uses the response transfer functions developed in Chapter 2 and examines the response of the aircraft from the pilot's viewpoint. The subjectivity which is inherent in the assessment of handling qualities has, inevitably, given rise to a n u m b e r of metrics and these are discussed in relation to the dynamic modes for the longitudinal and the lateral motion. This leads on to stability and control augmentation systems and a discussion of some control design concepts. Clearly, a chapter on handling qualities has to include a discussion of pilot-induced oscillations (PIOs). This topic is given a thorough and up-todate treatment which reflects the very recent research carried out in the United States. Chapter 5 'Automatic flight control system design considerations', J o h n Fenton: this chapter gives a clear and practical breakdown of the tasks which are necessary in the management of the development programme for a complex flight control system. The conciseness of the chapter stems from the detailed breakdown of the main areas, the development programme requirements definition and verification, system design considerations and AFCS architecture, into detailed subtasks. Chapter 6 'Ground and flight testing a digital flight control system', Terry Smith: discusses the techniques which have been employed by the UK's major aircraft manufacturer, British Aerospace, as it has progressed with the development of fly-by-wire combat aircraft. The chapter gives an excellent description of the need to progress a test programme in a way which minimises both risk and cost, from the philosophy, tools and techniques of flight testing through the elements of simulator and rig testing, ground testing and, of course, flight testing. Chapter 7 'Aeroservoelasticity', Brian Caldwell, Roger Pratt, Richard Taylor and Richard Felton: discusses how a safety-critical flight control system can be affected by the elastic behaviour of the aircraft structure, namely the p h e n o m e n o n of aeroservoelasticity or structural coupling. As with the previous chapter, the material draws on the experience gained at British Aerospace with a series of aircraft in which the open stability has been reduced to the point of severe instability in order to enhance manoeuvrability. The contributions from Richard Taylor and Richard Felton are based on the results of research programmes which were carried out at the Universities of Loughborough and Lancaster, respectively. Chapter 8 'Eigenstructure assignment', Lester Faleiro and Roger Pratt: represents one contribution to the work done u n d e r the GARTEUR Action Group on robust flight control in which a group of universities, research establishments and aircraft companies contributed u n d e r Jan Terlouw's (NLR) excellent stewardship. Eigenstructure assignment was chosen in this case because it appeared to offer a more visible methodology than other m o d e r n control techniques. The case study (RCAM) was based on a flight

xviii

Prefa~

profile for a civil aircraft which consisted of a base leg and a two-stage final approach. The chapter is intended as an honest assessment of eigenstructure assignment in this type of application. Chapter 9 'An H0~ loop-shaping design for the VAAC Harrier', Rick Hyde: describes one of the most exciting research programmes which has been carried out in the field of m o d e r n control engineering applied to flight control. H0~ designs were evaluated extensively by piloted simulation and on the VAAC Harrier at DERA Bedford where the controller was in competition with designs from British Aerospace and Smiths Industries. The early work benefited enormously from the rapport between Rick and the RAF's test pilot, Bj6rn Singer. A step-by-step guide is given to the linear loop-shaping design process with a clear description of the use of the knowledge of the aircraft's dynamics. This is followed by the work on implementation and flight testing which explains the approach that was taken to gain-schedule controllers, deal with antiwindup as well as describe the impressive results achieved during flight testing. I would like to thank George Irwin, co-editor for the series, for inviting me 'to write or edit a text of flight control': certainly, there have been moments when I have regretted yielding to George's Celtic persuasion. However, over twenty or so years I have benefited greatly from my association with the control community in the UK and, more recently, this has been equally true o f my association with the guidance, navigation and control activities within the AIAA in the United States and GARTEUR in Europe. My contribution to this book can be viewed as a partial repayment of a very large debt. Obviously, an edited text is the product of a team of authors. I have been extremely fortunate to be able to assemble a very strong team, but more than that, they have been great people to work with. Although, inevitably, experienced people have many calls on their time and from time to time this has caused the usual problems, everyone has come through and I have greatly appreciated their support and friendship throughout the preparation of the text. Additionally, I would like to thank the people who have volunteered to review individual chapters. Tony Lambregts (FAA) and Mike Walker (British Aerospace) are two people who are known to me, others have been acknowledged by individual authors. The process of publishing an edited text with several contributors is a demanding task. I have been extremely fortunate to work with Jonathan Simpson, then the IEE's commissioning editor for the project. Jonathan's quietly efficient style impressed me greatly and on many, many occasions I have been extremely grateful for his support and guidance. I would also like to thank Robin Mellors-Bourne, Director of Publishing, who managed the project in addition to his normal duties during a very difficult period and Sarah Daniels, Book Production Editor, who joined the project at a late stage and injected some much needed energy and enthusiasm. Finally, I would like to express my thanks to Penny Pilkington whose support and commitment I have greatly appreciated throughout this project.

Preface

xix

Penny has acted as the focal point for communications and retyped contributions and patiently, well mostly patiently, e n d u r e d the seemingly endless edits.

References [1] BABISTER, A.W.: 'Aircraft-dynamic stability and response' (Pergamon Press, 1980) [2] BLAKELOCK,J.H.: 'Automatic-control of aircraft and missiles' (Wiley, 1991, 2nd edn.) [3] COOK, M.V.: 'Flight dynamics: principles' (Arnold, 1997) [4] ETKINS, B, and REID, L.D.: 'Dynamics of flight: stability and control' (Wiley, 1996, 3rd edn.) [5] MCLEAN, D.: 'Automatic-flight control systems' (Prentice-Hall, 1990) [6] NELSON, R.C.: 'Flight stability and automatic control' (McGraw-Hill, 1998, 2nd edn.) [7] STEVENS, B.L., and LEWIS, EL.: 'Aircraft control and simulation' (Wiley, 1992) [8] TISCHLER, M.B. (Ed): 'Advances in aircraft flight control' (Taylor & Francis, 1996)

Nomenclature

A B

cg C

cL D

g G h

i, I

I= kq

k~ kw ko kr L m

M M

N N o

P q 1" $

t

state matrix input matrix centre of gravity output matrix drag coefficient lift coefficient direction cosine matrix; direct matrix acceleration due to gravity transfer function matrix height m o m e n t of inertia in roll m o m e n t of inertia in pitch m o m e n t of inertia in yaw identity matrix product of inertia about ox or oz axes pitch-rate transfer function gain constant axial-velocity transfer function gain constant normal-velocity transfer function gain constant pitch-attitude transfer function gain constant turbojet engine gain constant rolling m o m e n t mass pitching m o m e n t 'mass' matrix yawing m o m e n t n u m e r a t o r matrix origin of axes roll-rate perturbation pitch-rate perturbation yaw-rate perturbation Laplace operator time; maximum aerofoil section thickness roll-mode time constant

xxviii

U U

U /] V

V

W X X

X Y Y Y Z

Z

Re

%

A

7/ 0

I"

Nomenclature

spiral-mode time constant numerator zero in axial-velocity transfer function numerator zero in normal-velocity transfer function numerator zero in pitch-rate and attitude transfer functions turbojet engine time constant axial-velocity perurbation input vector total axial velocity axial component of steady-equilibrium velocity lateral-velocity perturbation eigenvector perturbed total velocity; total lateral velocity lateral component of steady-equilibrium velocity steady-equilibrium velocity normal-velocity perturbation total normal velocity normal component of steady-equilibrium velocity longitudinal coordinate in axis system state vector axial-force component lateral coordinate in axis system output vector lateral-force component normal coordinate in axis system normal-force component angle-of-attack or incidence perturbation equilibrium incidence sideslip angle perturbation equilibrium flight-path angle roll-control stick angle pitch-control stick angle rudder-pedal control angle transfer function denominator throttle-lever angle rudder-angle perturbation; damping ratio dutch-roll damping ratio phugoid damping ratio short-period pitching-oscillation damping ratio elevator-angle perturbation pitch-angle perturbation equilibrium pitch angle aileron-angle perturbation engine-thrust perturbation roll-angle perturbation

Nomenclature

¢ ~0 d f-On

% Ws

yaw-angle perturbation dutch-roll u n d a m p e d natural frequency d a m p e d natural frequency phugoid u n d a m p e d natural frequency short-period pitching-oscillation u n d a m p e d natural frequency

SUBSCRIPTS

0 b d e E p q r s u v w

free-stream flow conditions aeroplane body axes dutch roll equilibrium, steady or initial condition datum-path earth axes roll rate; phugoid pitch rate yaw rate; roll mode short-period pitching oscillation; spiral mode axial velocity lateral velocity aeroplane wind or stability axes; normal velocity

(

rudder elevator pitch ailerons thrust

0 ~-

EXAMPLES OF O T H E R SYMBOLS AND NOTATION xu

a shorthand notation to denote a concise derivative, a dimensional derivative divided by the appropriate mass or inertia parameters

.~

a shorthand notation to denote the dimensional Ou

N { (s)

a shorthand notation to denote a transfer function numerator polynomial relating the output response y to the input u

OX

xxix

Contents

Contributors Preface Glossary of terms Nomenclature 1 Industrial considerations for flight control C. Fielding and R. Luckner 1.1 Introduction 1.2 The general objectives of flight control 1.2.1 Military aircraft 1.2.2 Civil aircraft 1.3 The role of the flight control system 1.3.1 History 1.3.2 Military aircraft developments 1.3.3 Civil aircraft developments 1.4 Aircraft in-service requirements 1.4.1 Military aircraft operations 1.4.2 Civil aircraft operations 1.5 The benefits of fly-by-wire 1.5.1 Military aircraft benefits 1.5.2 Civil aircraft benefits 1.6 Flight control systems implementation 1.6.1 Military aircraft--design considerations and systems overview 1.6.2 Civil aircraft--design considerations and systems overview 1.7 Military aircraft--state-of-the-art and future challenges 1.7.1 Eurofighter Typhoon 1.7.2 Future challenges for military aircraft 1.8 Civil aircraft--state-of-the-art and future challenges 1.8.1 The Airbus fly-by-wire family 1.8.2 Boeing 777 1.8.3 Future challenges for civil aircraft 1.9 The flight control system development process 1.9.1 The current situation 1.9.2 The system development process 1.9.3 The flight control laws development process 1.9.4 Cost considerations--recurring and nonrecurring costs 1.10 Closing discussion 1.11 Acknowledgements 1.12 References 2 Aircraft modelling M. V. Cook 2.1 Introduction

xiii xxvfi

1 2 6 6 7 7 9 12 13 13 15 17 18 19 20 20 27 30 30 33 34 34 42 42 43 43 44 46 5O 51 53 53 56 56

Contents

viii 2.2 2.3

2.4

2.5

2.6

2.7

2.8 2.9 2.10

2.11

2.12 2.13

A mathematical framework Axes systems and notation 2.3.1 Earth axes 2.3.2 Aeroplane-body fixed axes 2.3.3 Perturbation variables 2.3.4 Angular relationships in symmetric flight 2.3.5 Choice of axes Euler angles and aeroplane attitude 2.4.1 Linear-quantities transformation 2.4.2 Angular velocities transformation Controls notation 2.5.1 Aerodynamic controls 2.5.2 Engine control The decoupled small-perturbation equations of motion 2.6.t The equations of longitudinal symmetric motion 2.6.2 The equations of lateral-directional asymmetric motion The equations of motion in state-space form 2.7.1 The equations of longitudinal motion 2.7.2 The equations of lateral-directional motion Aircraft-response transfer functions The transfer function matrix Longitudinal response to controls 2.10.1 The longitudinal transfer function matrix 2.10.2 The longitudinal characteristic equation 2.10.3 The short-period pitching oscillation 2.10.4 The phugoid Lateral-directional response to controls 2.11.1 The lateral transfer function matrix 2.11.2 The lateral-directional characteristic equation 2.11.3 The roll-subsidence mode 2.11.4 The spiral mode 2.11.5 The dutch-roll mode Conclusions Reference

3 Actuation systems

57 59 59 60 61 63 64 65 66 66 67 67 67 68 68 69 69 7O 72 72 73 74 74 76 76 79 81 81 84 85 86 87 89 89 9O

S. Ravenscroft 3.1 3.2 3.3

3.4 3.5 3.6 3.7 3.8 3.9 3.10

Introduction Actuation system technology--an overview 3.2.1 Control-surface types 3.2.2 Actuator operation Actuation system-performance criteria 3.3.1 Stall load 3.3.2 Maximum rate capability 3.3.3 Frequency response 3.3.4 Dynamic stiffness 3.3.5 Failure transients Actuation system modelling Nonlinear frequency response Saturation analysis J u m p resonance Failure transients Conclusions Acknowledgements

90 90 90 91 96 98 99 100 104 105 107 109 110 112 112 116 118

Contents 4 Handling qualities

ix

119

J. Hodgkinson and D. Mitchell 4.1 4.2

Introduction Longitudinal flying qualities 4.2.1 Control-input transfer functions 4.2.2 Modal criteria 4.2.3 Phugoid flying qualities 4.2.4 Short-period flying qualities 4.2.5 Criteria for the longitudinal short-period dynamics 4.2.6 Model criteria for the short period 4.2.7 Other short-period criteria 4.2.8 Equivalent systems 4.2.9 Equivalent time delay 4.2.10 The bandwidth method 4.2.11 The Neal-Smith method 4.2.12 Gibson's dropback criterion 4.2.13 Time-history criteria 4.2.14 Flight-path stability 4.3 Lateral-directional flying qualities 4.3.1 Roll mode 4.3.2 Spiral mode 4.3.3 Coupled-roll spiral 4.3.4 Dutch-roll mode 4.3.5 The parameter t%/~a 4.3.6 Phi-to-beta ratio, ~b//3 4.4 Stability and control-augmentation systems 4.4.1 The influence of feedback 4.4.2 The influence of actuators, sensors and processors 4.4.3 Multiple-input, multiple-output flying quality possibilities 4.4.4 Response types 4.5 Notes on some control design concepts 4.5.1 Integration in the forward path 4.5.2 Notch filters 4.5.3 Stick prefilters 4.5.4 Model prefilters 4.6 Pilot-induced oscillations ( P i t s ) 4.6.1 P I t categories 4.6.2 P I t and APC 4.6.3 Criteria for category I P i t s 4.7 Modal P I t criteria 4.7.1 STI high-gain asymptote parameter 4.7.2 A'Harrah-Siewert criteria 4.7.3 Dynamic stick force per g 4.8 Non-modal P I t criteria 4.8.1 Some current criteria 4.8.2 Effectiveness of the criteria 4.9 Effects of rate limiting on P I t 4.9.1 Criteria for category II P i t s 4.9.2 The consequences of rate limiting 4.10 Concluding remarks 4.11 References

119 121 121 121 122 123 124 126 126 127 131 132 132 134 134 136 136 136 139 139 139 140 141 142 142 144 146 147 147 147 149 150 150 150 150 151 151 152 152 155 155 155 156 161 164 164 165 167 167

x

Contents

5 Automatic flight control system design considerations

170

J. Fenton

5.1 AFCS development programme 5.1.1 Study phase/vendor selection 5.1.2 Interface definition 5.1.3 System definition 5.1.4 Software design and code 5.1.5 Hardware design and development 5.1.6 System integration and test 5.1.7 Qualification testing 5.1.8 Preliminary (final) declaration of design and performance (PDDP/FDDP) 5.1.9 Flight testing 5.1.10 Certification 5.1.11 Design reviews 5.2 Requirements definition and verification 5.2.1 Introduction 5.2.2 Design and test methodology 5.2.3 Safety considerations 5.3 System design considerations 5.3.1 Primary considerations 5.4 AFCS architecture 5.4.1 Introduction 5.4.2 AFCS flying control interfaces 5.4.3 AFCS system interfaces 5.4.4 AFCS configurations 5.4.5 Flight control computer data processing 6 Ground and flight testing of digital flight control systems

170 170 172 172 172 172 172 173 173 173 173 173 174 174 175 176 178 178 184 184 184 184 188 189

197

7: Smith

6.1 Introduction 6.2 Philosophy of flight testing 6.2.1 Ground testing 6.2.2 Simulator and rig testing 6.3 Aircraft ground testing 6.3.1 FCS build tests 6.3.2 Ground-resonance tests 6.3.3 Structural-coupling tests 6.3.4 Electromagnetic-compatibility testing 6.3.5 Engine-running tests 6.4 Flight test tools and techniques 6.5 Flight testing 6.5.1 FBWJaguar demonstrator flight test programme 6.5.2 The EAP demonstrator flight test programme 6.6 Conclusion 6.7 Acknowledgements 6.8 References

7 Aeroservoelasticity

197 2O0 201 202 209 210 210 210 211 213 213 214 214 217 223 223 223

225

B.D. CaldweU, R. W. Pratt, tL Taylor and R.D. Felton

7.1 Introduction 7.2 Elements of structural coupling 7.2.1 Flexible-aircraft modal dynamics

225 226 226

Contents

7.3

7.4

7.5 7.6

7.2.2 Inertial excitation of the flexible-aircraft control surface 7.2.3 Actuators, flight control computers and the aircraft-motion sensor unit 7.2.4 Aerodynamic excitation of the flexible-aircraft's control surface 7.2.5 Flexible-aircraft modal aerodynamics 7.2.6 Formulation for solution and design trade-offs FCS-SC structural coupling: design examples 7.3.1 Jaguar-first flight 1968 7.3.2 Tornado-first flight 1974 7.3.3 Experimental aircraft programme (EAP)--first flight 1986 7.3.4 Eurofighter 2000 (EF2000)--first flight 1994 Future developments 7.4.1 Limit-cycle prediction and specification of alternative clearance requirements 7.4.2 Active control for rigid body and structural-mode stabilisation 7.4.3 Flexible aircraft modelling Conclusions References

8 Eigens~ucture assignment applied to the design of an autopilot function for a civil aircraft L.F. Faleiro and R. W. Pratt

8.1 Introduction 8.2 The RCAM control problem 8.2.1 A landing-approach simulation 8.2.2 Performance specifications 8.2.3 Robustness specifications 8.2.4 Ride-quality specifications 8.2.5 Safety specifications 8.2.6 Control-activity specifications 8.3 Eigenstructure analysis and assignment 8.3.1 Eigenstructure analysis 8.3.2 Eigenstructure assignment 8.4 The eigenstructure assignment design cycle 8.4.1 Controller structure 8.4.2 Construction of a desired eigenstructure 8.4.3 Initial synthesis 8.4.4 Methods of controller analysis 8.4.5 Analysis of the longitudinal controller 8.4.6 Analysis of the lateral controller 8.4.70ptimisation of the controllers 8.5 Nonlinear simulation of the controlled aircraft 8.5.1 Performance specifications 8.5.2 Robustness specifications 8.5.3 Ride-quality specifications 8.5.4 Safety specifications 8.5.5 Control-activity specifications 8.5.6 Evaluation using a landing-approach simulation 8.6 Conclusions 8.7 References 9 An H ® loop-shaping design for the VAAC Harrier R.A. Hyde

9.1 Introduction

xi 226 228 230 230 230 234 235 236 237 248 260 260 284 297 298 299 301

301 302 304 305 306 306 306 307 307 307 310 316 316 320 324 324 327 329 330 331 333 337 337 338 338 339 343 346 348

348

xii

Contents

9.2 9.3 9.4 9.5

The VAAC Harrier Ha Loop shaping Linear design for the VAC Implementation and flight testing 9.5.1 Gain scheduling 9.5.2 Anti-windup 9.5.3 Flight modes 9.5.4 Flight testing 9.6 Flight clearance 9.7 The way ahead 9.8 References

350 350 354 359 359 360 362 364 366 371 372

Index

375

Glossary of terms

Accident (aircraft): an unintended event that causes death, injury, environ-

mental or material damage Active control technology: the use of feedback control to enhance the performance or controllability and handling of a vehicle Actuator: physical device for producing motion and/or force Adaptive control: real-time parameter identification and controller update Aerodynamic derivative: partial derivative defining changes in vehicle force or moment due to changes in control or motion parameters Air data system: provides flight-condition and velocity vector information from external aircraft measurements Airworthiness: an all-embracing term to describe an aircraft's ability to fulfil its role safely Aliasing: phenomenon in digital systems in which input signal frequencies above half the sampling frequency appear at lower frequencies on the output signal, owing to the sampling process Analogue (computer): using electrical signals that are directly proportional (i.e. analogous) to a continuous physical parameter Angle of attack (AoA): the angle formed by the vector addition of the aircraft body-axis normal and longitudinal velocity components Anti-aliasing filter: function for reducing aliasing by restricting the bandwidth of the signal to be sampled--usually an analogue filter with a natural frequency set to less than half the sampling frequency Authority limit" permissible maximum amplitude of a signal or physical parameter Autopilot- outer-loop automatic control system for reducing pilot workload and/or augmenting weapon-system performance Autostabiliser: simple stability-augmentation system, usually to provide increased damping and often with limited authority Averaging (rolling average): digital process used to provide a smoothing and anti-aliasing function Backlash: a form of hysteresis found in mechanical systems Bandstop filter: see notch filter Bandwidth: range of frequencies over which the amplitude of the frequency response of a device remains essentially constant (numerical definitions vary)

Glossary of terms

xxi

Bode diagram: frequency-response plots covering gain (usually in decibels, dB) against frequency and phase against frequency Break point: frequency at which attenuation (or amplification) appears to occur, for the frequency response of a real pole or zero term Built-in test: checks that are carried out automatically on the system or part of the system by failure-detection algorithms within the flight control system. These checks may be carried out continuously or at specific instances, for example, on start-up Carefree handling: protection of aircraft from both departure and exceedance of loading limits, regardless of pilot-input demands, through the functionality of the flight control system Certification: process for demonstrating that system safety is satisfactory for flight operation Characteristic equation: polynomial defining the linear-stability characteristics of the system (defined by setting the denominator of a transfer function equal to zero) Classical control: range of design and analysis techniques developed early in the 20th century, principally the methods referred to as Bode, Nyquist, Nichols, R o o t - L o c u s . . . Clearance: see certification Closed-loop control: outputs from the aircraft (or system) are measured and fed back to provide corrective action Command path: part of control system between physical input (e.g. pilot's stick) and the point where feedback is applied Conditionally stable: a system that is stable only for a range of values of a particular gain; the system can be made unstable by either increasing or decreasing the nominal gain value by a sufficient amount Control-configured vehicle (CCV): one which incorporates the control system capabilities and limitations at the onset of the project design Control law: architecture containing controller(s), feedback filtering, nonlinear compensation and scheduling Controller: algorithm or filter to provide desired control behaviour, usually acting on an error signal Cooper-Harper rating: a method for quantifying pilot opinion of an aircraft handling task, in terms of perceived controllability and operational effectiveness Crossover frequency: gain crossover occurs when the gain of a system equals unity (0 dB); phase crossover occurs when the phase equal - 1 8 0 degrees. These are the frequencies at which the stability margins are measured Damping: attribute which determines the nature of a response, in terms of the rate of decay of oscillatory behaviour DC block: see high-pass filter Dead-beat (response): exhibiting no overshoot when tracking a step input signal

xxii

Glossary of terms

Dead-zone: nonlinearity in which no output is achieved until the input exceeds some threshold Decade: frequency interval in which the frequency changes by a factor of ten Decibel (riB): defined at each frequency as 101ogl0(g) where g is ratio of powers, or 201ogl0(g) if g is a ratio of voltages or signal amplitudes Defect: the nonconformance of an item to one or more of its required parameters, within the limits defined in the specification Derivative control/action: a function proportional to the rate of change of the applied signal (i.e. differentiation with respect to time) Describing function: approximation of nonlinear behaviour (amplitude dependence) of a system element, by modelling the gain and phase characteristics of the fundamental components of its Fourier transform Digital: described by a function of regularly sampled values Dissimilar redundancy: multiplex arrangement where different lanes use different software a n d / o r hardware to perform the same function Disturbance: an unwanted signal or force which can impair the quality of control Drop back: a reduction in attained angle, following the removal of an angular rate demand Duplex: having two hardware lanes operating in parallel, with crossmonitoring for detection of a single failure Error: a state, resulting from a fault or human mistake, which is liable to lead to incorrect operation Error signal: a control system signal equal to the calculated value between the parameter value commanded and that achieved Failure: an occurrence in which a previously acceptable item is no longer able to perform its required function within the limits defined in the specification Fault: see defect Feedback: signal generated by sensor and applied with the aim of corrective action Feedforward: signal from the command path which bypasses the controller to boost the downstream command to an actuator--improving transient response without affecting stability Flight control laws: control laws (or algorithms) within the flight control system which have broarder capabilities, for example, the monitoring of independent signal channels for possible failures Flight envelope: boundaries which define the limitations imposed on the operation of the aircraft defined in terms of altitude, airspeed/Mach number and load factor Flight management systems: system designed to assist the flight crew in managing the aircraft's systems, for example, fuel and navigational Fly-by-wire (light): connection between pilot's control column, yoke or inceptor made electrically (or by fibre optics) rather than by mechanical

Glossary of terms

xxiii

system consisting of rods, cables and levers Hying qualities: see handling qualities Frequency response: variation of an output signal magnitude and phase characteristics, relative to a sinusoidal input signal, as frequency varies Full authority: allowing the maximum useable range Full-state feedback: all the system states are used as feedback signals Functional requirements document: specification of function requirements (e.g. control laws) Gain: control law parameter for providing a signal-scaling capability Gain margin: the factor by which the gain may be increased or decreased before system instability results Gain schedule: variation of a gain or gains within a control law with respect to some measured scheduling variable (s) Governor: a mechanical system for regulating a controlled parameter Handling (or flying) qualities: piloting characteristics with respect to how easy or safe the aircraft is to fly (for a particular task) Hang-off (also hang-on): transient response characteristics whereby the commanded response fails to achieve its steady-state value within an acceptable time; is associated with undershoot, and with overshoot Hard-over: a failure that causes a control surface to rapidly drive its output to the authority limit Hazard: a state of the system, often following some initiating event, that can lead to an accident High-pass filter: attenuates low frequency signals, allowing high frequencies to pass Hysteresis: nonlinear function in which the i n p u t / o u t p u t relationship for increasing an input is different from that for decreasing the input Inceptor: physical device with variable force a n d / o r motion, for enabling pilot input to the flight control system. Examples might be a centre-stick control column, a side stick or a throttle lever Incidence: see angle-of-attack Incident: an event which results in equipment or property sustaining damage or any person receiving any injury, or which might have resulted in an accident Integrating filter: function for performing integral action on a signal Integrity: freedom from flaw or corruption (within acceptable limits) J u m p resonance: undesirable nonlinear saturation p h e n o m e n o n with a sudden j u m p in its frequency-response characteristics l a n e : a signal path containing all the hardware and functional elements of the control system within a multiplex arrangement Limited authority: having access to only part of the full range available Limit cycle: bounded amplitude and fixed-frequency oscillation of a system, involving nonlinear beahviour Line-replaceable unit or item: equipment fitted into an aircraft Linear system: having no nonlinearities; scaling any input signal scales all the

xxiv

Glossary of terms

outputs by the same factor; the principle of superposition applies Linear quadratic Gaussian (LQG): linear design method which uses a quadratic cost performance and Gaussian noise to determine optimum feedback gains Low-pass filter: function which attenuates high frequency signals but allows low frequency signals to pass Minimum phase: a system which has no zeros in the right half of the complex plane Mission-critical: loss of capability leading to possible reduction in mission effectiveness; compare with safety-critical Mode (FCS): a selectable function of the FCS, e.g. terrain following Modern control: a range of design and analysis techniques developed, generally considered as post 1960 Multi-input multi-output (MIMO) system: a system which has at least two inputs and at least two outputs. Often it is understood that the system possessses significant interaction or cross-coupling Multiplex: having several hardware lanes to enable detection and isolation of equipment failures Multivariable control: theory and techniques for addressing multi-input multi-output systems Natural frequency (damped): the frequency at which a system will tend to respond when excited by a sudden input Nichols chart: frequency response rectangular plot with gain in decibels (dB) plotted against phase in degrees and with frequency varying as a parameter. The chart contains contours of closed-loop gain and phase characteristics superimposed, assuming unity negative feedback Noise: usually, an unwanted signal corrupting the desired signal Nonlinearity: characteristic which introduces amplitude dependency into a system; linear behaviour is not preserved, in that the output magnitude no longer scales with the input Nouminimum phase: having zeros in the right-half complex plane Notch filter: function which produces attenuation over a specified frequency range, normally with minimal attenuation either below or above that range Nyquist diagram: a polar plot of a system's frequency response in the complex plane, with frequency varying as a parameter Open-loop: without the use of any feedback Order: the number of poles in the characteristic polynomial, remembering that a complex pair consists of two poles Overgearing: where the control system gains have been increased beyond the point of optimum performance Overshoot: transient response characteristic whereby the commanded response exceeds its steady-state; usually measured as a percentage Pad6 approximation: a transfer function technique for establishing a loworder approximation to exponential functions (e.g. to model pure time delays)

Glossary of terms

xxv

Phase: the relative angle between a sinusoidal input signal and the corresponding output signal Phase advance filter: function for providing a low frequency phase lead, at the expense of increasing high frequency gain Phase margin: the amount of phase lag (or advance) a system can tolerate before instability is reached Phase-plane analysis: rectangular plot of two system states, usually position and velocity, for analysing system behaviour, particularly when nonlinear characteristics are present Phase-retard filter: function for providing high frequency attenuation, with the associated phase loss being recovered at higher frequencies Pilot-induced oscillation (PIO): p h e n o m e n o n whereby the pilot inadvertently triggers and sustains an oscillation of the aircraft through a control input, owing to adverse coupling with the system dynamics Plant: a device which is to be controlled, for example, an aircraft Pole: real or complex root of transfer function denominator polynomial, sometimes referred to as an eigenvalue of the system Power spectrum: plot of power against frequency where power is defined as the square of the signal magnitude Primary controls: those controls which are fundamental for the safe operation of the system, for example, elevators, ailerons and rudder Proportional, integral and derivative: three-term controller with inherent phase advance and tracking capability Quadruplex: having four hardware lanes for detection and isolation of up to two identical failures Qualification: process for demonstrating that the system meets the customer's requirements Random failure: a failure which results from a variety of degradation mechanisms in the hardware Rate limit: physical or functional limit on rate of change of a parameter, of particular significance in actuation systems Reconfigurable control: redistribution of system functions or hardware following a failure, to maintain satisfactory operation Redundancy: duplication of components or software, to improve system integrity Regulator: a control system in which the design driver is satisfactory disturbance rejection, in order to hold some desired parameter value constant; command tracking is usually of secondary importance Reliability: the probability that a system will be free from faults Resonant frequency: frequency at which the ratio of the magnitudes of a system's output to input is a maximum Rise time: the time taken for the system response to a step input to change from ten per cent to ninety per cent of its steady-state value Risk: the combination of the frequency, or probability, and the consequence of an accident

xxvi

Glossaryof terms

Robustness: the ability of a system to tolerate variations in system parameters

without u n d u e degradation in performance Roll-off: rate of gain reduction at extremes of frequency (usually specified as d B / d e c a d e or dB/octave) Root locus: parametric plot showing variation of closed-loop poles, as a function of a particular system parameter, almost invariably but not essentially, to the controller gain Safe: the state in which the perceived risk is lower than the maximum acceptable risk Safety: the expectation that a system does not, under defined conditions, lead to a state in which human life is endangered Safety-critical: failure or design error could cause a risk to h u m a n life Sample and hold: device for producing an analogue signal from a series of discrete digital pulses Saturation: a state where authority limits, rate limits or acceleration limits are reached Secondary controls: those controls which are not essential for safe operation of the system, but are likely to result in degraded performance if they are not available (for example, flaps) Self-monitoring: capability of a lane of computing to detect its own failures Sensor: physical device for detection of inceptor positions, feedback measurements or scheduling information Servomechanism: control system, literally slave mechanism, in which the design driver is accurate tracking of a varying input signal and where disturbance rejection is usually of secondary importance Servovalve: a hydraulic device applied to a control valve or ram for switching the pressure and controlling the direction and magnitude of flow of hydraulic fluid Settling time: time taken for the c o m m a n d e d response to remain within a specified percentage, often five per cent, of its steady-state value Sideslip: the angle formed by the vector addition of the aircraft body-axis lateral and longitudinal plane velocity components Similar redundancy: multiplex arrangement where different lanes have identical software and hardware to perform the same function Single-input single-output (SISO): system which has only one input with one associated controlled output Stability margin: a measure of system stability--see gain margin and phase margin Validation: process of determining that the requirements are correct and complete Verification): evaluation of results of a process to ensure correctness and consistency with respect to the inputs and standards provided to that process C. Fielding and R. W. Pratt

Chapter 1

Industrial considerations for flight control C. Fielding and R. Luckner

1.1 Introduction Flight control is an interesting and technically challenging subject for which a wide range of engineering disciplines have to align their skills and efforts, in order to establish a successful system design. Ambitious aircraft programmes and the hard competition between aircraft manufacturers motivate sustained striving towards flight control systems (FCSs), which provide improved performance and towards a more efficient development process. To achieve these goals, all available resources need to be utilised, requiring coordination and close collaboration between different and i n d e p e n d e n t organisations, in order to make the best use of: • the excellence of university institutes, which educate the next generation of engineers and provide basic research and theory; • the capability of research departments, which develop improved methodologies and new technologies; • the competence and capabilities of industrial design offices, which have to apply theory and new technologies to new products within stringent cost and time limits; • the significant experience of the customer in the operation of aircraft and in the definition of future aircraft requirements. An obstacle for efficient collaboration originates in the different methods of working. Typically, researchers are theoretically oriented and industrial engineers often apply empirical methods which can lead to practical solutions, even if the theoretical explanations are still missing. Although some existing communication difficulties between the two groups are obviously due to the different interests of the organisations to which they belong, there are other logically explainable reasons, which are very informatively described by McRuer and Graham in a historical survey of the first eighty years of flight control [1]. This survey notes that, in the beginning of flight control design (1900-1940), the development of theory and practice was independent. © 1999 British Aerospace PLC and DaimlerChryslerAerospace Airbus GmbH. Reproduced with permission.

2

Flight control systems

Technological progress was successfully driven by 'tinkerers and inventors' performing designs with little or no theoretical backup, with the stability and control properties of aircraft being evaluated in flight tests. Nevertheless, the first automatic control devices were invented before 1910 by L. Obry, H.S. Maxim, E. Sperry et al. In parallel, scientists and theoreticians (G.H. Bryan, L. Bairstow, Melville Jones etc.) contributed a theoretical background to flight dynamics, however, as the design calculations were very strenuous without the availability of computers, aircraft designers disdained dynamic stability analysis at that time as it requires the solution of fourth-order polynomials for both the longitudinal and lateral aircraft motions. With the advent of turbojet engines at the end of the forties and the enormous increase of the flight envelope in speed and altitude, all sorts of new problems arose. At that time, theory had made great progress, especially in the area of feedback control, with the key contributions to the understanding of stability by Nyquist, Bode, Nichols and others: the confluence of theory and practice was the logical consequence. Ever since, FCSs have been designed by applying practical and theoretical methods simultaneously and the digital FCS of modern high-performance civil and military jets would not be possible without the harmonisation of analytical and experimental techniques, which include the assessment of aircraft handling qualities based on developments of the stability theory to address pilot-in-the-loop operations. Technology has advanced to a level where it is now possible to design a complex FCS: high-performance computers and software are available, allowing us to use sophisticated methods, to build complex models, to design and implement intelligent functions and to produce an abundance of results--which can easily exceed what the analyst can mentally grasp and where it takes enormous effort to validate designs and the models upon which they are based. Today, industry has to evaluate any new method thoroughly before it can be adopted for the design process, and the efforts for application need to be balanced by resulting improvements. The intention of this chapter is to explain industry's considerations for flight control design and development to students who are naturally more closely related to the role of the research community than to industrial processes. The objectives for FCS development are explained and the current status of flight control technology is reviewed for both military and civil FCSs, with the emphasis on combat aircraft and large transport jets (Figure 1.1). The similarities and differences between the military and civil applications are identified throughout this chapter, which has been written from a European perspective, owing to the authors' background.

1.2 The general objectives of flight control When studying the mechanics of flight [2--4] and flight control [5] it is common practice to assume that the aircraft can he represented as a rigid

Industrial considerations for flight control

Figure 1.1a

3

State-of-the-art military aircraf development testing: Eurofighter Typhoon undergoing flight refuelling tests with a Vickers VCI O tanker aircraft

Figure I. I b State-of-the-art civil aircraft development testing: Airbus A320 at take-off during extremeflight testing for determination of minimum unstick speed [6, 7 para. 25.107] body, defined by a set of body-axis coordinates as shown in Figure 1.2. The rigid-body dynamics have six degrees-of-freedom, given by three translations along, and three rotations about, the axes. All forces and moments acting on the vehicle can be modelled within this framework. In this figure, CoG is the centre of gravity; Uo, Vo, Wo, Po, Qo, and Ro are the steady equilibrium, translational and rotational velocities; u, v, w, p, q and rare small perturbation changes to these velocities; ~7is the foreplane angle, •ib the inboard flap angle, 6oh the outboard flap angle and ~ is the rudder angle. Flying vehicles range from balloons and gliders through to hypersonic missiles and space vehicles. Each has its own flight envelope, which will depend on the individual vehicle's physical capabilities. Figure 1.3 shows a typical flight envelope for a supersonic aircraft, defined in terms of Mach number, covering velocity and air compressibility effects, and altitude to cover air temperature and density effects. The boundaries of the flight envelope are indicated by the physical limits shown in the Figure: the stall limit, at high

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6 Flightcontrol systems incidence and low dynamic pressure, where the aircraft's wing lift is not sufficient to support the aircraft's weight; the performance limit due to the rarefaction of the atmosphere preventing a jet engine from sustaining its operation; the temperature limit due to the kinetic heating of the airframe by the viscous friction of the air; the loading limit, at high dynamic pressure, due to the aerodynamic loads acting on the a i r f r a m e - - a limit which is deliberately specified to provide an adequate margin against aircraft flutter. The forces and moments acting on the vehicle vary substantially across such an envelope. If we can control these forces and moments, then we have control of the aircraft's translational and rotational accelerations, and hence its velocities, attitude and position. The FCS aims to achieve this control via the aircraft's aerodynamic control surfaces a n d / o r the thrust provided by the engines, which is normally controlled in its magnitude, but also, in some modern military aircraft, in its direction. The functions of an FCS can be structured into both primary functions, such as pitch, roll and yaw control, and secondary functions such as high lift, airbrake and lift-dump on the ground. Here, we will focus on the primary functions.

1.2.1 Military aircraft From an industrial viewpoint, when designing military aircraft the overall requirement is to design a vehicle which meets the military service customers' operational requirements, is safe to operate and which can be designed, manufactured and maintained at an acceptable cost and within agreed timescales. As an essential step towards achieving the aircraft's performance and safety targets, the FCS needs to be carefully designed, taking into account the requirements and constraints which will naturally be imposed through airframe and system hardware physical limitations. The aircraft's flight control laws (FCL) provide the basis for achieving the desired performance and aircraft handling characteristics and offer great potential for operational flexibility, in terms of the possible pilot-in-the-loop and automatic modes. The fundamental requirement is for the aircraft manufacturer, together with equipment suppliers, to design a FCS which is capable of providing good aircraft handling qualities over a wide range of operating conditions, to cover the carriage of many different internal a n d / o r external stores, and to enable a diverse range of missions to be flown effectively, with a low pilot workload. Additionally, it should be designed such that new moding, for example autopilot modes, can easily be added to the system at a later date.

1.2.2 Civil aircraft In civil aviation, the specification of a new aircraft is drawn up by the aircraft manufacturer by means of market surveys and discussions with potential airline customers. The general objective can be formulated as follows: 'the transport of a given number of passengers a n d / o r load from A to B: safely, for minimum cost, taking care of ecological needs and taking operational needs

Industrial considerationsfor flight control 7 into account' (all-weather operation, field length required for take-off and landing, highly reliable systems etc.). The customer wants to operate the aircraft safely at minimum costs. The passengers want to fly safely, comfortably and cheaply. Airworthiness is directly related to safety. Furthermore, airworthiness must be inherent in an aircraft and its equipment, and it is highly dependent on the accuracy of limitations and supporting information (flight manuals etc.) given to the operators and the pilots. The airworthiness regulations which are issued by the Airworthiness Certification Authorities represent the law. This fact assigns great legal importance to the Certificate of Airworthiness (CoA), especially with respect to product liability in the event of an accident. To be awarded a CoA the aircraft manufacturer has to demonstrate that a newly designed aircraft is airworthy: that is, that it complies with the airworthiness requirements. A civil transport aircraft, which is heavier than 5700 kg (12 500 lb), has to fulfil certification standards which are specified by the European and US regulations JAR 25 [6] and FAR 25 [7]. The CoA guarantees to the airline that a purchased aircraft is airworthy. It is then the airline's responsibility to keep that aircraft airworthy by operating and maintaining it under the strict rules, which are also defined by the authorities. The FCS is a flight-critical system which must be available for the aircraft to fly safely. The regulations' requirements relating to stability, control and handling qualities are not very specific. Therefore, each manufacturer develops its own proprietary design requirements and criteria, often making use of the more specific military design specifications and guidelines, for example Reference [9]. The demonstration of compliance requires: a systematic, understandable and well-documented design process; extensive testing and the proof of correct functioning under all possible operational conditions (including all kinds of failures) in simulation and flight tests.

1.3 The role of the flight control system 1.3.1 History The early generation of FCSs were mechanically based, as typically depicted in Figure 1.4, which shows examples of systems based on rods and levers (a), and cables and pulleys (b). There are direct mechanical linkages between the pilot's cockpit controls and the control surfaces which manoeuvre the aircraft, leading to implementations which have high integrity, in terms of the probability of loss of control of the aircraft. The maximum levels of pilot stick/yoke, and rudder-pedal forces required to steer and manoeuvre an aeroplane are limited by the physical capabilities of the pilot, which have not changed since the times of Lilienthal and the Wright brothers. When aeroplanes evolved in size and speed, the forces to move the control surfaces against the aerodynamic forces grew to a point

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where they exceeded the capabilities of any pilot. T h e pilots n e e d e d assistance. Aerodynamic balances (already used in 1910 on the Moisant and Bleriot XI m o n o p l a n e s [12]) and different types of tab were designed (beginning in the1920s). Further growth of aircraft and their control surfaces m a d e additional power sources necessary: hydraulic boosters were installed (at the end of World War II), dividing control surface forces between the pilot and the boost mechanism. Control feel was similar to that of u n a u g m e n t e d

Industrial considerationsfor flight control 9 aeroplanes. The next step was the introduction of fully power-operated controls. These are called irreversible, since the aerodynamic hinge m o m e n t of a control surface has a minimal effect on its deflection and cannot be felt by the pilot any longer. With the removal of the direct connection between the pilot's feel and control-surface forces, which provided a useful cue to indicate the aircraft's speed, artificial feel became necessary. The benefits of hydraulically-powered control surfaces are that aerodynamic drag is reduced and control-surface effectiveness is increased, by eliminating tabs. Reversible mechanical control systems are prone to control surface flutter, which may occur at high dynamic pressures. Hydraulic actuators introduce high mechanical stiffness, which substantially improves an aircraft's control surface flutter characteristics. The role of the mechanical linkages between the pilots' cockpit controls and the hydraulic actuators was reduced to one of signalling and no longer to transmit power. Flight dynamic effects, e.g. in the transonic and subsonic flight regimes, as well as the automation of flight, made it necessary to add signals from stability augmentation systems and the autopilot to the basic manual control circuit. Although the mechanical links are simple and reliable, signal processing can be done more easily by using electrical links involving computers. The electrical signalling allows the realisation of complex, highly sophisticated functions for improved safety and performance, which are calculated by the flight control computer. Although the early systems were analogue, at present digital electronic FCSs are the state-of-theart, with the use of inertial motion sensors and airstream direction and pressure sensor units. The removal of the direct mechanical linkages between the cockpit controls and the control surfaces, and their replacement with electrical signalling, has led to the term fly-by-wire, which allows the pilot to directly c o m m a n d the aircraft's motion, rather than commanding the controlsurface angles (in order to achieve the motion). T h e advantages that were gained during the evolution of the FCS have generally had to be paid for by the drawbacks and problems which had to be mastered. Each additional c o m p o n e n t that cured one problem tended to create other problems and increased the complexity of the overall FCS. New systems tend to be unreliable in the beginning and, since the FCS is a safetycritical system, new technologies are incorporated gradually and only when they are j u d g e d sufficiently mature and their benefits are proven. An excellent survey on the history of technologies related to aircraft stability and control is given in Reference [12].

1.3.2 Military aircraft developments In the 1960s and 1970s, alongside the electronic revolution, the flight-control designers began to expand their horizons. A n u m b e r of major programmes of the time, such as the Panavia Tornado and the General Dynamics F-16 became reliant on more sophisticated stability augmentation systems and

10

Flight control systems

autopilots, to allow them to meet their performance and mission goals. It was during this period that the terms Active Control Technology (ACT) and Control-Configured Vehicles (CCV) were introduced. ACT means the use of the FCS to actively compensate for deficiencies in the aerodynamics of the basic airframe, and CCV implies the concurrent and complementary design of the basic airframe together with the FCS, to achieve performance improvements. The potential benefits include: stabilisation and control of basically unstable airframes with highly nonlinear aerodynamics, which allows improved aircraft performance, high manoeuvrability and flight to high angles of attack, automatic prevention of stall departure/spinning, automatic structural protection and gust alleviation, all of which enhance safety and reduce the pilots' workload. The common element of both ACT and CCV is that they require a full-authority FCS, with aircraft-response feedback, which needs to work all the time to be effective--a fly-by-wire system becomes essential. The various benefits to be gained from the ACT/CCV concepts, as advocated by the flight controls community, were readily, if sometimes sceptically, welcomed by the aerodynamic designers, who were already struggling with design trade-offs to meet increasingly demanding performance requirements. 1 This prompted a number of fly-by-wire demonstration programmes which were generally successful, but most of which fell short of what would be required on a production aircraft. Most were based on existing airframes and essentially mimicked the system which they were replacing; little was really done to quantify the promised benefits, and the safety implications of full-time fly-by-wire were addressed by retaining the mechanical flying controls as a backup mode. They were also constrained to an extent by the available computing technology: airborne analogue computers had become a mature technology, whereas airborne digital computers were still, relatively, in their infancy with significant performance limitations in both computational speed and memory. In the UK, the British Aerospace (BAe) fly-by-wire (FBW) Jaguar programme [13], which first flew in 1981, was one of the first to tackle some of these problems. From the start, it was an objective to remove the existing FCS and to replace it with a new system to be designed, developed and cleared to production standards. This was to be a full-time, full-authority digital fly-bywire system with no backup mode. The aircraft was progressively destabilised longitudinally by ballast and strakes, with consequent improvements in performance demonstrated. The FCS successfully demonstrated for FBW Jaguar was further developed for BAe's Experimental Aircraft Programme(EAP), the EAP aircraft, which first flew in 1986 [14] and successfully demonstrated a number of the benefits (e.g. carefree handling and increased I O n c e ACT had become established, this situation was reversed, with the flight controls community taking a cautious approach towards the aerodynamic designers' more ambitious proposals.

Industrial considerationsfor flight control

11

performance through relaxed static stability) promised by the ACT/CCV protagonists in the early 1970s. There was also significant ACT development in Germany. MBB developed and demonstrated a quadruplex full-authority digital FCS for a single seat F104 G Starfighter, which had been modified to provide a CCV demonstrator aircraft [15]. This programme (1977-1984) ran almost in parallel with the FBW Jaguar programme, with the F-104 demonstrator being progressively destabilised by mounting a canard surface above its forward fuselage, and by adding aft ballast weight. The aircraft successfully demonstrated its digital quadruplex system during a flight test programme of 294 flights. The followon project was the Enhanced Fighter Manoeuvrability programme, in which the Rockwell/DASA X-31 post-stall experimental aircraft were fitted with a digital fly-by-wire system [16]. The two aircraft successfully demonstrated flight up to 70 ° angle-of-attack, during a flight test programme spanning 510 flights (1990-1994). In turn, the experience gained on these demonstrator aircraft has been applied to the development of the Eurofighter Typhoon aircraft's FCS [17]. With this aircraft configuration, most of the promises of ACT/CCV have now reached fruition. Elsewhere, and primarily in the United States, there have been many other successful military fly-by-wire demonstrator programmes and it would be inappropriate not to recognise their contribution to flight control technology: for example, the McDonnell Aircraft Company/USAF Survivable Flight Control System F--4 (first flight 1972), the General Dynamics AFTI/F-16 (1982), the McDonnell Douglas S/MTD F-15 (1988), the Grumman X-29 (1984) and more recently, the Boeing/McDonnell Douglas X-36. The most notable current examples in production are: the Lockheed Martin F-22 Raptor, the Boeing/McDonnell Douglas F-18 Hornet and the military transport aircraft C-17, the Northrop B-2, the SAAB JAS-39 Gripen and Dassault's Rafale. Such programmes have not been achieved without cost and effort, with significant demands being placed on equipment suppliers to provide faster digital computers with more memory, higher bandwidth actuators and improved sensors (for both aircraft motion and air data). There has been continual pressure to improve the reliability of equipment, to allow reduced redundancy levels (e.g. quadruplex to triplex) to cut weight and cost, while still achieving the required system availability and safety targets. At the system level, the redundancy management has had to become more sophisticated to provide an optimal fault tolerance by reliable fault detection, fault isolation and reconfiguration strategies. Monitoring functions have had to cope with increasing demands from flight crews, who need to be informed about the system status and who have to be supported by electronic check lists during flight, as well as from the maintenance staff, who need built-in test functions, data loggers for failure reporting and diagnostics in order to reduce maintenance effort and costs.

12 Flightcontrol systems 1.3.3 Civil aircraft developments The jet age for civil transport aircraft started after World War II with the De Havilland Comet 1 (first flight 27July 1949) and the Boeing 707 (1954). The four-engined 707 carried 200 passengers. Despite this aircraft's weight (150 000 kg), the FCS only needed hydraulic boosters for the rudder and the spoilers. Elevators and ailerons were aerodynamically balanced internally to keep the force levels down [18]. The early spring-tab design for the rudder was changed in order to avoid the possibility of rudder lock; i.e. when at high sideslip angles, reversed aerodynamic hinge moments drive the rudder to its stops [12]. The second generation was developed in the 1960s and early 1970s (e.g. Airbus A300, Boeing 727, 737, 747, Lockheed L1011 and McDonnell Douglas DC9, DC10). Hydraulic boosters and hydraulically-powered actuators were introduced and used for flight-critical functions, and artificial feel became necessary. Basic part-time stabilisation functions, such as yaw dampers, were added to the FCS. Autopilots based on analogue electric technologies were installed, which had autoland modes for all-weather operation. The autopilot commands were mixed into the mechanical signal path by means of electric motors which acted on cable quadrants. Hawker Siddeley and British Aircraft Corporation pioneered automatic landing on the Trident and the BAC 1-11. The 737 autopilot was the first to offer a mode called control wheel steering (CWS) which allows manual controller-augmented steering. The Russian Tupolev 144 (1968) and the Anglo-French Concorde (1969) are the only supersonic civil transports. The Concorde is equipped with a three-axis full-authority analogue electronic FCS with a mechanical backup on each control surface. The electrical links have triplex redundancy and provide direct pilot-to-control-surface commands, analogous to mechanical linkages. The use of electrical signalling simplifies and facilitates signal processing, e.g. to add damper feedback and to switch to the autopilot. The third generation (e.g. Airbus A300-600, A310, Boeing 747-400, 757, 767, McDonnell Douglas MD80, MD90, MDll) is characterised by glass cockpits and digital systems with improved functionality. Analogue equipment was increasingly replaced with digital systems. The transition from reversible to irreversible servo controls was completed, but the links between the pilot inputs and the actuators were still mechanical for all flight-critical functions. Electrical signalling gained importance and was introduced for less critical functions such as the roll spoilers, trimming and slat/flap control on the A310. A major achievement for flight automation was the introduction of flight management systems which allow pre-planned flight plans to be executed automatically. The fourth generation (e.g. Airbus A319/A320/A321, A330/A340, Boeing 777) is characterised by full-time, full-authority electronic FCS (fly-by-wire), as electronic and hydraulic equipment with a much lower probability of failure became available (that is, less than one total failure in a billion flying hours

Industrial considerationsfor flight control 13 is to be expected). The Airbus A320 (1987) was the first civil fly-by-wire aircraft. Its sidestick concept and the functions of the flight controls were evaluated on the Concorde and on the A300 testbed to reduce development risk. All A320 control surfaces are hydraulically powered and electrically signalled. A reversionary mode is provided, whereby the stabiliser and r u d d e r can be controlled mechanically. The architecture of the FCS is characterised by a n u m b e r of dissimilar redundant, duplex flight control computers with the capability of failure self-detection. In the Boeing 777, pilot commands are entered by traditional control wheels and processed by the FCS which has a triplex/triplex architecture. The normal c o m m a n d path is backed up by a reversionary c o m m a n d path (direct mode) and the ultimate mechanical backup mode, which makes use of the horizontal stabiliser and one spoiler pair. By 1998, fly-by-wire technology had been in airline service for over ten years. More than 1000 fly-by-wire civil aircraft are operating worldwide with more than 10 000 trained pilots.

1.4 Aircraft in-service r e q u i r e m e n t s

1.4.1 Military aircraft operations T h e r e are very many possible mission profiles for combat aircraft, covering a i r - g r o u n d and air-air operations, and including both offensive and defensive roles. Take-off and landing for combat aircraft might be via a conventional runway, a suitably wide road or prepared landing strip, an aircraft carrier's deck or (for vertical take-off and landing) a remote site such as a clearing in a forest. Reference [8] classifies military aircraft as follows: * * * •

Class Class Class Class

I: II: III: IV:

small, light aeroplanes; medium weight, low-to-medium manoeuvrability aeroplanes; large, heavy, low-to-medium manoeuvrability aeroplanes; highly manoeuvrable aeroplanes.

An aircraft's operational requirements, as defined by its customer (air force, navy or marine), ultimately define the characteristics of its airframe and systems, which are chosen in order to effectively fulfil the missions, and which in turn determine the design requirements for the FCS. Each mission will consist of a sequence of mission elements, for which task-tailored control modes might be designed to reduce pilot workload and to maximise the mission effectiveness. A typical mission might be constructed from a combination of the following elements, depending on whether the operation is land based or aircraft-carrier based, and on whether the aircraft is designed for conventional or vectored thrust (e.g. Harrier) take-off and landing:

* taxiing; • take-off: conventional/short/vertical/catapult launch/ski-jump;

14

Flight control systems

• acceleration and climb; • reconnaissance; • air-air combat manoeuvring (typically - 4 to +9 g, with no limits on pitch and bank angles); • close formation flying; • in-flight refuelling; • terrain following; • ground attack; • descent and landing approach; • landing: conventional/short/vertical/arrested shipboard. This list is indicative of the type of operational factor, which needs to be considered for the design of an FCS, in order to meet the mission requirements of a military aircraft. A military aircraft will carry out a combination of the above, depending on its role and capabilities (which should, ideally, be well matched, since the latter is driven by the former). Reference [8] defines the following flight-phase categories: • Category A: those nonterminal flight phases that require rapid manoeuvring, precision tracking, or precise flight-path control; • Category B: those nonterminal flight phases that are normally accomplished using gradual manoeuvres and without precision tracking, although accurate flight-path control may be required; • Category C: terminal flight phases that are normally accomplished using gradual manoeuvres and usually require accurate flight-path control; • Category D: terminal flight phases that are accomplished using V/STOL techniques and which usually require accurate flight-path control. For all aircraft classifications, and within each flight-phase category, there will be a series of tasks or mission elements. For each of these tasks, levels of aircraft-flying qualities are defined in Reference [8], permitting a quantitative measure of the flying qualities to be determined: • Level 1: flying qualities clearly adequate for the mission flight phase; • Level 2: flying qualities adequate to accomplish the mission flight phase, but with some degradation in mission effectiveness, or increase in the workload of the pilot, or both; • Level 3: flying qualities such that the aircraft can be controlled, but the mission effectiveness is clearly inadequate or the total workload of the pilot is approaching the limit of his capacity. For establishing more detailed pilot assessments of aircraft flying qualities in relation to mission tasks, the Cooper-Harper Rating scale [19] is often used for both inflight and piloted simulation assessments of aircraft. The ratings obtained are usually qualified with pilot comments. From a systems-operation viewpoint, the state of the system is defined in terms of its availability. This takes into account the possible failure modes of the system and has a significant impact on the FCS design, in terms of its

Industrial considerationsfor flight control 15 redundancy management. Good flying qualities alone are not enough, and the system must have sufficient integrity to meet safety and mission requirements. Reference [ 11 ] defines the following operational states: • Operational state I (normal operation) is the normal state of FCS performance, safety and reliability; • Operational state II (restricted operation) is the state of less than normal e q u i p m e n t operation or performance which involves degradation or failure of only a noncritical portion of the overall FCS; a moderate increase in crew workload and degradation in mission effectiveness may result from a limited selection of normally-operating FCS modes available for use; however, the intended mission may be accomplished; • Operational state III (minimum safe operation) is the state of degraded FCS performance, safety or reliability which permits safe termination of precision tracking or manoeuvering tasks, and safe cruise, descent, and landing at the destination of original intent or alternate, but where pilot workload is excessive or mission effectiveness is inadequate; phases of the intended mission involving precision tracking or manoeuvering cannot be completed satisfactorily; • Operational state IV (controllable to an immediate emergency landing) is the state of degraded FCS operation at which continued safe flight is not possible; however, sufficient control remains to allow engine-restart attempt(s), a controlled descent and immediate emergency landing; • Operational state V (controllable to an evacuable flight condition) is the state of degraded FCS operation at which the FCS capability is limited to manoeuvres required to reach a flight condition at which crew evacuation may be safely accomplished. Within the design-standards documentation (e.g. References [8-11]) there exists a wide and very detailed set of design requirements and guidelines, based on a vast a m o u n t of flying experience with many different aircraft types. This information provides an excellent starting point for any FCS design, but it will need to be supplemented by additional requirements, to cover any novel aircraft features which are not adequately addressed by the existing standards.

1.4.2 Civil aircraft operations Unlike military aircraft, civil transport aircraft are built for one general mission only: the transport of passengers or freight from one point to another. This mission consists of the following flight phases: • taxiing; • take-off including take-off run and rotation; • climb u n d e r different conditions where thrust and airspeed vary; • cruise with minimum direct operating costs; • turns (typical bank angles less than 30°);

16

Flight control systems

• descent with idle or reduced thrust; • approach (non-precision approach, 3 ° ILS approach etc.); • go-around in case of a missed approach; • flare; • roll out. The flight envelope of an aeroplane defines the operating boundaries in terms of altitude, Mach n u m b e r and normal load factor. The FCS must provide stability and controllability within the total flight envelope for all allowed weight and centre of gravity (CG) combinations, that is: between maximum take-offweight and the minimum weight, and with the CG between the forward and rearward limits. This has to be demonstrated in certification flight tests, for speeds between stalling speed and maximum speed for stability characteristics (VFc/MFc). Furthermore, the aeroplane must be designed to be free from aeroelastic instability for all configurations and design conditions up to 1.15 times the design dive speed (Vn/MD; [6,7 para. 25.335(b)]. To guarantee reliable airline service, the aircraft have to be perfectly capable of operating safely u n d e r a wide range of weather conditions, that is: cross wind at take-off up to 30 knots; low to nearly zero visibility and a high level of turbulence. Extreme conditions, such as volcanic eruptions or tropical thunderstorms, which can destroy essential components, as well as extreme windshear which exceeds aircraft performance, have to be circumnavigated. The permissible flight envelope that has to be certified is limited to those flight conditions for which an aeroplane may be flown and safely recovered. The limit manoeuvring load factors are defined in [6,7 para, 25.337]. Typical maximal values are: •

nz, mi n = - - 1 . 0

• ~z, min= 0.0 ~

g;

n~m~x=+ 2.5 g (clean) ; nz.max= + 2.0 g (slats a n d / o r flaps out).

The maximum altitude is limited by the maximum pressure differential for which the cabin structure and the pressurisation system are designed. As it is most important for a civil aircraft, to be able to cruise at flight conditions where the performance in terms of direct operating cost is optimal, engines are selected such that engine performance limits usually do not restrict the flight envelope or that they at least do not adversely affect the flight regime for economical operation. In normal airline operations, only a very small part of the certified flight envelope is used: • load factors are very low in order to provide good passenger comfort (vertical load factor, n z, between 0.85 g a n d 1.15 g); • aircraft bank angle is limited to less than 30°; • airspeed is varied between the minimum operating speed, which is 1.2 times the stalling speed (Vs) for take-off and 1.3 times Vs plus wind additions for

Industrial considerationsfor flight control 17 landing, and the maximum operating speed (VMo) or Mach number (MMo), which are reduced when slats and/or flaps are deployed or when the landing gear is down. The military specifications and design standards (e.g. [8--11] ) contain a great deal of experience and knowledge. As there are no quantitative handlingquality requirements defined in the civil regulations JAR/FAR 25 [6,7], the civil manufacturers define their proprietary handling-quality design guidelines on the basis of the military standards. Civil-transport aircraft fall into class III (large, heavy, low-to-medium manoeuvrability aeroplanes) and the flight phases, which are applicable reduce to the following: • Category B: those nonterminal flight phases that are normally accomplished using gradual manoeuvres and without precision tracking, although accurate flight-path control may be required. (This category includes: climb (CL), cruise (CR) and descent (DE).) • Category C: terminal flight phases that are normally accomplished using gradual manoeuvres and usually require accurate flight-path control. (This category includes: take-off (TO), approach (PA), go-around (GA) and landing (LA).) Civil aircraft FCS designers also use the levels of flying qualities that are used for military aircraft, as listed in the previous subsection. Because it is not required and sometimes not even necessary to provide excellent handling qualities up to the ultimate limits of the flight envelope, reduced design envelopes for level 1 handling-quality characteristics can be defined for flightcontrol law development. An example is given in Table 1.1 where the following notation is used:

H

altitude vertical load factor nz take-off speed; ref. FAR/JAR 25.107 [6,7] V2 flap extended speed; ref. FAR/JAR 25.1511 [6.7] VF: Vl±: landing gear extended speed; ref. FAR/JAR 25.1515(b) [6,7] lowest selectable speed VI.S VMO MMO maximum operating limit speed, Mach number; ref. FAR/JAR 25.1505 [6,7] 0 subscript for operational envelope min minimum maximum max

1.5 The benefits of fly-by-wire The major benefit of fly-by-wire flight control is the ability to tailor the system's characteristics at each point in the aircraft's flight envelope. This is achieved by using flight control laws (FCL) scheduled with flight condition.

18

Flight control systems

Table 1.1: Example for a handling-qualities design flight envelope Flight phase catergory

Flight phase

Airspeed

Vo.min

B

Vo,rnax

Altitude

Ho.,,i,,

Ho,m~x

Load factor

nz,o.roin nz.o,r,ax

climb (CL)

VLS min(VLE, VFE, VMo/MMo)

Oft

30 000ft

0.5g

2.09

cruise (CR)

VLS min(VLE, VFE, VMo/MMo)

Oft

30 000ft

0.5g

2.0g

descent (DE)

VLS min(VLE, VFE, VMo/MMo)

Oft

30 000ft

0.59

2.0g

take-off (TO)

V2

min(VLE,VFE, --400ft 10 000ft VMo/MMo)

0.5g

2.0g

approach (PA)

VLS min(VLE, VFE, VMo/MMo)

10 000ft

0.5g

2.09

VLS min(VLE, VFE, --400ft 10 000ft VMo/MMo)

0.5g

2.0g

landing (LA)

Oft

T h e introduction of digital computing for aircraft flight control has allowed c o m p l e x algorithms to be implemented.

1.5.1 Military aircraft benefits T h e functions p r o g r a m m e d within the FCL allow the p e r f o r m a n c e benefits offered by active control technology (ACT) to be fully realised and include: * carefree handling 2 by providing angle-of-attack control and angle-ofsideslip suppression which lead to automatic protection against stall and departure, and by the automatic limiting of normal acceleration and roll rate to avoid overstressing of the airframe; • handling qualities optimised across the flight envelope, and for a wide range of aircraft stores; • aircraft agility, thereby providing a capability for rapid changes in fuselage 2 Carefree functions are designed to assist the pilot in certain situations. Appropriate piloting and proper pilot education are still necessary,as the laws of physics still apply. The term 'carefree' is not used in civil aviation, in order to avoid any misinterpretation.

Industrial considerationsfor flight control 19

•

• • • • •

aiming a n d / o r velocity vector, to enhance both target capture and evasive manoeuvring; aircraft performance benefits associated with controlling an unstable airframe, that is, improved lift/drag ratio and an increase in maximum lift capability, leading to increased aircraft turning capability; the use of thrust vectoring to augment or replace aerodynamic control powers, in order to extend an aircraft's conventional flight envelope; reduced drag owing to optimised trim settings of controls, including thrust vectoring; reconfiguration to allow mission continuation or safe recovery following system failures or battle damage; advanced autopilots, providing significant reductions in pilot workload and weapon-system performance benefits; reduced maintenance costs, resulting from the reduction in mechanical complexity and the introduction of built-in test.

(Note that for a combat aircraft, any weight reduction due to the removal of the mechanical linkages from its FCS is approximately offset by the additional weight of the electronic boxes of its fly-by-wire system. Weight reduction becomes a benefit for large aircraft.) In order to realise these benefits, it is essential to establish appropriate control system and control law architectures. These are fundamental to the success of the system and will require a good knowledge of systems equipment engineering and safety, flight dynamics and flight control. There is, however, a significant cost associated with these performance benefits in terms of system complexity, but, usually, the performance and safety benefits which can be achieved easily justify the investment.

1.5.2 Civil aircraft benefits The benefits of fly-by-wire technology for civil aircraft are: • the improvement of natural aircraft dynamic behaviour, that is: stability, handling qualities, turbulence suppression and passenger comfort; • the provision of flight envelope protection that allows full pilot commands, if necessary, without the danger of either leaving the safe flight envelope or overstressing the aircraft; • the increase in safety by reduction of pilot workload in routine control tasks, which allows him to concentrate on higher level flight guidance tasks; • the reduction of airlines' crew training costs by offering commonality within an aircraft family (cross-crew qualification); • the more efficient use of crew resources, as one pilot can fly different aircraft types with the same type rating; • configuration changes can easily be implemented, offering development flexibility and growth potential;

20

Flightcontrolsystems

* reduced operational costs, through improved maintainability and a higher dispatch reliability; * aircraft weight can be reduced, as heavy mechanical parts can be eliminated. Unlike military aircraft, today's civil FBW aircraft still exhibit natural stability (under almost all flight conditions). This was originally necessary, since there was not enough operational experience when the FBW technology was introduced, and a simple reversionary mode with pilot controls directly linked to the control surfaces, had to be installed for safety reasons. Now that maturity and reliability has been confirmed in ten years of operational experience, the design of naturally unstable civil aircraft, which need full-time augmentation, seems to be feasible. This is worthwhile, as relaxed static stability of aircraft offers better performance and associated lower direct operating costs, although the trade-off between level of airframe instability and the difficulty of artificial stabilisation and its associated increase in complexity must be recognised.

1.6 Flight control systems implementation 1.6.1 Military aircraft--design considerations and systems overview In order to achieve the same level of integrity as that achieved with the earlier mechanical systems, multiple signal sources and several lanes of computing are necessary to provide redundancy, these being cross-monitored in order to isolate any failed equipment and to ensure safe operation [20]. A comprehensive built-in test capability is also needed, to ensure that the system is 'safe to fly' prior to each flight and to identify and locate failures. The current military aircraft trend is towards triplex redundant architectures with reliance on both cross-lane and in-lane monitoring to achieve the required level of integrity, and hence the associated safety of system operation. The FCS has to be designed to guarantee the necessary levels of reliability and integrity, by having a system architecture with the appropriate level of redundancy and associated redundancy management, as well as comprehensive built-in test capabilities. The system design is underpinned by a comprehensive safety analysis, covering both normal operation and failure modes. The information needed to schedule the FCL gains is usually derived from the air data system, an example of which is shown in Figure 1.5. This includes a set of suitably located external probes providing pitot and static pressures and local air-flow measurements, in terms of speed and direction (angle-ofattack and angle-of-sideslip) [21]. Finding suitable locations for the probes is part of the aircraft configuration design. The ideal locations are often not available, owing to restrictions imposed through the operating requirements for other aircraft equipment (e.g. nose-mounted radar). The probes also need to be positioned to avoid unsteady airflow, such as that generated by

Industrial considerationsfor flight control

21

Bus

a, b, c and Pressure Tranducers • is a

Temperature Transducer

Figure 1.5 Air data system--sensors and computing forebody vortices. The locally derived probe measurements are used within the flight control computing in order to compute the true velocity vector of the aircraft: that is, its magnitude and direction, the latter being defined by the angles-of-attack and sideslip. Although this sounds straightforward, it is usually difficult (but possible) to measure air data reliably and accurately, and significant work is needed to derive the complex algorithms which are necessary to provide robust global measurements from the various sources of local data. The air data system has to be calibrated by flight testing throughout the aircraft's flight envelope, before it can be used as part of the FCS. Once calibrated, the air data can be used for cockpit displays, for gain scheduling and to provide feedback signals for stabilisation and flightenvelope limiting purposes. The air data system is designed to provide high integrity information: for example, with the arrangement shown in Figure 1.5, b, c and d would be multihole probes used to resolve local flow angles from pressure data: such a system might provide triplex angles of attack and sideslip and quadruplex airspeed and altitude information. In practice, the quality and integrity of the air data will depend on the capabilities and locations of the individual sensors. The air data information is complemented with information from the aircraft's inertial sensors. The fighter aircraft's FCS has to be designed and certified for different aircraft configurations including the carriage of a wide range of aircraft stores [22,23]. It is usual to design the control system for a baseline configuration, such as the aircraft fitted with light stores, by using a nominal set of aerodynamic data, plus a set of parametric tolerances based on past project experience, and uncertainties in the available data, from wind tunnels and datasheet empirical calculations. If a range of significantly different stores is to be fitted to the aircraft, such as heavy underwing or underfuselage tanks, then it may be necessary to design FCL for each store group to account for their differing inertial and aerodynamic properties. Figure 1.6 shows a

22

Flight control systems

~der lie

! UUU I " U U I ' I U

:1 Flare l

Bombs

Figure 1.6

Tornado aircraft carrying a heavy store load

schematic of a Tornado aircraft carrying a heavy store load; the potential variations in aircraft mass, inertia and centre-of-gravity owing to the carriage and release of such stores are obvious. The aircraft and its FCS have to be designed for carriage of a large range of such stores, including a very large number of possible symmetric and asymmetric combinations. Other significant factors which need to be taken into account in the design are: fuel state, high-lift devices, airbrakes, wing sweep (for Tornado, F-111 etc.), performance schedules, powerplant interface (or integration), reversionary modes, undercarriage operation and ground handling, all of which have a significant effect on the design in terms of stability, handling and airframe loading. For all combinations of stores, the FCS can offer protection against overstressing of the airframe and provide automatic stall and spin prevention. Flight to high angle-of-attack leads to nonlinear aerodynamic behaviour as flow separation occurs, wing and tail fin effectiveness is reduced and controlsurface power varies, often becoming very low. Such aerodynamic nonlinearities have to be modelled and taken into account as part of the design. Significant aerodynamic nonlinearities are also experienced as a function of Mach number, as an aircraft passes through the transonic region from subsonic to supersonic flight. This is due to shock-induced flow separations and air compressibility effects causing the aircraft's aerodynamic

Industrial considerationsfor flight control 23 centre to move aftwards. The modelling of nonlinear aerodynamic behaviour is a challenging topic and although initial wind tunnel data can provide excellent predictions, flight testing with subsequent parameter identification, is necessary to provide a validated aerodynamic description of the aircraft's characteristics. The FCL are designed to provide good aircraft-handling qualities [24], a low pilot workload and a high degree of resistance to pilot-induced (or pilotinvolved) oscillations (PIO). To establish a successful design, appropriate design criteria are needed, first to establish a robust feedback design to provide stability with good disturbance rejection, and secondly, to provide the desired handling characteristics. The PIO phenomenon, whereby the pilot's commands are (involuntarily) in antiphase with the aircraft's response, leading to a sustained oscillation, has appeared occasionally from the 1950s onwards but has become much more prevalent in fly-by-wire designs. Studies in the UK from the 1970s have led to a good understanding of the problem and to design methods which can prevent it [25]. It has continued to attract much attention in the past decade after some spectacular accidents with considerable research being undertaken, primarily in the USA, aimed at eradicating this type of aircraft behaviour [26]. The aircraft's handling qualities should be verified prior to flight, by a thorough programme which combines: theoretical analysis, off-line simulation and pilot-in-the-loop ground-based (and possibly in-flight) simulation. The control law algorithms and control strategy used must be realisable in terms of the aircraft's cockpit interface, including the inceptors, switches and displays, which should be harmonised with the piloting control strategy. An example of a modern combat aircraft's cockpit is shown in Figure 1.7 (taken from the EAP aircraft [14]), with the following features: A is the pitch/roll centre stick, B are the rudder pedals for yaw control, C are the left and right engine throttle levers, D is the airbrake (in/out) switch, E is the FCS control unit and includes test, mode selection and reset switches, F are the three multi-function displays used for all flight data (navigation, engines, systems, weapons etc.) including FCS status and warnings, G is the head-up display which includes a limited amount of flight data, H are the autopilot mode preselection push buttons, I is the barometric reversionary instrumentspanel, J is the reversionary warning panel, and K is the undercarriage (up/down) selector. The increased complexity of electronics and computing in fly-by-wire systems has led to a simplification of the once complex mechanical controlsystem parts, with only the actuation systems and pilot's controllers remaining. For the latter, the associated artificial-feel systems have been simplified (in most cases) to a simple fixed-rate spring feel plus a viscous damper. The pilot has remained unchanged physically, and it remains essential to adapt the controllers and feel system to the pilot. A side-mounted stick may be necessary with a highly reclined seat designed for extreme g manoeuvres, but centre-mounted sticks work well and are to be found in the

24

Flight control systems

Figure I. 7 A modern cockpit of a fly-by-wire combat aircraft majority of combat aircraft. The choice of stick location requires a proper assessment of the overall cockpit design, of the seat, of the instruments, displays and switches, and how to fit them together for the best operational effectiveness. Ergonomic designs of controller, that allow modulation through the wrist, elbow and shoulder movement, are suitable for either location. Such designs have been found to be superior to those allowing only a wrist action, suited only to side sticks, both for precision of control and the application of sustained high-stick forces in manoeuvres. Further discussion can be found in Reference [27]. The FCS motion sensors for detecting the rigid-body motion of the aircraft also detect the higher frequency structural oscillations due to the many flexible modes of the airframe, as indicated in Figure 1.8 which shows the first wing bending mode of the EAP aircraft. The high frequency components of

Industrial considerationsfor flight control

25

Figure 1.8 Aircraft structural modes of vibration the inertial-sensor outputs usually require attenuation to avoid driving the aircraft's flying control surfaces at these frequencies and further exciting the flexible m o d e s - - o t h e r w i s e known as airframe/FCS structural coupling 3 [28]. The necessary attenuation is achieved by introducing analogue or digital filters, for example notch (band-stop) filters, into the feedback paths. T h e major constraints on filter design are the need to meet specified stability requirements for the flexible modes and the need to minimise the additional phase lag introduced by the filters at rigid aircraft control frequencies, in order to minimise the impact on achievable aircraft handling. The effects of stores carriage, fuel state and flight condition on the flexible modes of the airframe result in changes to the modal frequencies and response amplitudes and hence, the structural-mode filtering needs to be designed to accomnaodate such variations. Digital technology, which is used to implement FCL functions within a digital flight control computer, offers great flexibility and allows highly complex functions to be implemented. The drawbacks are the inherent delays, with their associated effect on closed-loop stability, and the clearance issues associated with safety-critical software. For digital FCL, the models used for the design and simulation must account for the digital-processing effects in order to be representative of the implementation, to avoid unexpected results during ground or flight testing of the system. Anti-aliasing filters will be n e e d e d to limit the bandwidth of the input signals, in order to remove higher-frequency components to avoid these aliasing down to lower frequencies owing to digital-sampling effects. A formal m e t h o d of control law specification is required in order to capture functionality and implementation requirements, including the ordering and timing of the control law elements. 3As part of aeroservoelasticity,structural coupling is closelyrelated and sometimesconfused with aircraft flutter which involves the interaction of the aerodynamic and airframe elastic forces, which increases with dynamic pressure and ultimately leads to a divergent and destructive oscillation.

26

Flight control systems

Equipment specifications need to be established to unambiguously and completely define the required levels of functionality, performance and reliability for the environment under which the equipment is required to operate. The equipment has to be designed and manufactured to meet its specification and, as part of the system qualification process, adequately tested to show compliance with its specification, as well as for validating the models used in the FCL design and clearance processes (described in Section 1.9). The hardware necessary for the functioning of the FCS includes advanced sensors and actuation systems [18], and digital computing with its interfaces. Usually, for military applications, a similar redundancy implementation is adopted whereby three or four sets of identical equipment are used in parallel in order to identify and isolate any failed equipment via cross-monitoring. Often, the multiplexing of the digital computing is supported with analogue a n d / o r mechanical (for stable aircraft) backup systems, to achieve the required system integrity. The system design and the development process for the system need to ensure that a common-mode failure (i.e. any software or hardware failure which simultaneously affects two or more lanes of a multiplex system, due to a common cause) cannot occur, or that its probability is extremely remote. This will involve the physical isolation of the electrical and hydraulic power supplies and computing, sensing and actuation lanes, the use of optical communication links between flight control computers (electrical isolation) for cross-monitoring and the hardening of the entire system against electromagnetic disturbances, together with careful design of the redundancy management system to prevent failures from propagating. Common-mode points in the design need to be minimised as far as possible, and where this is not achieved (e.g. mechanical components such as the pilot's inceptors, actuation system rams and bearings etc.) the design must be physically robust. The system implementation is backed up by a comprehensive failure modes and effects analysis, and extensive groundbased testing (including failure testing) of the complete system, in order to demonstrate that the system meets its safety requirements. The flight control computing software is safety-critical and is developed in accordance with very strict rules. The software testing is very extensive, but is necessary to demonstrate that the software and its inherent functional design are free from errors. Several air-vehicle accidents have initially been attributed to software faults but were later found to be due to procedural failures or design errors, with the software performing exactly as specified. Finally, it is worth noting that the integrity requirements for a combat aircraft's FCS are usually significantly less than those for civil aircraft. For example, an electrical or hydraulic system failure which would result in the loss of a Class IV aircraft might be specified to be less than 10 -5 per flight hour [11]. With current technology, a quadruplex digital fly-by-wire system with dual hydraulics is an order of magnitude better (typically, 2x 10- 6 per flight hour). It must, however, be noted that for fighter aircraft the pilot has

Industrial considerationsfor flight control 27 the ultimate backup of his ejection seat, whereas the crew and passengers aboard a civil aircraft have no such o p t i o n - - h e n c e the requirements for civil aircraft are, quite naturally, much more stringent.

1.6. 2 Civil aircraft--design considerations and systems overview Many of the system aspects that have been discussed in the previous section also apply to civil aircraft. In order to avoid repetition, we will now discuss the role that the FCS plays in the overall flight guidance and control system of a modern civil aircraft. A short overview of the entire system is necessary for a better understanding. Figure 1.9 shows its essential elements: • the displays for pilot information: primary flight, navigation, engine and systems displays (PFD, ND, ED, SD); • the control devices for pilot interaction; • the computer systems for the following functions: - flight control (FC) including basic dampers for pitch, roll and yaw flight guidance (FG): autopilot (AP) and autothrottle (ATHR) flight management (FM); • the sensors for measuring aircraft states; • the actuators for executing the commands. -

-

Such a system allows the pilot to fly the aircraft in three levels of automation: (i)

In manual mode, the pilot uses sidestick (or yoke) and pedals to command the target values (accelerations or angular rates), or he commands the control surfaces directly if the sensor feedback information is lost. For accurate manual piloting, the control devices have to provide sensitive tactile feedback. (ii) In automatic mode, the pilot uses the glareshield control unit, called the flight control unit (FCU) on Airbus aircraft, or mode control panel (MCP) on Boeing aircraft, to select command values for speed, altitude, vertical speed and heading. The modes are armed, activated or deactivated by push buttons. The autopilot/autothrottle calculates control signals which are executed by the FCS. The pilot monitors the actions of the autopilot on the primary flight display (PFD). (iii) In managed mode, the pilot activates a pre-programmed flight plan or enters a new flight plan on the keyboard of the multipurpose control and display unit (MCDU). This systems architecture reflects the typical way of piloting: long-term activities are managed, medium-term activities are done automatically and spontaneous actions are done manually. At any time, the pilots are the managers of this system and they make the choice on how to fly the aeroplane. They can disconnect the automated flight modes either by pushing buttons or by using force to override thresholds on the control

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Industrial considerations for flight control

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Table 1.2: ATA I00 numbering system for systems related to flight control ATA 22 automatic flight-control system: autopilot/flight director, autothrottle, flight

management ATA 24 electrical power ATA 27 flight controls: flight-control computer, pilot control devices, actuators

etc. ATA 29 hydraulic power ATA 31 instruments: primary flight display, navigation display, engine display,

system display, flight warning etc. landing gear extension/retraction, nose wheel steering, braking, anti-skid etc. ATA 34 navigation: air data inertial reference system (ADIRS), very high frequency omnidirectional radio range (VOR), distance-measuring equipment (DME), instrument landing system (ILS) etc. ATA 32 landing gear:

devices if immediate action is required (instinctive disconnect). Even in manual operation, the pilot can program the automatic system in order to get assistance: c o m m a n d values, which are entered into the automatic systems, are displayed on the PFD and navigational display (ND) and flight-director bars show pitch and roll commands, which the autopilot would demand. The aircraft systems and all aircraft documentation are structured according to a numbering system, which is defined by the Air Transport Association of America (ATA). The ATA specification 100 is the industry's r e c o m m e n d e d format and content standard for technical manuals written by the aircraft manufacturers, and used by the airlines in the maintenance of the respective product. The most important chapters for flight control and its related systems are given in Table 1.2. A m o d e r n civil aircraft has at least two FMSs and two APs and ATHRs, with each system typically equipped with a control and a monitor channel for failure self-detection (dual-duplex architecture). If, for example, one AP system fails, the other one takes over. The AP function is totally lost only if a second failure occurs. This safety philosophy is called fail operative, fail passive. The failures result in some operational restrictions but the flight mission can be completed. The FCS is the inner circuit of the overall system, is indispensable for aircraft control and so has to remain functional at all times. After a fault, at least one reversionary mode has to provide control of the aircraft. Flight-critical systems such as the FCS, require the highest integrity: system failures which would result in loss of the aircraft have to be extremely improbable, i.e. its probability has to be less than 10 - ° per flight h o u r (ref.

30

Flightcontrolsystems

FAR and JAR 25 paragraph 25.1309). This requires redundant, highly reliable components. Furthermore, additional r e d u n d a n t components are installed because airlines need good dispatchability, i.e. they want to continue with revenue flights safely, even after certain failures have occurred and while being far away from the next maintenance base. Four dual-channel systems, each with a failure probability of less than 10-4 per flight hour, are necessary to fulfil this requirement. Software is an essential part of every digital FCS. Flight-critical software has to be developed according to very strict rules and has to be extensively tested. The software development standards for airborne systems are defined in Reference [29]. These standards are adopted by the certification authorities. Software errors are especially critical. They would cause any identical r e d u n d a n t hardware to (apparently) fail at the same time. Such a fault, which has the same effect as an error in the specification, is termed a generic fault. Behind the p r o o f of failure-free operation of complex software such as the flight control software lies an enormous task. A 100 per cent test to prove correctness is either impossible or exorbitantly expensive. Confidence is, therefore, gained from the rigour of the software design and development process and by testing over as wide a range of combinations of inputs as is reasonable. An additional safety measure compared to the similar redundancy approach described above for military aircraft, is the provision to switch to a dissimilar r e d u n d a n t component. This approach guarantees that a flightcritical function is not lost ifa generic software fault or a hardware fault causes the failure of all identical r e d u n d a n t components. The dissimilar redundancy will cover the generic fault and will contribute to achieving the necessary system reliability and integrity with respect to software and hardware faults. The dissimilar system may be built with more simplicity and may have less functionality. Dissimilarity can be achieved either at the e q u i p m e n t level (software and hardware dissimilarity) or at the functional level, e.g. roll control can be achieved either by ailerons or by roll spoilers and, therefore, two functionally different systems can be built.

1.7 Military aircraft~state-of-the-art and future challenges 1.7.1 Eurofighter Typhoon After almost three decades of experience, the use of fly-by-wire for military aircraft is a very well established and standard practice. In terms of the stateof-the-art, the FCS for the Eurofighter Typhoon is at the leading edge of flight control technology and although only summarised here, is described in greater detail in Reference [17]. Figure 1.10 shows the Eurofighter Typhoon a i r c r a f t - - a canard--delta configuration which has been optimised to meet the operational requirements of the four partner nations: the UK, Germany, Italy and Spain.

Industrial considerationsfor flight control 31

Fore

Figure 1.10 The Eurofighter Typhoon aircraft The airframe is aerodynamically unstable in pitch and yaw and therefore relies on a full-time fly-by-wire system for stabilisation. Advances in FCS hardware technology have had to be made in order to stabilise the very unstable u n a u g m e n t e d aircraft. The result is a high-performance supersonic agile combat aircraft with the following control surfaces: • • • • •

two two two one one

inboard and two outboard trailing-edge flaperons; inboard and two outboard leading-edge slats; foreplanes; rudder; spine-mounted airbrake.

T h e trailing-edge flaperons are used symmetrically for pitch stabilisation and control, and for performance optimisation at low to moderate incidence. These surfaces are also used asymmetrically for roll control. The foreplanes are only used symmetrically and are scheduled with the flaperons to provide pitch stabilisation, control and trim. At high incidence, the trim schedules take into account lateral/directional control characteristics and help to provide satisfactory resistance to departure and subsequent spinning. The r u d d e r provides directional control throughout the flight envelope and provides stabilisation at high Mach numbers and at high incidence. The leading-edge slats are scheduled with incidence and Mach n u m b e r to

32

Flight control systems Duplex avionics system bus

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Figure 1.11 Eurofighter Typhoon FCS architecture showing interfaces to powerplant, avionics and utilities-control systems optimise: performance, lateral/directional stability at high incidence and transonic pitch characteristics. A schematic diagram of the Eurofighter Typhoon FCS is shown in Figure 1.11. It is a full-time full-authority quadruplex digital system, with all hardware and software components designed to meet their specified functions and to achieve the specified integrity. There is no backup system in the event of total system failure. The sensors used by this system enable the following information to be derived: • pitch, roll and yaw rates as the essential feedback for stabilisation; • angle-of-attack and angle-of-sideslip for departure/spin prevention and gain scheduling; • normal acceleration for automatic g-limiting; • Mach number and pressure altitude as the essential scheduling parameters; • pitch-stick, roll-stick and rudder-pedal commands; • discrete commands from the cockpit, e.g. undercarriage up/down, airbrake i n / o u t etc. The FCL provide the primary functions of aircraft stabilisation and control, exhibiting the following features:

Industrial considerationsfor flight control

33

• self-trimming manoeuvre demand, giving a highly agile response with tight tracking of the pilot's commands and excellent handling qualities; • minimised sideslip variation during rolling manoeuvres and automatic turn coordination; • automatic compensation for the effects of the gravity vector and inertial coupling; • minimal response to turbulence, seen as a minimal movement of the nose, even in severe turbulence. The more advanced functions provided by the FCL are: • automatic angle-of-attack limiting; • automatic g-limiting and roll rate limiting, to respect structural loading limits for the actual stores configuration; • automatic restriction of control-surface usage with dynamic pressure, to avoid local overstressing of the airframe. Beyond this significant capability, the aircraft's FCS is to be developed to cover a wide range of basic and advanced autopilot modes: • • • • • •

classical autopilot; flight director; autothrottle; autoapproach; autoattack; autorecovery, e.g. following pilot disorientation.

Seven demonstrator aircraft have been built and are now well into their flighttest programmes. With the signing of the production investment contracts by the governments of the partner nations, the Eurofighter Typhoon aircraft will soon be in service with the air forces of the UK, Germany, Italy and Spain.

1.7.2 Future challenges for military aircraft The world's first fly-by-wire advanced short take-off and vertical landing (ASTOVL) aircraft intended for production is being developed as part o f the US Joint Strike Fighter (~SF) Programme. For this class of aircraft, active control technology has great potential in terms of pilot handling and accurate aircraft control. The UK's vectored thrust aircraft advanced flight control (VAAC) programme [30] is investigating and demonstrating advanced control strategies with low pilot workload, based on flight experiments in a modified Harrier. Complementary research is being carried out by BAe to investigate aircraft handling qualities for jet-borne flight, in terms of evaluation tasks and desirable aircraft response characteristics. U n d e r the UK's integrated flight and powerplant control systems (IFPCS) p r o g r a m m e [31], the integration of the flight and powerplant controls is part of a wider development, aimed at risk reduction of the advanced technologies for application to future aircraft. Figure 1.12 shows the Pl12 project aircraft which is being used as a basis for the IFPCS developments.

Flight control systems

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Figure 1.12 P112 advanced short take-off and vertical landing aircraft While current applications have tended to be limited to a single integration, for example, FCS and powerplant control system, the implementation of a total vehicle management system is seen to be a significant future development. Such a system might integrate the functionality of traditionally separate airframe systems, potentially providing system performance improvements associated with efficient energy management, and a reduction in equipment space and mass requirements. In addition, such systems will make use of reconfiguration and advanced diagnostics to improve reliability and maintainability, and to reduce the cost of ownership. For future stealthy aircraft, advanced air data systems will be required, since external measurement devices will be minimal and optical (laser-based) devices are being considered. The unusual shaping of such aircraft, for example, due to faceting, and the need to reduce the number and size of control surfaces for low observability, the possible reliance on thrust vectoring and the development of novel control methods such as nose suction/blowing are likely to lead to highly nonlinear aerodynamic characteristics. It is probable that for some missions, u n m a n n e d air vehicles (UAVs) will become the preferred weapons platform. The introduction of such technologies will present combat aircraft designers with some interesting design challenges.

1.8 Civil aircraft--state-of the-art and future challenges 1.8.1 The Airbus fly-by-wire family The first civil fly-by-wire aircraft was the Airbus A320 which made its first flight on 22 February 1987. Twelve years on, a family of Airbus fly-by-wire aircraft exists, featuring the A319, A320, A321, A330 and the four-engined A340. Such

Industrial considerations for flight control

35

Rudder Elevators ~ .

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Figure 1.13 Airbus 330 control surfaces a family concept offers great advantages for the airlines: it allows t h e m to build up a fleet of different aeroplanes to match their individual air routes and needs, and permits all aircraft to be operated and maintained in a similar way. To achieve such benefits, the design task becomes m o r e of a challenge, since any modification has to be analysed for its implications on the commonality between the aircraft. Therefore, design philosophies are necessary which are thoroughly considered and which require clear fores i g h t - - f o r the entire aircraft including the implications for the FCS. T h e A320 FCS is described in References [32-34]. The architecture of the A330 and A340, which is similar to that of the A320, represents the state-ofthe-art in civil aviation and is described in m o r e detail. T h e A330 aircraft's control surfaces are shown in Figure 1.13: • • • • • • •

one trimmable horizontal stabiliser; two elevators; two inboard and two outboard ailerons; six spoiler pairs; one rudder; seven leading edge slats on each wing; two trailing edge flaps on each wing.

All flight control surfaces are electrically controlled and hydraulically powered. The stabiliser and the r u d d e r have an additional mechanical link as a backup. Two dissimilar types of c o m p u t e r are used for the processing of pilot and autopilot inputs, as well as for control of the primary control surfaces: (i)

T h r e e flight control primary computers (FCPC), which can calculate the normal, alternate or direct laws and are capable of controlling up to

Flight control systems

36

Pe

Figure 1.14 Airbus A330 FCS (simplified) eight actuator servo loops each. (ii) Two flight control secondary computers (FCSC), which calculate the direct laws and are capable of controlling up to ten actuator servo loops each. These computers are supplemented by two slat/flap control computers (SFCC), which control the high-lift devices (slats and flaps). The computer types are dissimilar in function, hardware and software, and each computer has a dissimilar control and monitor lane. The computers are installed in the avionics bay, which is u n d e r the cockpit. The ARINC 429 digital databus, which is a single source, multisink unidirectional data transmission bus, defines the data-exchange standard for digital data between avionics systems [35]. The flight control computers have ARINC 429 interfaces between each other and to the other avionics systems, such as the air data/inertial reference unit (ADIRU), radio altimeters, autopilot, flight warning computer, maintenance computer etc. Discrete signals (28 volts/open or g r o u n d / o p e n ) are used to transmit single, logical information, mainly on the system status. Analogue signalling is used for actuator control. T h r e e i n d e p e n d e n t hydraulic systems are installed, energised by either engine-driven pumps, electrical pumps or a ram air turbine. Figure 1.14 gives an overview of the A330 FCS. It shows the signal flow from the most important pilot controls via the five computers to the servo-valves of

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the actuators. The ailerons and the elevators have two actuators each. Normally, one actuator is active while the other is passive (damping mode). All actuators except the spoiler actuators can be signalled by one of two computers. The redundancy management system organises which computer commands an actuator, and which actuator moves the control surface. To avoid over-complicating the diagram, the only links drawn are those that are used for signalling under normal system conditions; each line in the figure represents multiple redundant wire links. In order to minimise the effects of faults or electromagnetic interference, wiring is installed in physically separated routes. Special precautions have to be made in zones which are exposed to engine burst, tyre and wheel burst, bird impact etc. The schematic diagram (Figure 1.15) shows the signal path from the pilots' control devices to the control surfaces, excluding system redundancies. Such a functional representation is used for flight control law design. In the cockpit we find the following controls and displays as shown in Figure 1.16: the sidesticks (A), which are located on the lateral consoles, are used to enter pitch and roll commands. They have constant spring-force characteristics. Interconnected rudder pedals allow yaw control through the rudder (B). The speedbrake control lever (C), the pitch trim wheel (D), the rudder trim panel (E) and the flap-control levers (F) are located on the central pedestal. The engine/warning display (G) and the primary flight displays (H) present status and warning information for the FCS. Control surface positions are presented on the system display (I) if the FCS page is selected. Priority lights are located in the glareshield (J), which are illuminated if either of the pilots has taken priority for his sidestick. Pushbutton switches at the overhead panel (K) provide control over each of the flight control computers.

Figure 1.16 FCS components in the A330 cockpit

Industrial considerationsfor flight control 39 Sensors that measure parameters which are used for feedback or to schedule controller gains include: • three air data/inertial reference units; • two radio altimeters (RA); • accelerometers. Additional sensors necessary, e.g. for ground spoiler logic, are: • wheel tachometers; • landing gear switches; • thrust-lever position sensors. The FCLs provide both primary control functions (pitch, roll and yaw) and secondary control functions (airbrake and ground spoiler). In addition, they calculate operational and limiting speeds, as well as parameters associated with the flight envelope protection functions, and display these on the PFD. For normal operation (that is, as long as no systems have been degraded owing to failures) four modes are provided: • • • •

g r o u n d mode; take-off mode; flight mode; flare mode.

The transition between these modes is smooth, with no adverse effect on the pilot's ability to control the aircraft. The normal laws provide complete flightenvelope protection as follows: • • • • •

load factor limitation; high angle-of-attack protection; high speed protection; pitch attitude protection; bank angle protection.

Envelope protection functions are designed to prevent specified boundaries from being exceeded. They assist the pilot by initiating corrective action if necessary, but they do not take over the pilot's decision-making role or his resPonsibility for safe flight. In the event of multiple system failures, the FCLs shed protection functions or degrade from the normal law, to the alternate law or to the direct law, according to the n u m b e r and nature of the successive failures. A short description of the four normal FCL modes follows. More information can be found in Reference [33].

1.8.1.1 Ground mode On the ground, sidestick deflections correspond directly to elevator, aileron and roll spoiler deflections. T h e r e is no automatic pitch trim. The pedals c o m m a n d the r u d d e r and the nose landing gear simultaneously. The nose

40

Flight control systems

wheel is controlled by the brake and steering control unit (BSCU). Control authority on the nose-wheel angle is limited to +_6° and the limits are reduced with increasing ground speed. High turn rates can be commanded at low ground speeds by the steering handles, which are located close to the sidesticks (up to + 75 ° nose wheel angle).

1.8.1.2 Take-off mode The take-off mode is not a separate mode: it is a blend of the ground mode and the flight mode. After lift-off the flight mode is progressively blended with the ground mode, in order to achieve a smooth transition from the direct sidestick/control-surface relation on the ground, to the load factor and roll rate demand laws used in flight. Furthermore, the envelope protection functions are gradually phased in.

1.8.1.3 Flight mode Pitch normal la~ the pitch normal law is a load factor demand law with an automatic trim function. At low speed, the load factor is blended with pitch rate. With the sidestick at neutral during level flight, this law provides shortterm flight-path stability and compensates for turbulence. Turn compensation is provided for bank angles of up to 33 °. As a consequence of the load factor demand law, the static stability with respect to speed, as required by the regulations (FAR/JAR 25.171, 25.173 and 25.175), is almost neutral. Static stability is restored at low speeds by the high AoA protection and at high speeds/Mach numbers by the high speed protection. Both are complemented by the pitch attitude protection. The pitch normal law includes the following functions: Load factor limitation: the load factor is limited to: • - 1.0 g a n d +2.5 g (for the clean configuration, i.e. slats/flaps in); • 0.0 g a n d +2.0 g (slats out). This still allows adequate manoeuvring capability, even in an abrupt avoidance manoeuvre, without risk of structural overload.

High AoA protection: the high AoA protection guarantees positive speed stability and it protects the aircraft against stall caused either by inadvertent pilot action or as a consequence of atmospheric turbulence. If the protected angle-of-attack ap~ot, which is equivalent to approximately 1.13 Vsl: , is exceeded, an angle-of-attack demand law becomes active. The sidestick input is interpreted as an angle-of-attack demand, which commands at,rot when the sidestick is at neutral, and Olmax, a limit angle that is below the stall angle, when the sidestick is in the fully aft position. 4 V~lgis the 1 g stall speed, as defined by a special condition to JAR/FAR 25.103, which takes the specific design characteristics of the Airbus fly-by-wire aircraft into account.

Industrial considerationsfor flight control 41 High-speedprotection: VMO(MMo) is the m a x i m u m operating limit speed (Mach n u m b e r ) that the crew may not deliberately exceed in normal operation. If airspeed exceeds a threshold of VMO+6 kts (MMo + 0.01), which is reduced in high forward acceleration or low pitch-attitude cases, the pilot's nose-down c o m m a n d authority is gently reduced to zero and a nose-up c o m m a n d is automatically introduced. Thus the airspeed can never exceed VMO+30 kts (MMo+ 0.07), even if the pilot suddenly applies full forward sidestick. For a long-term full nose-down sidestick c o m m a n d , the m a x i m u m airspeed is limited to VMO+15 kts (MMo+0.04). Pitch-attitude protection: pitch attitude is limited to +30 ° nose-up (+25 ° at low speed) and - 1 5 ° nose-down. The pitch attitude protection reduces the pilot's authority, beginning to do so, some 5 ° before a limit is reached in o r d e r to stop at the limit without any overshoot.

Roll normal la~.. the roll normal law comprises the following two functions: a a roll rate d e m a n d / b a n k angle hold law for bank angles up to 33 ° b a bank angle c o m m a n d law above 33 ° of bank. For a, the roll rate d e m a n d is proportional to sidestick deflection and limited to 15°/s. Bank angle hold is provided with the sidestick in its neutral position for up to 33 ° of bank, with automatic turn coordination and turn compensation. This allows turns to be flown in normal airline operations, without pitch inputs. Function b, is called bank-angle protection.

Bank-angle protection: above 33 ° of bank angle, positive spiral stability is introduced. Maximum bank angle is limited to 67 ° (45 ° in high AoA protection, 40 ° in high-speed protection). Turn compensation is reduced in accordance with the bank angle, so that it is necessary for the pilot to pull the sidestick. Level flight can be maintained with a 67 ° bank angle at the load factor limit of 2.5 g.

Yaw normal la~. the yaw normal law is a direct control-to-surface law (pedals to rudder) with m a x i m u m deflections limited by the r u d d e r travel-limitation function, which provides structural protection at high dynamic pressures. T h e following functions are provided: • yaw damping; • turn coordination; • automatic trim in case of engine failure.

Turbulence-damping function: this function alleviates the effect of atmospheric turbulence on the structural vibrations. It is a first step towards active control o f the structural dynamics. All long flexible fuselages, such as those of A330/ A340, tend to have longitudinal and lateral banana-shape-like structural m o d e s which can cause uncomfortable accelerations in the cockpit and the rear part of the fuselage. This function feeds acceleration signals back to r u d d e r and elevator, reducing the vibration level by approximately 50 per cent.

42

Flightcontrolsystems

Manoeuvre load alleviation: the inboard and outboard aileron pairs and the three outer spoiler pairs are deflected upwards automatically when manoeuvres with high load factors are flown. This redistributes lift to the inner wing, which reduces wing bending moments. Pitching moments are automatically compensated by the elevators.

1.8.1.4 Flare mode In order to provide a conventional flare (where the pilot has to pull the sidestick back progressively to achieve a gendy increasing pitch attitude during flare), the longitudinal control laws automatically change from flight to flare mode when the aircraft approaches the ground: • automatic trim is deactivated; • a modified normal law with load factor and pitch rate feedback is activated.

1.8.2 Boeing 777 Boeing's design philosophy for the 777 aircraft's FCS has been d e t e r m i n e d by the general requirement to provide commonality to the cockpit presentation of a conventional mechanical system such as that of the 747 [36]. This leads to a design which is different to the Airbus design philosophy. The pilots use conventional control wheels for pitch and roll commands. Two units provide the tactile feel of the control column. Control forces are increased with increasing speed. Under autopilot control, six back-drive actuators move the control columns, control wheels and pedals (only during approach and landing) to positions which represent the autopilot commands. The aircraft's FCL are described in Reference [37]. T h e system has a triplex/triplex architecture: three primary flight computers (PFC) process the pilot commands [38]. Each PFC has three lanes (command, monitor, and stand-by), which are dissimilar in hardware and in software. Control-surface commands are transmitted to four analogue actuator control electronics (ACE) units, which control the servo loops of the actuators. A reversionary c o m m a n d path (direct mode) is directly available through the ACEs. In the ultimate mechanical backup mode, the horizontal stabiliser and one spoiler pair are available. The 777 is the first aircraft to make use of the new ARINC 629 databus standard [39]. T h r e e ARINC 629 data-buses dedicated to flight control are used for the communication between the PFC and ACE.

1.8.3 Future challengesfor civil aircraft T h e desire for further reduction of accident rates, new aircraft programmes, maturing of new technologies and improvements of the design process will drive the future FCS evolution: (i)

Loss of control has become the main cause of aircraft accidents in the

Industrial considerations for flight control 43

(ii)

(iii)

(iv)

(v)

(vi)

US and will also dominate the accident statistics of the rest of the world when enhanced ground-proximity warning systems will have reduced the n u m b e r o f accidents related to controlled flight into terrain. FBW technology offers new opportunities to increase the overall level o f safety. Lessons learned from aircraft accident analyses have to be used for further improvements. The maturing o f new technologies promises further improvements, for example: * smart actuators, i.e. actuators which have either their own control loop or which are not supplied with hydraulic fluid by a central hydraulic system; • fly-by-light; i.e, signals are transmitted optically; • power-by-light, i.e. the control power is transmitted optically; • variable camber, where the wing camber is controlled by changing the aerofoil shape. The flexible structures of new large aircraft, such as the stretched derivative Airbus A340-600 or the proposed Airbus A3XX, require closer collaboration o f flight dynamics and structural dynamics in an interdisciplinary development process. The e n o r m o u s size of a very large aircraft with 600 passengers or more (e.g. A3XX) introduces new challenges for all disciplines, the main factor for flight control being the huge control surfaces on such aircraft: e.g. the tailplane will be as large as the wing of an A310, and although a wing is rigidly m o u n t e d to the fuselage, the stabiliser has to be moveable for trimming. Pure proportional enlargement is not always practicable or appropriate, hence new ideas and new solutions might be needed. The integration of new functions, such as the enhanced groundproximity warning system (EGPWS) or new air-traffic-control functions, which become possible with data links, will have an influence on future FCSs. A supersonic transport aircraft, which may be developed as a Concorde successor, presents new challenges for the FCS.

It is likely that the technology developments in civil aircraft will be applied to the development of future class III military aircraft such as tanker, transport, AWACS and maritime patrol aircraft. Adaptation of civil systems can lead to cost-efficient solutions, but enhanced manoeuvring capabilities are required, compared to civil transports.

1.9 The flight control system development process 1.9.1 The current situation Today, the development phase for a new civil aircraft programme lasts about three years, counting from the go-ahead (the official programme start, where

44

Flightcontrolsystems

the first parts are ordered and the contracts are placed) to the first flight. After about one year of flight testing, the first plane is delivered to the launch customer, who expects a mature product. As prototypes are no longer built, the design has to be perfected in laboratories. High-fidelity simulation with hardware-in-the-loop creates a virtual aircraft, the so-called 'aircraft minus one'. This approach requires a structured and well-defined FCS development process with extensive use of sophisticated computer-aided design methods. The situation for military aircraft is similar, with three years again being a typical timespan between contracts being placed and the first flight of a demonstrator aircraft, which is expected to be representative of the production vehicle. Such timescales are very demanding for the airframe, engine and e q u i p m e n t manufacturers, and good planning and coordination become critical items for success. For new military aircraft, the flight test programme typically spans several years since, compared with civil aircraft, a greater variety of new and often unproven technologies are integrated into the aircraft to achieve a superior performance: such technologies need to be demonstrated for highly dynamic missions, for numerous possible store loads and across a wide flight envelope. The military aircraft demonstrator development might be part of a competitive programme, resulting in a fly-off between demonstrator aircraft produced by two or more teams. This is a current US approach, a fairly recent example of which resulted in the Lockheed YF-22 being selected for production in preference to the Northrop YF-23. Currently, the Lockheed Martin X-35 and Boeing/McDonnell Douglas X-32 are competing for the Joint Strike Fighter production contract, which has an anticipated production run of about 3000 aircraft.

1.9.2 The system development process Several different types of model can be used to describe the FCS development process. We have chosen to use the V-model in Figure 1.17, where the analytical steps are listed on the left leg and the synthesis steps are shown on the right leg. It is noted that the process is essentially the same for both military and civil aircraft. The terms verification and validation are defined in many references, usually with different words and sometimes with different interpretations. For example, the definitions of Reference [29] are as follows: v e r i f i c a t i o n - - t h e evaluation of results of a process to ensure correctness and consistency with respect to the inputs and standards provided to that process. v a l i d a t i o n - - t h e process of determining that the requirements are the correct requirements and that they are complete. Testing activities for verification and validation are depicted between the two legs. Specifications are p e r f o r m e d top-down, starting with the aircraft specification at the aircraft level. The system specifications are derived from

W W

8 2

,

0

~>

r~

U.

0

W

s_

0

q) O C

n>

.J

a IL

I

I I


>

m w -m~

78

Flightcontrolsystems

and: 7,q~ Ue

Thus the two short-term transfer functions describing response to elevator may be written:

w(s) n(s)

(1)

z~( Uez~) (S2 -

kw s + ~ (s2 + 2s~,w~s+ w~)

(mq+ Zw)$+ (mqz w- mwUe))

q(s) mn(S-Zw) = 71(s) (~-(mq+Zw)S+(mqzw-mwUe))

(2.43)

kq(s + ~ ) -=

(s~ + 2(~0,s + oJ~)

(2.44)

where now, kw, kq, T~, To,a,~s and ~0s represent approximate values. Clearly it is now very much easier to relate the most important parameters describing longitudinal short-term transient dynamics of the aircraft to the aerodynamic properties of the airframe, represented in eqns 2.43 and 2.44 by the concise derivatives. The reduced-order characteristic equation may be written down on inspection of the transfer functions:

A(s) =sZ+2~soJ~s+oJZ=s2-(mq+Zw)S+(mqZw-mwUe)=O

(2.45)

and, by analogy with the classical mass-spring-damper system, the damping and natural frequency of the short-period mode are given, to a good approximation, by:

2~oJs = - (mq + zw)

(2.46)

oJs = ~v/mqz~- mwUe T h e terms on the right-hand side of eqns 2.46 may be interpreted in exactly the same way as those of the classical mass spring damper. Thus, it becomes apparent that the aerodynamic derivatives are providing stiffness and viscous damping in pitch although there is more than one term contributing to damping and to natural frequency. Therefore the aerodynamic origins of the short-period dynamics are a little more complex than those of the classical mass spring d a m p e r and the various contributions do not always act in the most advantageous way. However, for conventional aeroplanes the overall dynamic characteristics usually describe a stable short-period mode. Normally the derivative zw, which is d e p e n d e n t on the lift curve 1 slope of the wing, and the derivative mq, which is determined largely by the viscous paddle-damping properties of the tailplane, are both negative numbers. The 1The lift curve is a plot of the lift coefficient, Cb against angle of attack, a.

Aircraft modelling

79

derivative m w is a measure of the aerodynamic stiffness in pitch and is also dominated by the aerodynamics of the tailplane. The sign of m w depends on the position of the cg, becoming increasingly negative as the cg moves forward in the airframe. Thus the short-period mode will be stable if the cg is far e n o u g h forward in the airframe. The cg position in the airframe where m w changes sign is called the controls fixed neutral point and m w is therefore also a measure of the controls fixed stability margin of the aircraft. With reference to eqns 2.45 and 2.46, the corresponding cg position where (mqZ w - m~Ue) changes sign is called the controls fixed manoeuvre point and its value is a measure of the controls fixed manoeuvre margin of the aircraft. 2.10. 4 The phugoid

T h e phugoid mode is most commonly a lightly d a m p e d low-frequency oscillation in speed u which couples into pitch attitude 0 and height h. A significant feature of this m o d e is that the incidence or(w) remains substantially constant during a disturbance. Again, these observations are easily confirmed by reference to the eigenvectors in the solution of the equations of modon. The phugoid appears, to a greater or lesser extent, in all of the longitudinal motion variables but the relative magnitudes of the phugoid components in incidence a(w) and in pitch rate q are very small. Typically, the u n d a m p e d natural frequency of the phugoid is in the range 0.1 r a d / s to 1 r a d / s and the aerodynamic damping ratio is very low, typically 0.1 or less. However, the apparent damping characteristics of the mode may be substantially influenced by power effects in some aeroplanes. A reduced-order model of the aircraft retaining only the phugoid dynamics is very rarely required in flight-dynamics studies. However, an approximate model of the phugoid mode may be derived from the equations of motion by making simplifications based on assumptions about the nature of the motion. Following a disturbance, the variables w(ot) and q respond in the time scale associated with the short-period mode, thus it is reasonable to assume that w(a) and q are quasi-steady in the longer time scale associated with the phugoid. Whence, to a good approximation, it follows that: w=q=O Once again, it is assumed that the equations of motion are referred to aircraft wind axes and since the disturbance takes place about steady level flight then:

0e~- O~e =

and

0

Ue = V0

and it follows that: xo=-g

and

z o = m o=0

Also, as for the reduced-order short-period model: Zq -~ Ue

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Flightcontrolsystems

Additionally, it is usually assumed that the aerodynamic derivative xq is insignificantly small. Thus the equations of motion 2.23 may be simplified accordingly:

=

Zu Zw Ue

+

(2.47)

The second and third rows of eqn 2.47 may be manipulated algebraically to eliminate w and q and, following some rearrangement, the reduced order state equation is obtained:

Xu

\ mwUe-mqZw] I -gl ~ ~nwOe~mqZ~w}

+ix.- \ mwV-mqzw L \ mwUe-mqZw/

i "J J

(2.48) or

= Apx + Bpu

(2.49)

Equation 2.48 may be solved algebraically to obtain the reponse transfer functions for the phugoid variables u and 0. The characteristic equation describing the reduced order phugoid dynamics is given by: A(s) = det [sI-Ap] = 0 whence

s2+2 s+2 s2( (mu e qzu ;muzwzu) OJp=

/Is+g/--

Xu--X~ mwUe-mqzw,IJ

\mwUe-mq zw

=0

(2.5o) Thus the approximate damping and natural frequency of the phugoid mode are given in terms of a limited number of aerodynamic derivatives. More explicit, but rather more approximate, insight into the aerodynamic properties of the aeroplane dominating the mode characteristics may be obtained by making some further assumptions. Typically, for conventional aeroplanes in subsonic flight:

m,---*O, ]m,zw[lmqz~]

then the corresponding expressions for the damping and natural frequency

Aircraft modelling 81 become:

2(pop = - x u O)p=

(2.51)

Ue

Further analysis of the expressions for the aerodynamic derivatives, assuming that the trimmed lift is equal to the aircraft weight, enables the following approximate descriptions of mode damping and frequency to be derived in terms of the lift coefficient, CL, the drag coefficient, Co and the steady-state velocity V0:

1( o)

~'P~

CL

(2.52)

%___gX/~ v0 These expressions for damping ratio and natural frequency of the phugoid mode are obviously very approximate since they are the result of many simplifying assumptions. Thus, the natural frequency of the phugoid mode is approximately inversely proportional to the trimmed speed and the damping ratio is approximately inversely proportional to the lift to drag ratio of the aeroplane. Since one of the main objectives of aeroplane design is to achieve a high lift to drag ratio, it is easy to see why the damping of the phugoid mode is usually very low.

2.11 Lateral-directional r e s p o n s e to controls

2.11.1 The lateral transfer-function matrix The lateral-directional state equation is given in terms of concise derivatives by eqn 2.25. Thus substituting for A, B and I into eqn 2.33 the lateraldirectional transfer-function matrix is given by:

s-y~ G(s) =

1 5(s)

-yp

-l~

,-lp

--Tt~

--rip

- Yr $-- n r

0 -1 0 0 0 -1 -N~(s) N~(s) N~(s) Nf(s) N~(s) N2(s) N~ (s) X~ (s) U~(s) N~(s)

-Y¢~ -Yo ] - l~

- io

- sn~

on¢~

0

-1

Y¢ Y¢ ] n~ n~ 0 0 0 0

(2.53)

82

Flight control systems

The lateral-directional response transfer functions, given by eqn 2.53 completely describe the linear dynamic asymmetric response in sideslip, roll and yaw to aileron and rudder inputs. As in the longitudinal solution, implicit in the response are the dynamic properties determined by the lateraldirectional stability characteristics of the aeroplane. As before, the transfer functions and the response variables described by them are linear since the entire modelling process is based on the assumption that the motion is constrained to small disturbances about an equilibrium trim state, usually taken to mean steady level flight. Equation 2.53 describes two sets of five response transfer functions, one set describing motion in response to aileron input and a second set describing response to rudder input. As for the longitudinal response transfer functions, it is convenient to adopt a shorthand style of writing the transfer functions. The transfer functions describing response to aileron are conveniently written:

(2.54)

~(s)

p(s) = NP~(s)

=

kps( S2 + 2(4'w~s + w2~)

r( s) = N~ ( s) _

~(s)

(2.56)

A(s)

c~(s) = N~(s) =

(2.55)

k~(s 2 + 2(~w~s + w2~)

(2.57)

(2.58)

and the transfer functions describing response to rudder are conveniently

Aircraft modelling 83 written:

((s)

A(s)

¢(s)

A(s)

(2.59)

(2.60)

m

(2.61)

=

Ts

,;(s)

7r (s2+2~awas+w 2)

(2.62)

~X(s)

=

~'(s)

s+

_

A(s)

TO (s ~ + 2~'q,wcs+ w~) (2.63)

T h e solution of the equations of motion results in polynomial descriptions of the transfer-function numerators and c o m m o n denominator in the formulation described by eqns 2.53. The polynomials factorise into real roots and pairs of complex roots which are most explicidy quoted in the style o f eqns 2.54 to 2.63. Since the roots are interpreted as time constants, damping ratios and natural frequencies, the above style of writing makes the essential information instantly available. It should also be noted that the n u m e r a t o r and denominator factors are typical for a conventional aeroplane. Sometimes pairs of complex roots may be replaced with two real roots and vice versa. However, this does not usually mean that the dynamic reponse characteristics o f the aeroplane become dramatically different. Differences in the inter-

84

Flight controlsystems

pretation of response may be evident but will not necessarily be large. Transfer functions eqns 2.54 to 2.63 each describe uniquely different, but related, variables in the motion of the aeroplane in response to a control input. However, it will be observed that the notation adopted indicates similar values for some numerator terms in both aileron and r u d d e r response transfer functions, for example k r, TO, ~¢, and o~0, appear in both AFt(s) and AY¢(s). It must be understood that the numerator parameters are context d e p e n d e n t and usually have a numerical value which is unique to the transfer function in question. To repeat the c o m m e n t made above, the notation is a convenience for allocating particular numerator terms and serves only to identify the role of each term as a gain, time constant, damping ratio or frequency. As before, the denominator of the transfer functions describes the characteristic polynomial which, in turn, describes the lateral-directional stability characteristics of the aeroplane. The transfer-function denominator is therefore c o m m o n to all response transfer functions. The response of all variables to an aileron, or to a r u d d e r input, is dominated by the d e n o m i n a t o r parameters namely, time constants, damping ratio and natural frequency. The differences between the individual responses are entirely d e t e r m i n e d by their respective numerators, the response shapes of the individual variables are d e t e r m i n e d by the c o m m o n denominator and coloured by their respective numerators.

2.11.2 The lateral-directional characteristic equation The characteristic equation commonly factorises into a zero root, two real roots and a pair of complex roots which are most conveniently written:

The zero root results from the inclusion of yaw angle in the state equation and indicates neutral stability in yaw or heading. In other words, lateral-directional dynamics are evaluated about the steady total velocity vector which assumes an arbitrary direction in azimuth, yaw or heading. The first non-zero real root describes the non-oscillatory spiral mode, the second non-zero real root describes the non-oscillatory roll subsidence mode and the pair of complex roots describe the oscillatory dutch-roll mode. The stability modes provide a complete description of the lateral-directional stability properties of the aeroplane with respect to the total steady velocity vector and subject to the constraints of small perturbation motion. Unlike the longitudinal dynamics, interpretation of the lateral-directional dynamics is not quite so straightforward as the stability modes are not so distinct; there usually exists a significantly greater degree of mode coupling or interaction. This tends to make the necessary simplifying assumptions less

Aircraft modelling

85

appropriate with a consequent reduction in the fidelity of the models. The connection between the observed dynamics of the aeroplane and its aerodynamic characteristics is described below. It must be appreciated that analytical progress is very difficult unless some gross simplifying assumptions are made. Means for dealing with this difficulty include the derivation of reduced-order models as for the longitudinal models.

2.11.3 The roll-subsidence mode T h e roll-subsidence mode is a non-oscillatory lateral characteristic which is usually substantially decoupled from the spiral and dutch-roll modes. Since it is non-oscillatory it is described by a single real root of the characteristic polynomial, and it manifests itself as an exponential lag characteristic in rolling motion. Provided the perturbation is small, the roll-subsidence mode is observed to involve almost pure rolling motion with little coupling into sideslip or yaw. Thus a reduced order model of the lateral-directional dynamics retaining only the roll mode follows by removing the side force and yawing m o m e n t equations from the lateral-directional state eqn. 2.25 to give:

(2.65)

Further, if aircraft wind axes are assumed then 1~ = 0 and eqn 2.65 reduces to the single degree-of-freedom rolling m o m e n t equation:

]k= lpp + l ~ + l ~

(2.66)

The roll response to aileron transfer function is easily derived by taking the Laplace transform of eqn 2.65, assuming zero initial conditions, and assuming that the r u d d e r is held fixed, ~'= 0, then:

sp(s) = lpp(s) + l~(s)

(2.67)

which, on rearranging may be written:

p(s)

l¢

=

kp

(2.68)

T h e transfer function given by eqn 2.68 is the approximate reduced-order equivalent to the transfer function given by eqn 2.55 and is the transfer function of a simple first-order lag with time constant T r. For small perturbation motion, eqn 2.68 describes the first second or two of roll response to aileron with a reasonable degree of accuracy and is especially valuable as a means for identifying the dominant physical properties of the

86

Flightcontrol systems

airframe which determine the roll-mode time constant. For example, the rollm o d e time constant is determined approximately by: 1

T~ ~ - -

lp

(2.69)

where lp is the concise derivative describing the aerodynamic damping in roll. Typically, the value of the roll-mode time constant would be in the range 0.2 to 1.5 seconds.

2.11.4 The spiral mode T h e spiral mode is also non-oscillatory and is determined by the other real root in the characteristic polynomial. When excited, the mode dynamics are usually slow to develop and involve complex coupled motion in roll, yaw and sideslip. The mode is usually excited by a disturbance in sideslip, u, which typically follows a disturbance in roll, ¢ causing a wing to drop. The sideslip puts the fin at incidence/3 which produces lift, and which in turn generates a yawing m o m e n t to turn the aircraft into the direction of the sideslip. T h e yawing motion produces differential lift across the wing span which, in turn, results in a rolling m o m e n t causing the low wing to drop further thereby exacerbating the situation. The tendency is, therefore, for the aircraft to diverge in the direction of the sideslip. However, the dihedral effect of the wing generates a negative restoring rolling m o m e n t due to sideslip which acts to return the wing to a level attitude. Therefore, the situation is one in which the fin effect, or directional static stability, and the dihedral effect, or lateral static stability, act in opposition to create this interesting dynamic condition. Typically, the opposing effects are very nearly equal and the mode may be stable, neutrally stable or unstable. Since the mode is non-oscillatory it manifests itself as a classical exponential convergence or divergence and, since it is nearly neutral, it is slow to develop; the time constant is very large, typically 100 seconds or more. Since the spiral mode is very slow to develop following a disturbance, it is usual to assume that the motion variables u, p and r are quasi-steady relative to the timescale of the mode. Whence, approximately, 1)= p = ~:= 0 and the lateral-directional state eqn 2.26, referred to wind axes, may be written:

[i] [Y:YYrY;I[i ninrol l l r + ol

(2.70)

Since wind axes are assumed, 16 = n~ = 0 and if the controls are assumed fixed such that unforced motion only is considered s¢= ~'= 0, then eqn 2.70 simplifies to:

Aircraft modelling

Ey:yy ll rolr ]ii

87

(2.71)

The first three rows in eqn 2.71 may be rearranged to eliminate the variables v and r and, omitting the insignificant aerodynamic derivatives, a reducedorder equation retaining the variables roll rate, p, and roll angle, ~b, only is obtained:

= fir (lrnl, llU.r )

Y~b

p

(2.72)

Since q~---p, eqn 2.72 may be reduced to the single degree-of-freedom equation describing, approximately, the unforced rolling motion involved in the spiral mode:

~ + ( YA( lrn~__ -- l~nT) ) \ yr(l~%-lpn~) ~b= 0

(2.73)

The Laplace transform of eqn 2.73, assuming zero initial conditions, is:

yr(lvnp- lpn~).

Ts

(2.74)

and eqn 2.74 is the reduced-order lateral-directional characteristic equation retaining a very approximate description of the spiral-mode characteristics only. Whence, an approximate expression for the time constant of the spiral mode is defined:

Ts -~ yr(l~np-lpn~) y~(lrn~- l~nr)

(2.75)

2.11.5 The dutch-roll mode The dutch-roll mode is a classical damped oscillation in yaw, about the oz axis of the aircraft, which couples into roll and, to a lesser extent, into sideslip. The motion described by the dutch-roll mode is therefore a complex interaction between all three lateral-directional degrees of freedom. Whenever the yaw oscillation is excited the relative velocity of the air over the port

88

Flight control systems

and starboard wing panels also varies in an oscillatory m a n n e r giving rise to oscillatory differential lift and drag perturbations. This aerodynamic coupling gives rise in turn to an oscillation in roll which lags the oscillation in yaw by approximately 90 ° . The phase difference between yawing and rolling motion means that the forward-going wing panel is low and the aft-going wing panel is high. Consequently, the classical manifestation of the dutch-roll m o d e is given by the path described by the wing tips relative to the horizon, which is usually elliptical. For the purpose of creating a reduced-order model to describe the dutchroll mode it is usual to make the rather gross assumption that dutch-rolling motion involves no rolling motion at all. This assumption is based on the fact that the mode is first a yawing oscillation and that aerodynamic coupling causes rolling motion as a secondary effect. Whence, the lateral-directional state eqn 2.26, referred to wind axes, may be simplified by writing, ~6=p= ~b= ~b= O. Since aircraft wind axes are assumed, IO = n o = 0 and if the controls are assumed fixed such that unforced motion only is considered se = ( = O, then eqn 2.26 simplifies to:

[:l[ ]..

(2.76)

Writing eqn 2.76:

i d = AdX d the reduced-order characteristic equation describing the approximate dynamic characteristics of the dutch-roll mode is given by:

Ad(s) = d e t [ s I - A d ] = s - y ~ -YT - n~ s - n r = $2__

(2.77)

(nr+yv)s+ (nryv_ n~yr) = 0

T h e r e f o r e the damping and frequency properties of the mode are given approximately by:

2(d°sd-~ - ( nr + Y~) w2-~ (nryv - n~y~)

(2.78)

Comparing the damping and frequency terms in eqn 2.78 with those of a mass spring d a m p e r it is easy to identify the roles of those aerodynamic stability derivatives which are dominant in determining the characteristics of the dutch-roll mode. For example, n r is referred to as the yaw-damping derivative and n~ is referred to as the yaw-stiffness derivative, and both are very

Aircraft modelling

89

dependent on the aerodynamic design of the fin and the fin volume ratio. Although the dutch-roll-mode approximation gives a rather poor impression of the real thing, it is useful as means for gaining insight into the physical behaviour of the mode and its governing aerodynamics.

2.12 Conclusions This chapter provides a background to the mathematical models used in the analysis and design of flight control systems, reviewing axis systems and the equations of motion for both longitudinal and lateral-directional motion for small perturbations about a trim condition. From these equations, transferfunction and state-space representations have been developed together with reduced-order models which offer greater insight into the aircraft's dynamic behavior.

2.13 Reference [1] COOK, M.V.: 'Flight dynamics principles'. (Arnold, Hodder Headline Group, 1997)

© Institution of Electrical Engineers, 2000.

Chapter 3

Actuation systems S. Ravenscroft

3.1 Introduction Actuation systems are a vital link in the flight control system, providing the motive force necessary to move flight control surfaces. Whether it is a primary flight control, such as an elevator, rudder, taileron, spoiler or foreplane, or a secondary flight control, such as a leading edge slat, trailing edge flap, air intake or airbrake, some means of moving the surface is necessary. Performance of the actuator can have a significant influence on overall aircraft performance and the implications of actuator performance on aircraft control at all operating conditions must be considered during flightcontrol system design and development programmes. Overall aircraft p e r f o r m a n c e requirements will dictate actuator performance requirements, which can lead to difficult design, control and manufacturing problems in their own right. In this chapter an overview of current actuation system technologies as applied to m o d e r n combat aircraft is presented, and their performance and control requirements are discussed. The implications for aircraft control are considered and an overview of selected modelling and analysis methods is presented.

3.2 Actuation system technologyman overview

3.2.1 Control-surface types Aircraft have a n u m b e r of different flying control surfaces. Some are for primary flight control (control of roll, pitch and yaw manoeuvring and stabilisation) and others are secondary controls (high-lift or lift-dump devices, for example). The type and use of a control surface has a significant impact on the requirements for the actuation system for that surface, in particular the actuator post-failure operation. Primary flight control capability is critical to safety and loss of control in one or more of the primary flight control axes will, in most cases, hazard the © 1999 British Aerospace PLC. Reproduced with permission.

Actuation systems 91 aircraft. The advent of concepts such as active control technology, controlconfigured vehicles and relaxed static stability, resulting in highly unstable combat aircraft to improve performance and agility, have led to an even greater reliance on primary flight control surface availability to the extent that many m o d e r n combat aircraft could not be controlled without the continued operation of the primary flight control surfaces. Accepting that failures within an actuator are inevitable at some time in the life of a fleet of aircraft, the actuation systems for primary flight control of such aircraft are designed to comply with a fail-op-fail-op philosophy; that is the actuator will continue to operate at, or very close to, full performance following one or two failures to meet the safety and integrity requirements. For many secondary control surfaces, it is not necessary to ensure full operation following failures. Although the loss of operation of a secondary surface may introduce flight restrictions, such as requiring a flapless landing or limiting the maximum incidence angle the aircraft can achieve, these will not directly lead to the loss of an aircraft. However, the nature of the failure may, in itself, produce a hazardous situation, such as possible engine flameout if air-intake cowls fail in a closed position, or handling and speed restrictions if an airbrake fails in the open position. In such cases a fail-op-failsafe or simply fail-safe philosophy is used, where one design feature is to ensure that the secondary control surface can be moved to a safe position or simply frozen following a failure. In the examples given above, the actuators may be required to open the intake cowl or close the airbrake following a failure, albeit at a lower rate than would normally be achieved. A similar philosophy exists for landing gear, where the safe state is gear down; the actuators have an extend only capability following loss of normal extend and retract functions. Although secondary flight controls are, of course, very important components of an aircraft and the provision of emergency operation modes can produce interesting engineering challenges, it is the primary flight control actuators that have most influence on basic aircraft stabilisation and handling qualities. T h r o u g h o u t the remainder of this chapter we will concentrate primarily on actuators for primary flight control surfaces.

3.2.2 Actuator operation Most flight control actuation systems on current aircraft are electrically or mechanically signalled and hydraulically powered. Until the early 1970s most actuators were mechanically signalled, but the advent of fly-by-wire technology has led to many actuators now having electrical signalling as the primary, if not only, form of demand. The d e m a n d signal is used to drive a spool valve, opening ports through which high-pressure hydraulic fluid flows. The fluid is metered to the actuator ram, causing the piston rod to extend or retract and providing the force to move the control surface. Movement of the spool valve could be achieved by mechanical input, using mechanical feedback of

92

Flight control systems

actuator r a m position to close the valve when the actuator reaches the d e m a n d e d position; by hydraulic means, using an electrohydraulic servo valve, in effect a mini actuator, to drive the spool; or, as is b e c o m i n g m o r e c o m m o n , by a direct m o t o r drive. These concepts are shown diagramatically in Figure :3.1. Redundancy features such as the n u m b e r of servo valves or m o t o r coils and bypass valves are not shown in this figure. A typical actuator with servo valves providing the motive force for a t a n d e m main control spool valve is shown in Figure 3.2. This particular actuator configuration uses four servo valves to drive the main control (spool) valve, each signalled by one of four flight control computers, four linear variable differential transformers (LVDTs) to measure main-ram displacement and four LVDTs to measure main-control-valve displacement, producing a q u a d r u p l e x r e d u n d a n t actuator. By comparing each of the four signals up to two failed lanes may be isolated, one lane at a time, by a majority vote, to m e e t system safety requirements. Post-failure operation requirements have a significant effect on actuator design philosophy. Redundancy is necessary in primary actuators to ensure continued operation following a failure to m e e t the fail-op-fail-op requirement. This often takes the f o r m of multiplexing, or the addition of a n u m b e r o f identical lanes of control. For example, in the Eurofighter 2000 primary flight control actuators, all feedback sensors are quadruplexed, each o f the four sensors feeding their signal back to one of four flight control c o m p u t e r s (FCCs). T h e four FCCs c o m p a r e signals across a cross-channel data link, to identify whether any of the signals differ significantly from the others. A consolidated or average signal is p r o d u c e d for use in control and m o n i t o r i n g algorithms and each FCC produces an actuator drive signal to one of the four coils in the direct drive valve m o t o r which moves the main control valve to control the t a n d e m actuator. A typical actuator with a direct m o t o r drive for first stage actuation is shown in Figure 3.3. Whereas the Eurofighter 9000 actuators use a linear m o t o r to displace the main control valve, this actuator uses a rotary, brushless DC motor, rotary motion being converted to linear motion through a crank mechanism. A further difference from the Eurofighter 2000 q u a d r u p l e x actuator is the use o f a triplex architecture, with only three coils in the direct drive m o t o r and three feedback sensors (LVDTs) for each main control valve and main ram. For a triplex actuator to survive two similar but i n d e p e n d e n t electrical failures to achieve fail-op-fail-op some element of in-lane fault detection, rather than simply a majority vote between lanes, is needed, for example comparison with a model. T h e level of redundancy refers to the n u m b e r of electrical lanes used and not the n u m b e r of hydraulic supplies. The actuators depicted in Figures 3.2 and 3.3 b o t h use two i n d e p e n d e n t hydraulic supplies with an actuator r a m of t a n d e m construction. In order to maintain separation of the two hydraulic systems the actuator design must minimise, if not eliminate, leakage of fluid between systems and a rip-stop ram design is used to ensure that fatigue

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damage in one side of the cylinder will not cause a crack which will also damage the other side of the cylinder, leading to the potential loss of both hydraulic systems. Following a failure in one of the hydraulic supplies, the remaining hydraulic system will continue to provide enough power to move the actuator against air loads. However, the movement of the ram will cause hydraulic fluid to be pushed into and out of the cylinders on the side o f the failed hydraulic supply, which could cause a drag force to restrict movement of the ram. In order to overcome this drag force, bypass valves are fitted to the actuator in Figure 3.3, to connect each side of the piston in the affected cylinder together in the event of loss of hydraulic pressure. Control of actuator position is achieved with a closed-loop, feedback control system. Ram position is measured, often using an LVDT, although potentiometers or other devices could also be used. Main-control-valve position, which is roughly proportional to ram velocity (excluding the effects o f external loads on the ram, or the effects of nonlinear valve port shapes), is also measured to give improved damping characteristics. Loop closure could be p e r f o r m e d in analogue circuitry, but is more often implemented, at least in part, in digital computers. Typical control loops, for an actuator with servo valves for main valve actuation, are depicted in block diagram form in Figure 3.4. The inner (spool position) loop is analogue, as the high bandwidth of this loop would necessitate a very high sampling rate. In this case outer-loop closure is p e r f o r m e d digitally, with feedback signals sampled at 80 Hz. In analysing the performance characteristics of the actuator it is important not to neglect the effects of digital control, including sample and computational delays, which have an effect on loop stability and actuator frequency response, and nonlinear effects caused by sampling, which can cause such effects as dither.

3.3 Actuation system-performance

criteria

An essential part of a specification for an actuation system is the definition of the system-performance requirements as these requirements will be a primary consideration for the supplier throughout the design phase. Before the airframe manufacturer accepts an actuation system the supplier must demonstrate that the specified performance requirements have been met. With long-lead-time items such as actuation systems and considering the expense involved in the testing of hardware or of modifications late in the design cycle, modelling is an important part of performance assessment both for the supplier and the airframe manufacturer. A primary flight control actuation system has to provide the necessary speed and power of control-surface response to give the aircraft the required stability and manoeuvrability. The basic performance requirements are: • the actuation system should be able to move the control surfaces with a following or opposing load, while maintaining a rate of movement

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adequate for control purposes; • the actuation system should be able to hold the control surface at a required position with a load applied in either direction up to a defined maximum-load magnitude; • the effect of the actuation-system frequency-response characteristics (gain and phase lag) on low frequency (rigid aircraft) FCS loop stability margins should be minimised; • interaction with high frequency (flexible aircraft) vibration modes should be minimised. In addition, requirements for system reliability and integrity, size, weight and installation details and the appropriate technology level have to be considered, in as far as these will have an impact on the actuation system performance. Particular performance requirements that will be considered now in more detail are: • • • • •

stall load; maximum rate capability; frequency response; dynamic stiffness; failure transients.

3. 3.1 Stall load The stall load of an actuator is the maximum force applied directly onto the main ram that can be supported by the available hydraulic supply pressure before the ram will begin to sink. The load can be in either direction (extend or retract) and the criteria will apply equally for both. The stall load is a basic design parameter for the actuator ram and determines the required piston area for a given hydraulic supply pressure available at the actuator. Requirements on the actuator's load capability are usually defined as: • minimum required output thrust (two systems operating with a defined pressure drop across each piston); • minimum single-system thrust (with a defined pressure drop across the pressurised piston, the other being bypassed); • maximum static-output thrust (two systems operating with a defined pressure drop across each piston). These requirements are used by the supplier to determine the size of the actuators within the limitations set by the available standard hydraulic seal sizes. The first two will determine the minimum size (and in particular piston area) to meet load and performance requirements, and the third sets an u p p e r limit on the size to prevent damage to aircraft structure. The magnitude of the design stall load will be based on the maximum aerodynamic hinge m o m e n t predicted at any point in the flight envelope.

Actuation systems 99 This maximum estimated value may be factored upwards to provide the required design stall load. This additional factor is required to ensure that there is sufficient excess capability in the actuator to provide manoeuvring forces in the most severe flight conditions. For unstable aircraft, the loadcarrying capability will be defined such that the maximum load experienced in flight will be no greater than 70 per cent of the single-system stall load, in order to ensure that there is always adequate rate capability for control purposes (following a hydraulic system failure), to maintain control o f the aircraft u n d e r the most adverse conditions. If the aircraft is stable then the maximum flight load may only be slightly less than the single-system stall load on the basis that recovery can be made to a flight condition where thrust capability is adequate. The primary factors affecting the stall load are: • piston area; • hydraulic supply pressure; • n u m b e r of hydraulic systems operating. Secondary factors are: • unequal piston areas on each side of the piston; • force fight in a tandem ram configuration; • cross-piston leakage. When a force is applied that exceeds the stall load the pressure required to support the load is greater than that which is available from the hydraulic supply, the ram stalls and tends to sink and the outer-loop feedback will try to compensate. The dynamic behaviour at this point can potentially be predicted by an actuator model, although post-stall behaviour is not normally regarded as being of significance for performance assessment. When the ram sinks u n d e r the applied stall load a hydraulic flow back through the valve ports against the supply is implied. Because of the main-ram position feedback control the main valve will move hard over to its maximum travel when the ram sinks, so the ports will be fully open for this reverse flow. Some actuation systems are provisioned with non-return valves which prevent reverse flow through the valve ports. If reverse flow is allowed then the sinkage of the ram reduces the static stiffness effectively to zero beyond the stall, causes the normal hydraulic pressure maxima to be exceeded and may even r e n d e r the aircraft uncontrollable.

3.3.2 Maximum rate capability Rate requirements are defined as a required rate, extending and retracting, for a given load and pressure differential across the piston. The required rates are usually defined at no-load conditions and about 60 to 70 per cent of the stall load, for two-system and single-system operation. The supplier uses the rate requirements, along with size information derived from consideration of

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the loading requirements, to d e t e r m i n e the fluid flow needed, and h e n c e the necessary valve size. T h e m a x i m u m rate at which the actuator main ram can be driven corresponds to the m a x i m u m opening of the valve ports. T h e m a x i m u m rate is reduced when the actuator is required to move against the load and increased when required to move with the load. A steady load will be present in practice when a control surface has to be deflected against the airflow, either for a steady manoeuvre or a trim requirement. T h e factors affecting the m a x i m u m rate capability are: • • • • • •

steady load; supply and return pressures; n u m b e r of operating hydraulic systems; piston areas; main-valve p o r t geometry; m a x i m u m main-valve displacement; • cross-piston leakage; • valve-block pressure losses.

From a p e r f o r m a n c e point of view the m a x i m u m rate capability must be sufficient to move the aerodynamic control surface at a speed which is required to give satisfactory pilot-handling qualities. Also, the requirements of automatic flight control systems, including any active control feedback functions where control rate is a factor, must be taken into account, since stability of the aircraft control loops u n d e r large-amplitude motions may be affected by the rate limit. T h e hydraulic supply pressure at the actuator must be maintained close to the nominal design level in order to maintain the m a x i m u m rate capability, as well as other actuation system p e r f o r m a n c e parameters. This must be taken into account when specifying the aircraft hydraulic system supply, including the pumps, accumulators and hydraulic pipe pressure losses at m a x i m u m flow. Figure 3.5 shows a typical plot of m a x i m u m rate capability as a function of steady external load, up to stall conditions for each direction of main-valve opening. The effect on m a x i m u m rate of a cross-piston leak is also given on the plot. With a cross-piston leak there are areas of operation with high steady load for which the main ram will sink against the d e m a n d e d direction as fluid drains across the piston. This should be avoided in an actuation system design by ensuring that valve port size and piston areas are adequate to prevent sink for all operating conditions, taking cross-piston leakage into consideration.

3.3.3 Frequency response Requirements for the actuation-system frequency response u n d e r particular test conditions, e.g. load, amplitude, m e t h o d of loop closure, are defined in the specification d o c u m e n t as boundaries within which the frequency

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response must lie. The gain and phase-lag boundaries are applied to the response of the ram-to-body displacement to an input d e m a n d with representative control-surface inertia loading. An example of typical gain and phase boundaries applied to a fly-by-wire actuation system is shown in Figure 3.6. Bounds are placed on the maximum and minimum gain and on the maximum allowable phase lag, and a particular range of d e m a n d amplitudes is defined to encompass the linear range of operation of the actuation system. The frequency-response boundaries are used by actuator suppliers to assist in determining the distribution of gain around the control loop along with other criteria such as hysteresis, failure transients and valve port size and shape. Frequency-response boundaries are defined to ensure that the effects of the actuator on low frequency (rigid aircraft) modes are minimised with the ram movement to demanded-movement gain of approximately 0 dB and the phase lag at a minimum, while providing sufficient gain roll-off at high frequencies to reduce interaction with aircraft and control-surface structural vibration (flexible aircraft) modes. It should be noted that the gain and phase boundaries are to be respected when control-surface structural modes are included, so it is usually the case that output inertia loading will have to be modelled. T h e frequency response of the actuation system is a very important consideration, since this is a significant measure of the actuation system performance. The total actuation system is normally a fairly high-order system with as many as 12 state variables for a well-specified model (based on current experience), depending on the degree of detail required for analysis. Nevertheless the basic response is a first-order lag resulting from the integration of valve flow (proportional to main-ram velocity), coupled with ram-position feedback. All other states correspond to higher frequency effects such as servo valve or direct-drive valve and inner-loop dynamics, filters, sensors and inertial loads. The basic design and build quality of the actuator is aimed at achieving the required performance for the specified range of frequencies and amplitudes. It is invariably intended that the characteristics are as close to linear as possible. The basic first-order response is the primary factor in determining the actuation-system response bandwidth. The higher-order terms cause variations from the basic response, and can result in undesirable resonances which amplify response at some frequencies. Such linear properties will be evident t h r o u g h o u t the broad mid-range of amplitudes. In specifying the required performance it is necessary to set frequencyresponse gain and phase-lag boundaries which must not be violated and meeting these criteria will determine the feedback control gain, whether electrical or mechanical. Variations from linearity occur t h r o u g h o u t the working range, but these are normally small enough to be acceptable; it is at extremes of input amplitude that significant deviations from linearity become evident on the frequency response.

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The upper-gain boundary is aimed primarily at the linear-system characteristics, to avoid the presence in the system of any excessive resonances. It applies to all amplitudes. The lower gain boundaries apply for very small levels of input excitation and different boundaries are specified for different amplitudes. These levels are taken to correspond with the amplitudes to be applied in the actuation-system tests. The factors affecting low amplitude response are ram and valve friction, valve laps and leakage, hysteresis, electrical tolerances and bearing backlash. Meeting these boundaries will determine the degree of refinement required in manufacturing accuracy of valve ports, ram friction, bearings, components etc. Phase boundaries apply only to maximum allowable phase lag, whether at low or high amplitude. The high-amplitude boundary is intended to define the performance required for the main linear range of operation. Satisfying the phase-lag criterion is important for the flight control system, which is designed assuming a specified standard of actuation-system performance. The usual single number quoted for the actuation system in this regard for comparison purposes is the phase lag at 1 Hz, this being a typical frequency associated with aircraft-handling qualities for pilot control. The large amplitude gain and phase boundaries discussed above can be assumed to apply for the stated amplitudes up to the amplitudes that will result in main-ram rate limiting. No frequency response criteria are specified for very large amplitude inputs that will cause the valve to open to its full extent. The frequency-response boundaries of Figure 3.6 assume that the input is applied directly as an analogue demand. If the input is digital, as when the d e m a n d is injected into a digital computer, then an additional phase lag is incurred in the input path, so the boundaries as shown are no longer applicable and a modified set of boundaries is required. Although it is necessary to meet the gain and phase requirements when the actuator is controlled by the digital flight control computer, it may not be possible for the actuator supplier to test the equipment in this configuration, particularly during the early development stages of an aircraft programme. In practice, a set of frequency-response boundaries is specified covering digital loop-closure methods (the requirement for aircraft control) and analogue loop-closure methods (to allow the supplier to test the actuator before a flight control computer becomes available). Failure cases and external loading conditions are also considered.

3.3. 4 Dynamic stiffness Dynamic stiffness, or impedance, is the ability of the actuator to resist an external oscillatory load, that is, to act as an effective spring and damper. Impedance characteristics are measured by installing the actuator in a suitable test rig, applying a steady load to the ram if required, then applying an incremental oscillatory load at a range of frequencies and measuring

Actuation systems 105 incremental ram displacement relative to jack body. Results are presented as dynamic stiffness, in real and imaginary form representing stiffness and damping respectively, with the units force/displacement ( N / m or lb/in). Impedance requirements are defined in the actuation-system specification as boundaries within which the measured impedance must lie. Typical impedance boundaries, based on those used for a previous fly-by-wire aircraft project, are shown in Figure 3.7. Test conditions are defined, including requirements on steady-load and oscillatory-force amplitude. Impedance considerations will influence actuator sizing and possibly the reversion modes following failures. The criteria usually specified for impedance are based on the need to avoid control-surface flutter. There are no specific criteria set out for the lower frequency range associated with flight control system design, as the impedance which is present in the basic design is generally sufficient and no design constraints need be imposed. At the higher frequencies associated with flutter it may be critical that the actuation system contributes enough stiffness, in conjunction with the stiffness of the back up structure, to the control-surface rotation mode so that the flutter-speed margins are met. The margins with a fully operational actuation system will be greater than when failures are present. When a hydraulic system fails the r a m / b o d y impedance is more or less halved and the impedance boundaries are relaxed. The overall impedance includes the effects of attachment and o u t p u t structural stiffness and so will not be halved when a hydraulic system fails. If the structural stiffnesses are very high relative to the actuator r a m / b o d y impedance, then the overall impedance will be almost halved. If they are relatively very low, halving the r a m / b o d y impedance will have little effect on overall impedance.

3.3.5 Failure transients Requirements for failure transients are usually defined as boundaries on the ram-to-body displacement following the occurrence of the failure. Different classes of failure must be considered, including electrical-lane failures, hardover failures (for example, one lane of a multilane electric m o t o r demands full current, requiring the other lanes to compensate, until the failure is confirmed and isolated, as well as to control the actuator) and hydraulic-supply failures. Figure 3.8 shows typical failure transient boundaries. The actuation system is assumed to be in a state of steady equilibrium prior to the failure, with or without a steady applied force. The class 1 boundaries apply to a first failure or a second failure if the first failed lane has been switched out. The class 2 boundaries apply to a first hydraulic failure and subsequent electrical failures. Failure transients are particularly affected by intersystem force fight and main-valve pressure-gain characteristics, requiring a high-fidelity actuator model to predict results accurately.

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3.4 Actuation system modelling During the design phase of an actuator development programme both the equipment supplier and the airframe company purchasing the equipment will use mathematical models to represent actuation-system dynamics. Models are produced for a variety of purposes from simple representation of the actuator dynamics for use in the overall flight control-system analyses to more detailed representation of the actuator itself for use in control and failure monitor system design or performance prediction. The complexity of the model used will be determined by the type and depth of analysis to be performed and can vary from a first- or second-order transfer function through to highly detailed representations of digital computing effects, magnetic characteristics in direct-drive valve motors and the nonlinear flow and pressure characteristics of hydraulic fluid through a valve block. In the following descriptions, a relatively simple model of an actuator is discussed, referring to the block diagram of Figure 3.4. Sampling effects are repre-

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sented, as are nonlinearities in the f o r m of servo valve and main control-valve displacement limits. Nonlinear orifice flow and fluid compressibility effects are neglected, however, with flow rate, and hence actuator rate, being represented in the model as a linear function of spool displacement using flow gains. Such a model could not be used to assess pressure transients in stopping or starting an actuator, and does not include any representation of loading on the actuator, but will allow an assessment of basic frequency response and failure transient characteristics, including the effects of saturation limits. Servo-valve dynamics are represented in the model as a first-order lag with a time constant of 1.3 ms. A gain defining servo valve spool displacement per milliAmp of current d e m a n d and a displacement limit (e.g. + 0.3 m m ) complete the representation of the servo valve. Fluid flows through the servovalve to move the main control valve. The complete dynamics of the servo-valve flow and resultant force on the main valve, including the effects of friction or backlash, could be included in the model if the effects have a significant effect on the analysis to be p e r f o r m e d . H e r e a simple flow gain and integrator links main valve rate (and position) to servo-valve displacement. Again a travel limit is included (e.g. +3.0 m m ) which may be c o m b i n e d with the integrator to f o r m a limited integrator, setting main valve rate to zero when the travel limit is reached. Inner-loop closure is p e r f o r m e d with a differential amplifier, feeding back main-control-valve position measured using an LVDT, the representation of which is a gain ( V / m m ) and a second-order filter associated with the d e m o d u l a t i o n of the raw a.c. LVDT signal into a d.c. voltage. T h e representation of the main ram could take a n u m b e r of forms, f r o m a simple flow gain and integrator to detailed orifice-flow and fluid-compressibility equations, including representations of external loads and mass-springd a m p e r equations to represent the control-surface structure. T h e level of detail depends on the intended use of the model. In the example shown a flow gain and the integrator effect of the main ram are c o m b i n e d to p r o d u c e an overall gain of 60 ( m / s ) / m . No main-ram position limits are included, as it is m o r e usual to provide a d e m a n d limit in the flight control laws, preventing the actuator from being driven onto the r a m e n d stops. Outer-loop closure is p e r f o r m e d digitally. Ram position feedback is measured by LVDTs and sampled at a rate of 80 Hz. It is i m p o r t a n t that the delays due to sampling and computation are included in the model, in addition to the demodulation, anti-alias filter and loop-closure control-filter dynamics, to give an accurate representation of loop stability and overall frequency response. A model of this type would be used for simulation analyses, to evaluate the response to step, ramp, sinusoidal or other input demands. Transfer function analysis could also be p e r f o r m e d , to d e t e r m i n e gain and phase relationships between input and output for a range of frequencies and amplitudes. T h e m o d e l could also be linearised, to allow linear frequency-response calcula-

Actuation systems 109 tions. In the following sections examples of the results obtained from such analyses are presented to give an indication of the type of work carried out with such a model. 3.5 Nonlinear

frequency response

O n e of the main uses of mathematical models of actuators is to d e t e r m i n e the frequency-response characteristics (the response amplitude and phase lag when responding to a sinusoidal input d e m a n d ) . Linear models can be created and the frequency-response characteristics calculated using traditional, linear-analysis techniques. In this way the ability of the actuator design to m e e t specified frequency response characteristics can be proven. This is particularly i m p o r t a n t in flight control system design, as the aircraft control laws are designed with an assumed gain and phase characteristic for the actuators (usually in the f o r m of a second- or third-order transfer function), and any significant deviation from these ideal characteristics can lead to a reduction of aircraft gain and phase stability margins. However, the linear m o d e l only shows actuator frequency response u n d e r m o d e r a t e amplitude conditions, but in reality response characteristics would vary with d e m a n d amplitude. Nonlinear models are used to assess amplitude effects on frequency response, with a transfer function-analysis m e t h o d for analysis of the response to sinusoidal input demands. T h e m e t h o d is very similar to test methods, when a transfer function analyser or spectrum analyser is used to inject sinusoidal d e m a n d s to the actuator, and to analyse the gain and phase relationship between d e m a n d signals and the resulting actuator response. At larger d e m a n d amplitudes the actuator will start to reach internal limits, such as c u r r e n t or voltage limits in motors and spool displacement limits in servo valves and main control valves. The relationship between the limits reached in terms of amplitude and the frequency of the d e m a n d signal at which each occurs has a significant impact on the nonlinear frequency response of the actuator, and can lead to stability problems (see the c o m m e n t s on j u m p resonance, Section 3.7). In the actuator example presented in Figure 3.4, the position limit of the main control valve represents a limit on the rate of m o v e m e n t of the actuator ram, and the servo-valve position limit forms a rate limit on the main control valve and, hence, an acceleration limit on the main ram. If the combination o f input d e m a n d amplitude and frequency is such that one of these limits is reached, the response of the ram will be affected with a consequent effect on frequency-response characteristics. This effect is illustrated in Figure 3.9. These results, p r o d u c e d using a nonlinear model based on the block diagram of Figure 3.4, show that gain reduces and phase lag increases as d e m a n d amplitude increases. A d e m a n d amplitude of 0.5 m m represents a linear response, in this case, as neither the spool n o r the main control-valve position limits are reached. Even at d e m a n d amplitudes up to 2 m m across the

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An analysis technique closely allied with the production of nonlinear frequency-response data is that of saturation analysis. A linear model of the

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actuator is used to calculate the frequency response from i n p u t - d e m a n d signals to the locations of the various limits, such as servo-valve posidon or main-control-valve position. T h e gain information from this analysis can then be used to d e t e r m i n e the d e m a n d amplitude which will cause the limit to be reached across a range of frequencies. Figure 3.10 shows the results of such an analysis, based on the actuator model of Figure 3.4. From this figure it can be seen that saturation will not occur for sinusoidal d e m a n d s of up to 2 m m in amplitude. For d e m a n d s between 2 and 4 m m the servo-valve position limit will be reached if the frequency of the d e m a n d signal is above 12 Hz, but the main valve limit will not be reached for any d e m a n d signal. For d e m a n d s with a frequency below 12 Hz, the main-control-valve position limit will be reached before the servo-valve position limit, if the amplitude o f the d e m a n d signal is higher than 4 m m . A d e m a n d signal o f 6 m m amplitude will cause the main control-valve limit to be reached if the frequency is above 6 Hz. These results support the findings from the nonlinear frequency response discussed above, giving confidence that no untoward nonlinear effects are likely to affect actuator response. However, it is possible to have combinations

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o f gains and limits around the control loop which can cause a j u m p resonance effect, with serious performance implications for the actuator, as discussed below.

3.7 Jump resonance U n d e r conditions of large amplitude d e m a n d when servo-valve travel limits are e n c o u n t e r e d an actuation system can display sudden large increases in phase lag. This p h e n o m e n o n is described by the term j u m p resonance, although there is no gain peak associated with the sharp phase variation, and is caused by an effective acceleration limit. In practice, if in some extreme manoeuvres it is possible to reach such limits, the additional phase lag caused by the j u m p resonance can lead to severe temporary reduction of aircraft stability margins, with consequent potential handling difficulties. To avoid this problem at the design stage it is important to ensure that the valve ports (for both the main control valve and the servo valve) and travel limits are sized adequately. Increased valve-port width can be compensated for by a reduction of electrical gain, maintaining the overall loop gain required for actuator stability and response. Jump-resonance is characterised by a very rapid increase in phase lag over a narrow frequency band, as shown in Figure 3.11. This figure shows nonlinear frequency response results obtained from a model configured to exhibit jump-resonance effects. As d e m a n d amplitude increases the frequency at which saturation occurs reduces and a reduction in gain is seen, along with an even more dramatic increase in phase lag. The presence of any potential for j u m p resonance can be predicted from saturation-analysis results. Figure 3.12 shows the saturation characteristics for the actuator with j u m p resonance. Saturation of the servo-valve position limit will occur before saturation of main-control-valve position leading to an effective actuator acceleration limit, for the majority of d e m a n d amplitude and frequency combinations. The crossover frequency, where the two saturation loci intersect, is at a relatively low frequency (2.5 Hz), within the bandwidth of aircraft control. An actuator such as this is likely to cause severe handling deficiencies in an aircraft, and the valve ports and control gains would need to be redesigned to give a better balance, and to produce the sorts o f characteristic exhibited in Figures 3.9 and 3.10.

3.8 Failure transients C o m p u t e r models of an actuation system are used to predict the transients which occur following a failure within the system. Although redundancy features are included in the actuator design to ensure continued operation following failures, it is also important that the actuator does not produce an

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excessive transient when transitioning from one level of redundancy to another. Boundaries, within which the transient must lie, are defined in an actuator specification, and failure to comply with this r e q u i r e m e n t will lead to excessive actuator transient m o v e m e n t immediately following a failure, which could p r o d u c e structural damage in the area of the actuator mountings or a high transient acceleration at the crew's stations or at sensitive equipment, owing to aircraft response to control-surface movement. T h e effect of the failure can be countered either by a failure-absorption m e t h o d , where the presence of the failure is countered by the rest of the system with no special action being taken, or by failure rejection, where the failure is detected and an appropriate action removes the effects of the failure, leaving the remaining parts of the system to continue operating. For either a p p r o a c h the transient response induced following a failure must be assessed, and a design be p r o d u c e d which will m e e t the specified requirements. For the failure-rejection approach, the failure detection and isolation

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algorithms must also be designed. Failure-detection algorithms are often referred to as built-in-test, or BIT. A n u m b e r of levels of BIT will exist on an aircraft actuation system, ranging from start-up checks and preflight checks carried out automatically by the flight control system, through to the continuous monitoring of actuator operation, referred to as continuous built-in test, or CBIT. The level and m e t h o d of CBIT depends largely on the actuator design, but the following typical example will illustrate the principles. Ram-position measurement for feedback control is often p e r f o r m e d using linear variable differential transformers (LVDTs), with three or four used to provide the necessary levels of redundancy. The individual LVDT signals are consolidated in each computer, to produce an average signal which is used for actuator control-loop closure. In this way slight build tolerances, temperature effects etc. on each LVDT can be averaged out, minimising the difference in drive signals between lanes which would produce a force fight on mechanical components. However, this m e t h o d also means that any fault in one of the LVDTs will be propagated to the consolidated ram-position signal in all of the flight control computers. In order to reduce this effect averaging algorithms are used, weighted towards the median to reduce the influence of extreme signals and failed sensors. A typical voter algorithm for a triplex system is shown in Figure 3.13. The incoming signal samples are first sorted to determine the highest, median and lowest values. The voter algorithm then produces a consolidated or averaged value based on the three input values. A n u m b e r of alternative algorithms could be used, including simple averaging of the three values or selection of the median. To minimise the influence of faults on the consolidated value the algorithm will limit the authority of the highest or

116

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lowest signals, weighting the average towards the median. Having produced algorithms that limit the influence of faulty sensors on control-loop closure, it is also necessary to determine which lane is faulty and to reconfigure the voter monitor to ignore that lane. This is the purpose of the CBIT algorithms. In the case of the LVDT monitor u n d e r consideration here, the faulty lane could be identified by comparing each lane's signal with the consolidated value. As we have already established that the influence of the faulty lane on the consolidated signal is limited, any lane which shows a significant difference to the consolidated value (more than a certain tolerance value) can be considered faulty. In order to minimise the n u m b e r of nuisance failure warnings the tolerance value is selected to allow for a difference in build standard of the LVDTs and, to remove the effects of glitches causing spurious failure warnings, a fault must be present for a certain period o f time, such as five consecutive computer iterations, before it is confirmed as a failure and the appropriate action taken. In this case the appropriate action would be to change the voter algorithm to simple duplex averaging, using the two healthy signals only. Simulation is used in defining the voter algorithms to minimise the influence of the faulty signals, and to design CBIT algorithms. An actuator model is produced including various redundancy features and signalconsolidation algorithms. Typical faults can then be simulated and the effects on actuator response predicted, as shown in Figure 3.14. In this Figure a transient response for the actuator model shown in Figure 3.4 is given, as the outer-loop (ram-position) consolidation changes from triplex to duplex.

3.9 Conclusions Actuation systems for m o d e r n combat aircraft flight control are, in general, highly complex devices relying on state-of-the art technology. They are often required to operate at, or very close to, full performance following multiple failures, requiring sophisticated control and monitor algorithms. Closed-loop control systems, often implemented in digital computers, are designed to give actuator performance in accordance with specified requirements, which are driven by the need for high performance and failure tolerance to provide high agility and control basically unstable airframes. Two control loops are usually used, the inner loop with main-control-valve position feedback (similar to main ram rate feedback) and the outer loop with mainram-position feedback. Monitor algorithms, again usually implemented in digital computers, detect c o m p o n e n t failures so that the overall actuatorcontrol system can take the appropriate action to remove the effects o f the failure. This may involve isolation of a servo valve or direct-drive motor coil, or reconfiguration of voter algorithms to exclude signals from faulty feedback sensors.

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Dynamic mathematical models play an important role in the design and analysis of control and monitor algorithms. Both linear and nonlinear models and a wide range of analysis techniques are used to design the control systems, and prove that performance requirements defined in the e q u i p m e n t specification can be met. The complexity of the model will reflect the analysis to be performed, and it is vital that consideration is given to this point to ensure that any model produced is appropriate to the task. In this chapter an overview of typical performance requirements, modelling methods and analysis techniques has been given. For future aircraft projects, flight control actuation may use electro hydrostatic actuators, electro-mechanical actuators or further developments of the more conventional hydraulic actuator. Whichever technology is used, control and monitor systems will be designed using methods based on those defined here.

118

Flight control systems

3.10 Acknowledgments The author wishes to thank Dr. Robert Stirling of Stirling Dynamics Limited for his assistance in the preparation of this chapter. Thanks are also due to Dowty Aerospace Wolverhampton, for permission to use Figure 3.2, and to John Tucker, Dave Allison, Mike Walker and Peter Chambers of British Aerospace Military Aircraft and Aerostructures for their comments.

© British Aerospace plc, 2000. Published with permission of the copyright owner.

Chapter 4

Handling qualities J. Hodgkinson and D. Mitchell

4.1 Introduction In this Chapter, we first introduce in simple terms what we mean by handling qualities, how we specify them, and how we achieve them. Then we introduce pilot-induced oscillations (PIOs) because they are one of the more serious consequences of failure to design for good handling qualities, and because current PIO studies offer an interesting example of state-of-the-art research in handling qualities. Handling qualities have been variously defined. For our purposes they are those characteristics of the dynamic behaviour of the aircraft that allow precise control with low pilot workload. A major objective of flight control system design is to bestow good handling (or flying) qualities on the aircraft. Engineers, oblivious to the philosophical fact that measuring a quality transforms it into a quantity, define metrics for handling qualities. Precision of flight can be quantified in terms of rounds on target for gun tracking, circular error probability for bombing or sink rate for landing, for example. Workload is more difficult to quantify, and for the time being we simply ask the pilot how easy or difficult his job is. Much of the achievement of handling-qualities practitioners has been in acquiring reliable information on pilot workload from pilots. Goodness is generally with reference to the pilot's comments in flight or in the flight simulator, and as summarised by Cooper-Harper ratings (Figure 4.1). The scale has ten points, where one is excellent and ten represents the worst qualities possible. Coarser gradations, levels 1, 2 and 3, are also defined. The scale is dichotomous. This feature improves repeatability by leading the evaluation pilot through a series of decisions regarding the task performance and the pilot workload. Among the factors affecting pilot opinion are piloting task, what failures are present and atmospheric environment. US specifications have distinguished between different task difficulties by defining flight-phase categories A, B and C [1]. Category A consists of demanding tasks like air-to air combat and refueling, category B includes less demanding tasks like cruise and climbs and descents and category C includes terminal tasks such as landing and take-off. The idea behind incorporating failure probabilities into flying-quality specifications is simply that the more

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Handling qualities 121 likely a failure, the better the consequent and subsequent flying qualities should be. Gusts make an airplane m o r e difficult to fly, so we sometimes p e r m i t worse flying qualities in turbulence. This does not m e a n that the aircraft itself is worse. O u r a p p r o a c h is to use classical control to identify those p a r a m e t e r s in the aircraft response which the pilot uses in p e r f o r m i n g his task. We will then define values of those parameters of the response which c o r r e s p o n d to good through to bad characteristics or, in our language, level 1, 2 or 3. T h e notation in this Chapter largely conforms to the n o m e n c l a t u r e defined at the beginning of this book. The occasional differences are due to the variations in accepted practice between the notations in use in the UK and the United States.

4.2 Longitudinal flying qualities

4.2.1 Control-input transfer functions T h e relevant transfer functions which describe the longitudinal notion were covered in Chapter 2. They are repeated here for completeness. For pitch attitude O(s) to elevator ~/(s) O (s) -

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(2.38)

where the subscripts p and s refer to the phugoid and short-period modes, respectively. If 77 is used as the input, this refers to the stick deflection. Notice that when the polynomials in the transfer functions are factored, the factors are given names, like 1/T, that are reminders of the response from which they 0 come. Notice too, for example, that the notation N n is the n u m e r a t o r of the transfer function for response of 0 to r/. These transfer functions are for aircraft either without feedback control systems or for aircraft with control laws which do not a u g m e n t the order of the aircraft response. For these, the concept of a u g m e n t e d stability derivatives is applicable.

4.2.2 Modal criteria T h e coefficients in eqns 4.6 and 4.7 describe i n p u t / o u t p u t relationships along with the c o m m o n notation for the modes of motion. These equations also show some useful relationships between the response quantities (these apply to conventional aircraft). T h e two modes are the short period, generally with frequencies f r o m one to ten rad/s, and the phugoid, with frequencies below that. If a m o d e of the

122

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response does not appear in the time response of a particular variable to an input, it will be manifest in the transfer function as a numerator term which cancels or nearly cancels the modal term in the denominator. For example, there is usually very little angle-of-attack variation in the phugoid oscillations, therefore the second-order numerator in N~ is closely equal to the secondorder phugoid in the denominator. Recall that from Chapter 2:

w(s) -_ N~(s) kw(s + 1/T~) (s2 + 2(~w,~s + w 2) 71(s) A(s) = (s2+2(pwps+w~)(s2+2(,w,s+w~)

(2.36)

4. 2.3 Phugoid f l y i n g qualities The phugoid is a long-period (low frequency) mode in which forward speed (kinetic energy) and altitude (potential energy) are interchanged. The resulting oscillations are in pitch, speed, altitude and flight path, but as mentioned already the angle-of-attack remains roughly constant. The denominator of the transfer function for speed and pitch motion is:

+

(4.1)

where U0 is the steady-state velocity, Ue in Chapter 2. Here the constant term, - g Z J U o, is the undamped natural frequency squared, ¢02n,for the phugoid. The derivative: ,

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mg= ~I pU2 SCL for the aircraft, we can substitute this in the remaining expression for the derivative to get: Zu ~ _ 2__g

U0 So the phugoid frequency:

(4.3)

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and the period of the phugoid in seconds, as McRuer et aL [2] point out, is about a fifth of the true airspeed in miles per hour. The above analysis is obtained from a two-degree-of-freedom model of the phugoid. In the three-degree-of-freedom model, the derivative M u appears. Aeroelastic and thrust effects that are highly configuration dependent introduce this parameter. The total damping of the phugoid mode is Xu, which is a measure of the drag of the aircraft. In high-speed flight, altitude can change significantly in phugoid motions and this can affect the phugoid damping because air density changes with altitude. The phugoid period will also be decreased as a consequence of the density gradient. The requirements for the phugoid are in terms of damping ratio for stable phugoids and time-to-double-amplitude for unstable phugoids. For level 1, (p should be at least 0.04 and at least zero for level 2. Time-to-double-amplitude, T2 should be at least 55 seconds for level 3. No distinction is made between classes of aircraft. Time-to-double-amplitude is -0.693/(pWnp and (p is negative if the phugoid is unstable. Pilots can control phugoid oscillations quite readily by closing a low-gain pitch loop. Nevertheless, this does require the pilot's attention and side tasks are difficult if poor phugoid characteristics are present. 4.2.4

Short-period f l y i n g qualities

The short period is a relatively rapid mode which governs the transient changes in angle-of-attack, pitch, flight path and normal load factor that occur at relatively constant speed following rapid control (generally elevator) or gust inputs. The mode is usually a stable underdamped second-order oscillation. For small angles, the angle-of-attack ot~- w~ Uo and L , ~ - Z,0 so we can use: Z. = UoZ~,-~ - UoL,~~ - Uo / To2

(4.5)

Define the parameter n / a in g per radian, as the steady-state normal load factor per steady-state angle of attack, so: n/ a = UoLJ g

This gives us a number of useful relationships which govern the short-period motions and the response variables to elevator input as follows:

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4.2.5 Criteria for the longitudinal short-period dynamics The stick force required to develop unit steady-state normal load factor, stick force per g is the short-period steady-state gain.

Handling qualities 125

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The stick forces in a steady manoeuvre must not be so great that the pilot cannot comfortably attain the maximum g load on the aircraft, and not so light that he inadvertently overstresses the aircraft. Fighters require light forces to avoid fatigue in prolonged manoeuvring up to 9 g for example. Transport aircraft, with their gradual manoeuvring and low maximum g capability, typically have higher stick forces. At flight conditions with low dynamic pressure, i.e. at high altitudes a n d / o r low speeds, the acceleration generation capability of the aircraft is low, so higher overall stick force per g is allowed at these conditions. Similarly, at higher dynamic pressures, we could allow lower stick force per g, Fin, so that the pilot can attain the maximum load factor that the airframe allows without excessive effort. F,/n is therefore specified to be a function of acceleration sensitivity, n/a, the steady-state normal load factor per unit angle-of-attack, n/a is a measure of flight condition, corresponding to high or low dynamic pressure. A floor minimum value of Fs/n is specified to prevent sensitivity problems. Classical airplane dynamics produce a constant Fs/n with flight condition so the variation with n/a is really a concession to aircraft with artificial feel systems and real flexibility effects. Classical airplane dynamics do not produce a constant stick deflection per g. Larger deflections are required for a given g at lower n/a. A dynamic value of Fs/n is also specified by requiring that the floor value be maintained during a sinewave sweep of the pilot's longitudinal controller for a frequency range spanning the effective short period (see Figure 4.2). To understand both the steady and the dynamic Fin, consider the transfer function for nz/F~:

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n~

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where the numerator is just a multiplier depending o n / ~ a measure of the effectiveness of the stick-force-to-elevator system, M n, the surface effectiveness, U0, the true speed and L,~, the dimensional lift-curve slope. The denominator consists only of the gravitational constant and the second-order short-period mode. From this transfer function and the final value theorem, the steady-state for a step input is:

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The minimum stick force per g is determined by plotting the amplitude ratio of the nz/F s transfer function, which will have a maximum at the resonant frequency.

4.2. 6 M o d a l criteria for the short period Short-period natural frequency is specified via the control-anticipation parameter (CAP): O92 nsp

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again, where n / a ~- UoL~/g. CAP boundaries are specified in the form of Figure 4.3. The short-period damping ratio is specified alone as a parameter according to Figure 4.4. The step-time histories and frequency responses of the various damping ratios are shown along with this Figure.

4.2. 7 Other short-period criteria A number of criteria have emerged that attempt to deal with longitudinal dynamics in the presence of feedback control systems. Sometimes these systems have introduced phase lags and delays from various mechanisation features like actuators, sensors, filters etc. The consequent mathematical model of the system becomes far higher than the fourth-order dynamics we

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4.2. 8

Equivalent systems

The equivalent system concept [3] is simply to match the augmented, highorder dynamics with a low-order equivalent which has the same form as an unaugmented aircraft, plus a time delay to approximate the phase lag of system components. Equivalent systems form the basis of all current modal criteria (longitudinal, lateral and directional) in the military specifications in the United States. The process works best if frequency responses are matched in the range 0.1-10 rad/s for estimating short-period parameters. For the phugoid, extension down to 0.01 generally works. With the gain in decibels, the phase in degrees and a weighting on the phase match around 0.02, a sumof-squares mismatch function is minimised. The approach is a vast improvement on picking one, dominant mode from the s-plane array (see Figure 4.5).

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Handling qualities 131 4.2. 9 Equivalent time delay A key addition to the low-order equivalent is a time delay of T seconds. This parameter T approximates the high frequency phase lag generated by the high-order terms in the response. A useful rule of thumb is to look at the additional phase lag at 10 rad/s, and to r e m e m b e r that 0.1 seconds of delay produces 57.3 degrees of lag at that frequency. For demanding piloting tasks for fighter aircraft, a delay of 0.1 s, i.e. 100 ms, is enough to preclude level 1 flying qualities and 150 ms is excessive even for large transports if they are required for precision landings, in-flight refuelling, formation flying or other tight tasks. For fighters, the level 2 limit is 200 ms, and for level 3 it is 250 ms. Delay worsens the pilot loop closure only when the loop gain is increased by the pilot in an attempt to get tighter control and a faster pilot-in-the-loop response. This p h e n o m e n o n - - t h e aircraft becoming more out of control as the pilot works harder to control i t - - i s very disconcerting to the pilot; R.E. Smith has called the effect the flying-qualities cliff. Large delays in demanding tasks often result in pilotinduced oscillations. The degradation in pilot rating has been summarised by plots like Figure 4.6. Unfortunately, there are insufficient research data available to determine whether the stick force or stick-position characteristics should be used in the equivalent system m e t h o d (or in any other method, for that matter). In an attempt to quantify the acceptable mismatch in determining an equivalent system, Wood and Hodgkinson [4] examined the added dynamics that would cause a noticeable difference in pilot rating. When the dynamics (from the Neal-Smith variable stability experiment [5]) were overlaid, they had the form of hour-glass-shaped envelopes of allowable mismatch against frequency, as shown in Figure 4.7. The envelopes show that differences a r o u n d a centralised frequency are more noticeable than at the frequency extremes. The equivalent system form must be appropriate for the response type. If novel response types are used, whatever the axis of control, the equivalent

Figure 4.5 Definition of equivalent-system mismatch, and comparison of po~-zero arrays and frequency responsesfor high-order system, its dominant root approximation, and its low-orderequivalent system 2O

a Minimise cost (i.e., mismatch) functional: = Z ( G2 + KP~): K= 0.02 i=1 - - high-order-response - equivalent response b x O high-order poles, zero X O low-order equivalent poles, zero c - - high-order system dominant-root approximation . . . . equivalent with delay - - - equivalent, no delay (Note: amplitude ratios for equivalent with/out delay, coincide.) -

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form must comply with the physics of the dynamics. For example, a pitchangle command system can generally be matched with a zero-over-second-order equivalent plus a time delay, yielding a damping ratio, natural frequency and time delay which are useful for specifying flying qualities and for comparing the qualities of design changes. The damping and frequency here are not strictly the classical short-period values, and would not strictly be compared with classical criteria since the response is not classical, but we would expect them to be in the same general range of values.

4.2.10 The bandwidth method From the frequency response of the pitch attitude to the longitudinal controller, the bandwidth frequency is the frequency where the phase margin is 45 degrees, or where the gain margin is 6 dB (see Figure 4.8). The bandwidth hypothesis [6] is that the pilot can adequately follow input commands with frequencies up to the bandwidth without causing instability. The phase roll-off or slope at high frequency, that causes this characteristic is essentially the same as equivalent time delay and is measured using a parameter called phase delay, ~'p.Figure 4.8 defines bandwidth and ~-p.

4.2.11 The Neal-Smith method Neal and Smith [5] proposed for pitch-angle control a pilot model of the form shown in Figure 4.9. Here the pilot shifts his parameters so as to reduce

Handling qualities 133 20.0 amplitude ratio, dB

0

s 2 + 11.6s + 4.96 -20.0 0.1

i 1.0

180.0 [--L

~

phase, dB

I 10.0

~

68.89s 2 + 1100.12s- 275.22

I 100.0 frequency, rad/s

e

.0059s

0

.

.

.

.

S2 + 11.66S + .0389 -180.0 0.1

-0.0072s

~

I

i

1.0

10.0

I

[ I

I

100.0 frequency, rad/s

Figure 4. 7 Envelopes of allowable mismatchfor longitudinal equivalent systems

steady-state closed-loop errors to reasonable levels (this is the 3 dB droop) and to reproduce rapid closed-loop commands (this is the fixed bandwidth frequency--not the same definition of bandwidth as we used previously). See Figure 4.10 for a Bode plot of the resulting closed-loop dynamics. The Neal-Smith criterion is a two-dimensional plot of pilot compensation against pilot-in-the-loop resonance (see Figure 4.11, which contains some recommended corrections to the boundaries made by Rickard [8]). Compensation is defined as the phase angle of the pilot's compensation measured at the specified bandwidth frequency, and the resonance (a measure of the pilot-in-the-loop oscillatory tendency) is presented in dB. The boundaries reflect the fact that pilots dislike PIOs and they dislike generating lead or lag. Figure 4.11 summarises the pilot comments corresponding to the

134

Flightcontrolsystems 1;p- 180 - (¢#)2~18o 2m18o

amplitude ratio of e

I ,

Flong

gain margin = 6dB

I s

phase angle of e

F,o.g

phase

............

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

..... .t ....

e';=

Figure 4.8 Definition of bandwidthfrequency and phase delay

different regions on the Neal-Smith plane, and uses a range of bandwidths as a design guide. Figure 4.12 shows that Neal--Smith pilot compensation is strongly correlated to equivalent frequency, as we would expect.

4.2.12 Gibson's dropback criterion Both the equivalent systems and the bandwidth criteria have had problems correlating configurations with excessive lead compensation and Gibson's dropback criterion (Figure 4.13) is a way of screening these configurations. Gibson [9] suggests the ratio of dropback to steady-state pitch rate, dropback/qs s should be less than 0.25 for precision tracking and less than 1.0 for landing.

4.2.13 Time-history criteria A number of workers have proposed measuring features from step-time histories as a generic way of determining flying qualities. Although in a design effort the step history is easily calculated, it is difficult to test and measure. A true step has infinite slope at its leading edge and instantaneously changes that slope to zero following an elapse of zero time. Inputs like this can be approximated electrically, but are quite different from even the most abrupt inputs of pilots.

E ~J

E

to o

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+

ot 5"

(M

÷

v

+

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÷

¢U l

~T

~÷

J

I

°~

"4

Handling qualities 135

136

Flight control systems

Hr, ax I~ T~ ~ . . . . . . . . . . . . . .

~............. ~ ..................... ~J .....

~.......... ~

N

-/(-6~'c) ' I deg I -901

o

log (.o

( BVlOmin

Figure 4.10 Neal-Smith criterion: pilot-in-the-loop tracking standards 4.2.14 Flight-path stability At speeds well above stall, airspeed is generally controlled with power and the flight path is controlled with the elevator. At very slow speeds, however, pilots are trained to add power to bring the flight path back to the desired value and to control the speed by using the elevator. The two control strategies correspond to operation at speeds above or below the speed for minimum drag, or the speed for minimum thrust required. The criteria for flight-path instability are generally stated as a restriction on the slope of the plot of flightpath angle against speed, using elevator control only.

4.3 L a t e r a l - d i r e c t i o n a l f l y i n g q u a l i t i e s Here we are considering the three equations for rolling moment, yaw rate and side force, as we see in Chapter 2, and the modes of motion which result from solving the equations.

4.3.1 Roll mode For an aircraft rolling about its x axis:

sp- Lps = I%

(4.11)

Handling qualities 20 abrupt response, .&.. ~ .. ~

strong PIO @,,.' tendencies, . have to fly it smoothly t 16 / closed-

--,

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'

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strong PIO tendencies

@ i. loop ,.. resonance , 12 Neal and Smith s b o u n d a r y

137

'

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~"~ Ii I I = I / ~ / kZ,) .~1 A .."

in'~al . response . final response difficultto predict, tendency to overcontrolor dig in, initialforces heavy, lightening up as response develops 40

60

80

100

pilot compensation, deg

key(bandwidth,rad/s)

Figure 4.11

•

1.5

•

2.0

•

2.5

• •

3,0 3.5 4.0

Neal-Smith criterion showing Neal and Smith's boundaries with Rickard's level 1/2 boundary, typical pilot comments for the various criterion regions and the effect of changing Neal-Smith bandwidth on configurations with various pilot ratings Note: Position command, pilot delay = 0.2 s Various LAHOS configurations (Smith, 1978) Pilot rating shown in circles, @

T h e transfer f u n c t i o n for roll-rate response to aileron is then: P_

Le,

~a S--Lp o r in generalised forms: p_ 6~

K T~+I

(4.12)

138

Flight control systems

0

80

pilot compensation. deg

0

40

J Zpc=114"2-33"8me(00~

-40 0

Figure 4.12

1.0 2.0 3.0 equivalent short-period frequency, we, rad/s

4.0

Comparison of pilot compensation in Neal-Smith c~terion against equivalent short-period frequency. (Note: line fitted to data with correlation coefficient of 94 %)

pitch attitude I

4, dropback i' overshoot

~/,,,,~_

(negative dropback)

attitude dropback

time control input removed

Figure 4.13

Gibson's dropback criterion

or

----K/ (1/TR)

(4.13)

in the shorthand notion where (s+a) is written simply (a). Typically, the roll-mode time constant is of the order of one second or so for fighters and somewhat longer for larger aircraft. If it is much longer (the

Handling qualities

139

requirements range from 1.0 to 1.4 s for level 1, 1.4 to 3.0 s for level 2, and 10 s for level 3), the initial slope region of the step-time history persists t h r o u g h o u t roll manoeuvres. The pilot's perception is then that he is c o m m a n d i n g roll acceleration, not rate, as he prefers. The Bode plot interpretation would be that, in the likely piloted crossover region (essentially his usual frequency range of interest) around say 3 rad/s, the response in roll rate drops off, so we would have to differentiate the response (multiply it by s) to make it look like a gain-type response,/~ This means that the pilot would see an sp or ~type response, which is not impossible to control but requires full attention, i.e. it leaves little or no reserve for side tasks.

4.3.2 Spiral mode T h e spiral mode is a slow recovery (or divergence) from a bank-angle disturbance. Usually it is very slow and so can be approximated by the ratio of the low-order coefficients of the transfer function denominator. Specifications prevent too rapid divergence. We often treat the spiral mode separately from the shorter-period roll and dutch-roll modes because it is generally at a far lower frequency and is differently handled by the pilot.

4.3.3 Coupled-roll spiral When bank angle is fed back to aileron, a low frequency oscillation can result. Unusual combinations of stability derivatives can also result in a low frequency oscillatory mode, similar to the phugoid, which is sometimes called the lateral phugoid. Although it is not generally associated with good flying qualities, total damping values (i.e., the product (r~OJn) of 0.5, 0.3 and 0.15 are currently used as the levels 1, 2 and 3 boundaries, respectively, based on data from the variable stability aircraft, NT-33.

4.3.4 Dutch-roU mode T h e dutch-roll mode is the lateral-directional short-period oscillatory mode. It generally occurs at frequencies similar to those of the longitudinal shortperiod mode, i.e. of the order of one to five radians per second or so. T h e dutch-roll mode can helpfully be considered very approximately as the m o d e through which the sideslip of the aircraft is controlled with the rudder. More realistically, the dutch roll is a nuisance mode in the basic roll response to lateral control. Along with its frequency and damping characteristics are specified measures of how much it appears in the lateral response (the magnitude of its residue) and its phasing. T h e r e are parallels between this sideslip response to r u d d e r and the response of angle-of-attack to elevator. The damping term is the sum of the rotational damping, N r and the resistance o f the aircraft to the velocity that generates the sideslip, Yr. The frequency or stiffness is mostly the rotational resistance of the aircraft to the

Flight control systems

140

Level

1

Flight-phase category

Class

Min srd*

Min ~r~fJd* (rad/s)

Min wd (rad/s)

A (CO and GA)

IV

0.40

0.40

1.0

A

I, IV, II, III

0.19 0.19

0.35 0.35

1.0 0.4

B

All

0.08

0.15

0.4

C

I, II-C, IV

0.08

0.15

1.0

II-L, III

0.08

0.10

0.4

2

all

all

0.02

0.05

0.4

3

all

all

0

-

0.4

* The governing requirement is that yielding the large value of (d, except that a (d of 0.7 is the maximum required for Class III. When the product w21 qb/fll is greater than 20 (rad/s) 2, the minimum specified dutch roll total damping ~'dt0,~is increased by A~'dto,,a values as follows; level 1: Asrdto,~= 0.014 (w,,~21¢/fll - 20) level 2:A(dmn=O.OO9(o)na2lqb/[31 20) -

-

level 3: AsrdW.e=0.005 (w.d21¢/fll -- 20)

Figure 4.14

Dutch-roll damping and frequency requirements

velocity w h i c h g e n e r a t e s the sideslip. T h e similarity o f Yv to Zw, Mq to N Ta n d o f N B to M s is q u i t e direct. T h e y can b e c o n s i d e r e d c o n c e p t u a l l y to b e the s a m e derivatives r o t a t e d t h r o u g h 90 d e g r e e s . T h e r a p i d i t y o f t h e d u t c h roll a n d t h e d e g r e e o f its o s c i l l a t o r y d e c a y a r e s p e c i f i e d by t h e u n d a m p e d n a t u r a l f r e q u e n c y a n d t h e d a m p i n g ratio, respectively. T h e s e c r i t e r i a a r e specified in F i g u r e 4.14. N o t e t h a t t h e total d a m p i n g , i.e. the p r o d u c t o f t h e u n d a m p e d n a t u r a l f r e q u e n c y a n d the d a m p i n g ratio, is also specified. T h e r e is c o m m o n l y significant d u t c h - r o l l c o n t e n t in t h e l a t e r a l o r roll r e s p o n s e to lateral c o n t r o l . We n e x t discuss c r i t e r i a w h i c h cover this effect, w h i c h is d e l e t e r i o u s since t h e p i l o t p r e f e r s a relatively p u r e roll r e s p o n s e to control.

4 . 3 . 5 The parameter w 4 J w d T h e l u m p e d p a r a m e t e r r e s p o n s e to lateral c o n t r o l is:

¢ = U ~ , =K¢(s2 + 2~¢wcs+(w2¢) 6a A (TRS+I)(TsS+I)(s2+2(dWnS+W2)

(4.14)

M a t h e m a t i c a l l y , if 56= (d a n d e0¢~ w.,, t h e n the two s e c o n d - o r d e r t e r m s c a n c e l e a c h other.

Handling qualities

141

bank angle, ~)

sideslip angle, -

t

Figure 4.15 Time responsedefinition of 8/,B roll-to-sideslipratio in the dutch roll Physically, the cancellation would mean that the bank-angle response does not contain any dutch-roll oscillations. Often, the parameter e0C/0a,~, which is usually abbreviated to eo¢,/ead,is a measure of the vertical separation of roots in this dipole, and requiring this parameter to be about unity has been used as a crude way of keeping the dutch roll out of the bank-angle response. However, it can be shown that yawing m o m e n t due to roll rate, Np, (the dynamic version of adverse yaw) causes the zero to move in a circular locus a r o u n d the pole, giving lateral root separation. The time-history equation for sideslip following a step aileron input is:

fl---: Co+ Csea't+ CReW"t+CDRe-g~'~t COS ( o a , a ~ + ~a

¢13)

(4.15)

and the criteria (not reproduced here for brevity) restrict the ratio of oscillatory rolling to average rolling as a function of the phase parameter 4'13 [1].

4.3.6 Phi-to-beta ratio, qS/fl The phi-to-beta ratio distinguishes between dutch-roll oscillations which occur in sideslip, with the wings roughly level, and dutch-roll oscillations which occur in bank angle, with roughly zero sideslip. Figure 4.15 defines qS/fl ratio in terms of time responses, which is readily calculated from the modal response ratios in the transfer functions. Current specifications state that when the product wz,dd?/fl is greater than 20 (rad/s) 2, the minimum specified dutch-roll total damping, (d0~,,t, is increased to prevent high roll accelerations due to side gusts. In addition to roll accelerations due to side gusts, pilots object to lateral accelerations due to roll manoeuvres. T h e specified maximum values of the parameter;

n~t'u°t'"x[ Pmax

tepinput,t _ - - t ~ t - - l - - I - - ~ force ~ ~ ' , ¢ ~ _ ~ graFdi?n?t' ~ . ~ !

'~'°

LL[

~++ I

0.01

I

P

I

~ ~ ~

t--t-t-I

~+

IIII

I I I I I 1 i2 ~ ~

MIL-STD-1797A

0.10 short-period damping ratio, ~sp • PIO occurrence z~ No PIO occurrence

1.00

Figure 4.25 PIO criteria using dynamic stickforce per g

Handling qualities

155

4. 7.2 A'Harrah-Siewert criteria A'Harrah and Siewert proposed their own criteria for prevention of PIO, especially for low-altitude, high-speed flight, in the 1960s. The most mature of these recently resurfaced as the US Federal Aviation Administration searched for ways to regulate against PIOs in commercial airliners. Early draft advisory circulars proposed the A'Harrah-Siewert criteria, but later versions have not. A'Harrah-Siewert PIO criteria [23] use an airplane response metric and a control metric. The response metric is defined as the time to one-tenth amplitude of the short-period response, compu ted as T l / 10 In (0.1) / ((spC0sp), and the control metric is a combination of stick force and position per g, (FJ nL)~x (6/nL), in units of in-lbS/g 4. The PIO boundary for their criteria is shown in Figure 4,24, along with their flight data introduced in Figure 4.23. Correlation is very good for the flight data, as there are only two PIO cases clearly on the nonPIO side of the boundary (and both are at least near the boundary), and two nonPIO cases on the PIO side. This makes the A ' H a r r a h Siewert criteria appear to be very effective. (One significant shortcoming, n o t e d by large-airplane manufacturers, has been that the control metric for wheel-and-yoke transports is orders of magnitude larger than the highest value in Figure 4.24, and this has understandably raised some concern.) =

4. 7.3 Dynamic stick force per g T h e developers of the US military specifications in the 1960s were aware of the work of both STI and A'Harrah and Siewert. Based on research at Cornell Aeronautical Laboratory (later Calspan), however, the choice for the military requirements was a dynamic stick force per g parameter that is primarily a function of short-period damping ratio. The requirements on stick force per g from the military standard [12] are shown in Figure 4.25, along with the now-familiar data collected by A'Harrah and Siewert [23]. The requirements of Figure 4.25 are even more effective at correlating the data, better than either the high-gain asymptote or A'Harrah-Siewert criteria. One PIO case lies on the nonPIO side, and one nonPIO case is on the PIO side of the boundary. Thus, we may conclude that, for conventional airplanes where short-period damping and control response are the primary causes of PIO, dynamic stick force per g is a very effective PIO criterion.

4.8 N o n - m o d a l PIO criteria Flying-qualities criteria introduced up to now have been directed towards airplanes responses for controlling inputs look similar to those of unaugm e n t e d aircraft, whether augmentation is used or not. As long as the basic characteristics of the airplane resemble those of the conventional response type in Figure 4.21, the modal criteria may be applied. The modal criteria are applicable even to less conventional-looking responses if the source of the

156

Flightcontrolsystems

unconventional form is well approximated by a time delay at frequencies below about 10-20 rad/s. T h e n we can apply the equivalent-systems approach and make use of the same criteria, along with a new limit on equivalent time delay. Examples of such high frequency dynamics include the typical noise, structural and anti-aliasing filters applied to the output signals of aircraft motion gyros and accelerometers. T h e r e are cases where this adherence to the traditional criteria breaks down, however. Historically this has been a result of the addition of lag or lead/lag filters in the pilot's command path with break frequencies near the pilot's operating frequency. The dynamics often are not conventional looking on a frequency-response plot, and use of traditional criteria (by applying equivalent-systems techniques to the responses) has resulted in controversy [24]. Another example of the shortcomings of traditional criteria is the unconventional response type, where the basic response form is not even close to that of the conventional airplane. Consider, for instance, the attitude response type where the short-term response to pitch control inputs looks like this: 0

K0e-r~

8e = IS2 + 2~',OS + ,oZl

T h e r e is certainly nothing wrong with fitting an equivalent system to an attitude response type to obtain this transfer function. Note, however, that this equivalent airplane does not have the same form as that for the traditional airplane: it is missing the zero 1~To2 and a free s in the denominator. The second-order lag that dictates the response clearly is not the same as the traditional short-period mode with which we are familiar. Therefore, it would be incorrect to blithely plot this root on the traditional criteria and make judgements about the short-period flying qualities of the airplane. What is needed, then, is a way of judging the flying qualities of aircraft which defy the traditional modal criteria.

4.8.1 Some current criteria Numerous flying-qualities researchers have proposed n o n m o d a l criteria for prediction of category I PIO. Typically these criteria apply well to the database u p o n which they are based, but break down when confronted with data from other experiments. The following is a brief summary of four longitudinal PIO criteria.

Airplane bandwidth~pitch-rate overshoot Pitch-attitude bandwidth criteria were developed for evaluation o f the handling qualities of highly augmented airplanes where more conventional criteria cannot be easily applied [26]. The criteria are included in the

Handling qualities 157 handling-qualities interface standard MIL-STD-1797A[12]. (The limits in MIL-STD-1797A have been found to be much too stringent and have been adjusted significantly, especially with the addition of a requirement on pitchrate overshoot [25].) They have been adapted to the prediction of PIO susceptibility as sketched in Figure 4.26. All of the bandwidth parameters are to be measured with the feel system included at all times (even if force sensing is used for aircraft commands). This differs from the approach taken by most other researchers. The argument is made that the feel system is not transparent to the pilot, and that it will therefore influence both pilot opinion of flying qualities and probability of encountering a PIO [26]. The developers of the bandwidth-based PIO criteria observed that, if a PIO occurs, the likely frequency for the oscillations is well approximated by the pitch-attitude neutral-stability frequency, tol800, with a slight adjustment of an additional 0.5 rad/s [27]. The hypothesis is that, in a PIO, the pilot adds little in the way of dynamics to the pilot-vehicle system (i.e., the pilot displays synchronous tracking behaviour [21]). The added 0.5 is an admitted fudge factor which probably indicates the addition of some small amount of lead as the pilot attempts to cope with the PIO.

Neal-Smith The Neal-Smith criteria [5] were also designed for the evaluation of flying qualities of highly augmented airplanes. The original requirements explicitly referred to handling-qualities levels but only indirectly addressed PIOs (Figure 4.11). Although there is a region (corresponding to handling qualities level 3) where PIO tendencies are mentioned, there is no clear P I O / no PIO dividing line on Figure 4.11. Strong PIO tendencies are indicated throughout the level 3 region, so this is clearly a region where PIO is predicted, but tendencies to oscillate in the middle of level 2 might also signify a milder PIO tendency. As with all the nonmodal criteria considered here, the Neal-Smith criteria are frequency-domain based. Unlike the others, however, application is best performed using transfer function models of the airplane, rather than frequency-response plots (in their original development [5], application was entirely graphical and it was possible to avoid obtaining transfer functions). This is a shortcoming of the criteria, since it raises the issue of the best way to obtain the transfer function, especially from flight test data. A significant complication of the criteria is the requirement to perform closed-loop analysis of the pilot-vehicle system. This requires assumptions about the pilot model to be used. Neal and Smith established several ground rules which they applied to their own flight research data to derive the boundaries. These ground rules have been varied, relaxed, tightened and ignored by other researchers over the years, but there is no real evidence that these variations are significantly more successful than the original version. As

158

~ ,q

Flight control systems

/

_

/: t~

$

°

F

g

~

~ ¢0

1,1-

:::::::

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eq.

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t,-

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6

¢,q

'4

Handling qualities

159

originally developed by Neal and Smith, the parameters in the criteria are obtained by finding the dynamics of the pilot model given in Figure 4.10, i.e.,

by: (TlS+ 1)

Yp= I~ (TLS+ I) e-'P for the pitch-attitude dynamics of the airplane described by Y~= O/bes. The pilot time delay, rp, is a fixed value (Neal and Smith assumed 0.3 s) and K p, 7"/ and TL are varied to meet specific performance constraints. In the original Neal-Smith analysis, the performance criteria were a specified closed-loop bandwidth, BW (where the phase of the closed-loop system, / ( 0 / 0 c ) , is - 9 0 degrees), of either 3.0 or 3.5 rad/s and closed-loop droop of exactly - 3 dB. The parameters of the Neal-Smith criteria are the closed-loop resonance, ]0/ 0clm~,, and the phase angle of pilot compensation, /_pc, at the bandwidth frequency. Determination of the best pilot model is not a trivial task when performed manually. Most users of the Neal-Smith criteria have developed software which will perform the loop-closure process automatically.

Smith-Geddes The Smith-Geddes P I t criteria were developed from basic principles of closed-loop piloted control of pitch attitude and normal acceleration [28]. They were initially aimed towards handling qualities, and they owe as their foundation the Neal-Smith database. The criteria have undergone some revisions as well as extension into the roll axis. Smith and Geddes define three types of P I t . These types are not to be confused with the categories of P I t mentioned earlier. The parameters of the Smith-Geddes criteria, as currently applied [29], are as follows: (i)

Slope of the pitch-attitude-to-stick force transfer function, S, defined between 1 and 6 rad/s, in units of dB/octave. (ii) Criterion frequency, too defined as 6+0.24S. If a P I t is predicted this is the expected P I t frequency. (iii) Phase angle of the O/Fe~transfer function measured at toe If the phase angle /-O/Fe~(jtoc) is more negative than - 1 8 0 °, a type III (attitudedominant) P I t is predicted. (iv) Normal acceleration parameter, ~(/'toc). If the phase is between - 160 and - 1 8 0 o, a type I (acceleration-dominant) P I t is predicted if, in addition, the normal acceleration response at the pilot's station is such that ~(Jtoc) = Ln~/Fs(Jtoc) - 14.3toe ---(,~ ' ::,

J-~--i~ I .:'l" ~ :

i ~

~',

:'

~

..

;" " \ :1 ) / t "~ ~, .~ . . . . . . . ~ ( . . . . ( ..~,.li.l.~.~.

',,'

i,,.., ...... ,,~:..).

:\

: ~-

,I

i,, !

:/" i ...........

,i

!

,~ ~

....

.... z ..... ,,~ ...........

,

\

-i

",( :

..... (~]p) u!eo doo-I ued 0

~--~

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259

260

Flightcontrolsystems

7.4 Future developments T h e cost of a solution to the structural-coupling problem, in terms o f the additional phase lag introduced into the FCS, is not insignificant when compared with the lag from other sources such as primary actuators, as indicated by the example of Figure 7.5. As expensive development efforts are applied to reduce overall system lags in order to realise the p e r f o r m a n c e potential of the FCS, a commensurate effort must be made to minimise the cost of the SC solution. The approach to structural coupling at British Aerospace is therefore u n d e r continual review; a n u m b e r of the directions where work is required or underway are outlined below.

7.4.1 Limit-cycle prediction and specification of alternative clearance requirements For consistency with the factors motivating the design and clearance methodology applied to EAP, structural coupling has been treated as a flightsafety issue. As already described, however, it is unlikely that structural failure could result directly from a structural-coupling encounter, because of the limited energy which the FCS can input, and because of system's constraining nonlinearities. For a flexible aircraft, an unstable mode will manifest itself as a limit-cycle oscillation in these circumstances, which may be very undesirable, but is not necessarily critical to flight safety. The real concerns are with the coupling of the flutter modes, structural and FCS hardware fatigue and effects on actuator performance, which may themselves have safety implications. To fully understand these concerns, a m e t h o d must be devised for predicting the amplitude and frequency of a limit-cycle oscillation within the system. The following section investigates the case of a structural m o d e which is unstable in the closed loop, through an application of nonlinear system theory to both a simple example system, and a more representative aircraftsystem model. The possible advantage of such a consideration in terms of an alternative structural-mode clearance procedure will then be considered.

7. 4.1.1 Description of limit-cycleprediction technique Limit-cycle criteria and prediction The existence of limit cycles in a nonlinear system can be predicted from a solution of its characteristic equation, with the nonlinear elements replaced by their describing functions [22]. In order to simplify the analysis, the only nonlinearity that will be considered is the software rate limit function within the FCS. The purpose of the rate limiter within the control software is to prevent saturation of the actuator main valve and, as such, is the main nonlinearity which limits the performance of the actuator. This in turn dictates the amplitude of any limit cycle which may occur. Consider the system as shown in Figure 7.16 in which an actuator is used in

Aeroservoelasticity

r(t) ) ( ~

~

261

c(t)

Gn0tO,E) Ratelimit Actuator Load

Structural Filters

Figure 7.16 System block diagram a position-control system in which the load exhibits a structural m o d e within the bandwidth of the closed-loop system. In this case, the characteristic equation for the system can be written as:

1 + G,(jw, L) G1(jto) Gz(jto) Gv(jto ) = 0

(7.1)

T h e solution of the characteristic equation gives the limit-cycle condition, which can be predicted from a r e a r r a n g e m e n t of eqn (7.1) 1

G1(rio)G2(jw ) Gr(jto ) - Gn(Jt°, E)

(7.2)

Provided that the describing function for the rate limiter can be derived, and that the linear c o m p o n e n t s within the system can be adequately modelled, it will be possible to predict the existence of limit-cycling conditions within the system.

Derivation of describing function for a rate-limiting function In order to derive a describing function for the rate limiter, consider the i n p u t / o u t p u t characteristics of such a device as shown in Figure 7.17. In this case, the characteristics are shown after a length of time sufficient for a steady relationship to be achieved. In addition it is assumed that the input signal is a pure sinusoid which triggers the rate limiter to give an output waveform which is triangular [23]. From Figure 7.17, the amplitude of the triangular output waveform can be derived as:

Y=~fl

2w

where fl is the m a x i m u m rate as shown in Figure 7.17.

(7.3)

262

Flight control systems i

I

----

i Y

<E

Input i

0

Figure 7.17

i

~

"~ tm

= ESino~t ~

i

i

i

~

"-6Time (s)

i

2~

co

I n p u t ~ o u t p u t characteristics o f rate-limit f u n c t i o n

Fourier analysis o f such a triangular waveform o f amplitude Y, reveals that the a m p l i t u d e o f the f u n d a m e n t a l is:

4/3

Y10,= - -

(7.4)

0)77

with an infinite n u m b e r o f harmonics. Neglecting these h a r m o n i c s , the gain o f the rate limiter can be expressed as" I G , ( j w , L) I -

4/3 wETr

higher-order

(7.5)

for an i n p u t sinusoid o f the f o r m as shown in Figure 7.17. In o r d e r to derive the phase response o f the rate limiter, c o n s i d e r the i n p u t / o u t p u t relationship o f Figure 7.17 o n c e again. F r o m the figure, it can be seen that the phase lag between the two signals can be r e p r e s e n t e d by the time delay, r. In o r d e r to obtain an expression for this time delay, it is necessary to locate the time at which the i n p u t signal is equal to the o u t p u t signal, such that: E sin cotm = 2-~

(7.6)

C o n s i d e r i n g that t moccurs after t = 7 r / 2 w , the above e q u a t i o n can be solved for t m such that 7r

1

7r/3

co

0)

2E0)

t m = -- - -- a sin - -

(7.7)

Aeroservoelasticity

263

Therefore, the time delay, r, can be expressed as

(7.8)

- a sin

r=--

¢.0

Finally, since the phase lag between the input and output signals can be expressed as

/_G,(jw, E) = - ~'w

(7.9)

the describing function of the rate limiter u n d e r the assumptions applied earlier is therefore

IGn(joJ, E)

I= 4fl

(7.10)

o~ETr

/_ G,(jw, E) = -

-asm~

+)

(7.11)

Since the gain of the rate limiter will never be greater than unity, and the phase o f the rate limiter will never be greater than zero, limitations can be applied to the above expressions. This results in the requirement that:

EoJ~ >4/3

(7.12)

/O

for the gain expression to be valid, and: EoJ~-2

(7.13)

for the phase expression to be valid. The above expressions therefore allow the prediction of the existence of the limit-cycling condition from the solution of the characteristic equation for the system as given in eqn 7.2. This is provided that the linear elements of the system can be accurately modelled, or a frequency response obtained from suitable testing.

Prediction of limit cycles in an example system In order to demonstrate the use of the describing function in the prediction of limit-cycles, consider the system as shown in Figure 7.16, with characteristic equation as given in eqn 7.2. Given that the linear elements of the system can be represented by the transfer functions:

264

Flight control systems

20

'i

_

(:

.::

/

'-

! ---~

i

~ncreasing o

G1G2GF(j°))

..................

: .... ,

..... : ..... :

.... :

-~-s~ ..... ~ .......S01utipn at ~=9"6 HZ,.E=0"04 • ~

-40

-35

-30

-25

-20

-15

-10

-5

•......

0

5

Real

Figure 7.18 Nyquist diagram showing limit-cycle solution 1 G1(s) = (0.026s + 1) (0.00005917s 2 + 0.007693s + 1)

(7.14)

1 Gz(s) = s2 + s+ 4000

(7.15)

GF(S) = 1

(7.16)

where the e l e m e n t Gl(S ) represents a typical servo hydraulic actuator, and G2(s) represents a lightly d a m p e d modal system. In the absence of the rate limiter, the system is unstable in the closed loop resulting in an u n b o u n d e d oscillatory response in the presence of an initial disturbance. For the system including the rate limiter, however, the characteristic equation can be solved in order to predict any resulting limit cycle. O n e m e t h o d of solution of the resulting characteristic equation is to plot both sides of eqn 7.2 on a Nyquist diagram and find the intersection of the two loci. Unfortunately, the describing function for the rate limiter is both frequency and input-amplitude dependent, resulting in an infinite n u m b e r of loci. However, solutions of the characteristic equation can either be located through suitable iterative techniques, or through plotting the describing function for the rate limiter as a function of Eto. T h e intersection therefore identifies the frequency of the limit cycle on the loci of G1C~GF(to) and the value of Eto and hence to on the loci of the rate-limiter describing function. T h e corresponding Nyquist diagram for the example system is shown in Figure 7.18. In this case, the nonlinear characteristics have been plotted for a

Aeroservoelasticity 15

10

,

!

........

.........

!

!

!

......

!

....... ,..........

, ................... .

265

,

........

5

_Fo -5

-10

: -15 -5

-4

i ~ S o l u t i o n at a h = 9 . 6 H z , E - - 0 . 0 4 -3

-2

-1

0 Real

1

2

3

4

5

Figure 7.19 Nyquist diagram showing limit-cycle solution single frequency, o~, which intersects the locus for Gl GzG~(jo2) at G1GzG3(jwl). This point represents the solution of the characteristic equation, and therefore predicts the frequency and amplitude of the resulting limit cycle. From Figure 7.18, the value of the frequency at which the two loci intersect is 9.6 Hz, and the corresponding limit-cycle amplitude, E, is 0.04. Figure 7.19 shows the intersection of the two loci in more detail. A simulation of the system results in the limit cycle shown in Figure 7.20. From the figure, the limit-cycle frequency is 9.64 Hz with an amplitude of E=0.038. These results match well those predicted by the describing-function technique. From this simple example at least, the prediction of limit cycles within a system involving a rate limiter seems feasible. The following section extends this analysis to consider a system based on a typical aircraft-system model.

Limit-cycle prediction in an aircraft system T h e previous section demonstrated an application of describing-function theory to the prediction of limit cycles. However, the example system used was relatively simple compared with an aircraft-system model. Assuming the aircraft flight control system to be analogue, and that the sensor dynamics can be neglected at present, the block diagram for the aircraft system can be considered as shown in Figure 7.21. The three control-surface actuators are assumed to be identical, and have been linearised in order to make use of the earlier describing-function analysis. T h e derivation of the characteristic equation for the system is straight

Flight control systems

266

0.04

1

0.03

r

. . . . . . .

i

. . . . . . .

.

.

.

.

.

.

.

.

.

........ !....... "!""w -0 04 ~

0

0.5

1

.

.

.

~

.

.

.

.

.

.

i

.

i

. . . . .

i

t

I

. . . . . . . .

illvviltlillllHlllllIllllllllllll 1.5

2

2.5

3

3.5

4

4.5

5

T i m e (S)

Figure 7.20

Time-domain simulation results of example system

forward, and results in the equation:

1 - H(jw) GACT(JW)GT(jto, A l, A 2, A3) = 0

(7.17)

where

Gr(jto, A l, A 2, A3) = GAca(jtO)Gl(jto)Gu(jto, A 1) + Gacz(jto)G2(flO)GN(jto, A2") + Gac3(jto) G3(jw) GN(jto, As)

(7.18)

Now, the amplitude of the input signals to the rate limiters (A1,Az,A3) can be derived from the error signal and the particular FCS path-transfer function, such that for example: A

1 =

iG](jw)IE

(7.19)

This enables the characteristic equation for the system to be expressed as a function of 0J and Eonly, as was the case for the earlier example. Although the resulting equation is more complex than for the earlier example, the principle is exactly the same in that a solution of the characteristic equation will predict the existence of limit cycles within the system. The characteristic equation is therefore:

H( jto) GACT(jto ) = where

1

GT(jW, E)

(7.20)

~ / = 1

I

~

w

~f w

+

~F

~t

m

. . . . .

!, i

Aeroservoelasticity

-q

267

268

Flightcontrolsystems

Table 7.3 Predictedaircraftsystem limit cycles w(Hz)

E(V)

16.0 16.4 24.0 66.0 73.6

0,0142 0.0332 0.0371 0.0040 0.0106

or(j,,,, E) = CAc~( jo~) 61( jo,) CM ( jo~, E) + C~c2( jo~) G2(jo~) CN2(jo,, ~ ) + Gac~(jw)G~(jw)G~(jw, E) (7.21) and

[GNx(JO,), E)

I=

Z-GNx(jw, E ) = -

4[3

(7.22)

)

-asin21Gx(jw)lE w

(7.23)

T h e solutions o f this characteristic equation for a reduced-order model of the flexible aircraft with ten modes are as shown in Table 7.3. These solutions were obtained using the same principle as shown in Figure 7.18. The results therefore predict that there exist five possible operating points for the system, each point representing a limit cycle of differing amplitude and frequency. A time-domain simulation of the system for an arbitrary initial disturbance, results in a limit cycle as shown in Figure 7.22. The amplitude and frequency of the actual limit cycle is 0.035 and 16.4 Hz, respectively. This compares well with the second of the predicted limit cycles in Table 7.3. The above results demonstrate that it is possible to predict the existence of limit cycles even in a complex system such as the aircraft model shown in Figure 7.21. In this case, the theoretical analysis predicted the existence of five possible limit-cycle conditions. In reality, the system will operate at only a single limit-cycle condition. Table 7.3 gives the values for the five solutions o f the limit-cycle analysis. The second pair of values, 16.4 Hz and 0.0332 V, correspond to the limit cycle which actually occurs. The practical significance of the other values was not investigated, but it is possible that they correspond to unstable limit cycles which could not, of course, be realised in practice.

7. 4.1.2 Prediction of limit cycles in the presence of phase uncertainty T h e above section has described a m e t h o d for predicting the existence of limit cycles in a nonlinear system. In this case the only nonlinear element that

Aeroservoelasticity 269 0.04

0.03

0.02

0.01

o

uJ

-0.01

-0.02

-0.0~

-0.04

0

0.5

1

1.5

2

2.5 Time (s)

3

3.5

4

4.5

5

Figure 7.22 Limit-cycle condition for reduced-order aircraft model has been considered is the software rate limiter. Comparison of the predicted limit cycles with those obtained from time-domain simulation has shown that a simplification of the nonlinearities still produces a good estimate of the limit-cycle frequency and amplitude. Unfortunately, this procedure relies on the existence of reliable frequencyresponse data for all the linear elements of the system. In the case of the real aircraft system, this is not the case as has been discussed earlier. Although ground vibration tests provide reliable measurements of the open-loop gain of the aircraft system, there exists a large degree of uncertainty in the phase response of the system. This is due in part to uncertainties in the modelling of the unsteady aerodynamics and also in the phase relationships between the many possible signal paths which exist within a typical flight control system. As has been discussed earlier, clearance procedures allow for this uncertainty in the phase by neglecting its influence on the stability of the system and by assuming in-phase addition of all the signal paths. If the phase response of the system cannot be relied upon, then the use of these limit-cycle prediction techniques is restricted. The following section discusses to what extent the limit-cycle condition can be analysed in the presence of such uncertainties.

Limit-cycle prediction in the presence of phase uncertainty Consider the characteristic equation of the aircraft system as given in eqn 7.20. If no phase information is available, then the solution of the characteristic equation yields only a value for the gain, such that:

Flight control systems

270

]H(jw) it GACT(j0)) I -

I G T (j0), E)

(7.24)

where

IGT(j0), E) i = IGAcl(j0))IIGI(j0))IIGM(j0), E) + IGAc2(j0) ) IIG2(j0) ) IIG~(j0), E) I + ] Gac3(j0)) IIG~(j0))If Gin(j0), E) I

(7.25)

4[3 0)J Gx( j0) ) IETr

(7.26)

and

GNx( j0), E) -

Whereas in the earlier case there was a single solution, there now becomes an infinite n u m b e r o f possible solutions. In reality, the actual solution that exists is d e p e n d e n t on the phase response. Since this phase response is not reliably known, then it has to be assumed that a limit cycle could occur at all frequencies. Substituting for eqn 7.26 into eqn 7.25 where appropriate, the characteristic equation can be expressed as:

]H( j0)) [I GAcr( j0)) I = 4[3 -( I GAcl( j0)) I + I GAc2(j0)) I + I GAc3(j0)) I) 0)E~r

(7.27)

which can be rearranged to result in an equation for the amplitude of the limit cycle in terms of the error signal, such that:

E= 4fl IGAcT(J0))I(IGaca(Jw)l + IGAc2(joI + IGAca(J0))I)IH(j0)I

(7.28)

0)71"

Consideration of eqn 7.28 reveals that the limit-cycle amplitude at any given frequency is simply the maximum output of the rate limiter multiplied by the loop gain between this point and the point at which the limit-cycle amplitude is desired. In this case, where the limit-cycle amplitude is given in terms of the e r r o r signal, the amplitude is as given by eqn 7.28. In addition, the worst case is assumed where the three signal paths are considered to act in unison as in the current design methodology. It would also be possible to account for changes in flight condition within the form of eqn 7.28 by augmenting the aircraft gain terms accordingly. Now, consider that:

4[3

--

0,)71"

I GAcr(j0))l = X( j0))

(7.29)

Aeroservoelasticity 271 1 0 -1

10'

~ :~

: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

. . . . . .

i. . . . . . . . .

~ . . . . . . . . . .

,

. . . . . . .

~ . . . . . . .

2

1 0 -3

EIO

-4

1 0 -s

. . . . . . . . . . .

1 0 -e

0

~. . . . . . . . . . . .

~ . . . . . . . . . . .

i . . . . . . . . . . . .

:. . . . . . . . . . . .

i

t

L

. . . . . . . . . . . .

I

. . . . . . . . . . . .

i

i

i

10

20

30

40

50

60

70

Frequency

:. . . . . . . . . . . . .

80

( H z )

Figure 7.23 Actuator performance limit, X(l'oJ) where X(jo) is the maximum output of the combination of the linear actuator and rate limiter at any given frequency. This enables the amplitudes o f the limit cycles to be predicted from the performance limit of the actuator and the gain response of the remaining linear elements of the system. In addition, the linearisation of the actuator is no longer necessary in order to predict such limit-cycle amplitudes. Instead, experimental measurement of the maximum output amplitude of the actuator as a function of frequency will suffice. The presence of uncertainty in the phase response has therefore restricted the prediction of the limit cycles within a system to the estimation of only amplitudes of the limit cycle.

Application of the prediction of limit-cycle amplitude to an aircraft system In order to demonstrate the prediction of the maximum limit-cycle amplitudes in a typical system, consider the aircraft-system model as shown in Figure 7.21. In this case, however, the model will contain a nonlinear actuation system model as opposed to the linear version used earlier. In addition, all of the structural modes will be included in the analysis. From eqns 7.28 and 7.29, the elements required to calculate the limit-cycle amplitudes at the error-signal position are as shown in Figures 7.23 and 7.24. Combining these two figures according to eqn 7.28, along with the necessary scaling between ram extension and control-surface motion, results in a maximum boundary for the limit-cycle amplitude at the error-signal location [23,24]. This boundary is as shown in Figure 7.25.

Flight control systems

272

80] =

i

60

.....

.

4o

.........

i ........

.

.

i

.

.

.

.

.

.

.

.

:

.

.

.

i

.

.

.

.

.

i

.

.

i

0 F r e q u e n c y

Figure 7.24

100

$

(Hz)

Loop gain, (I Gacl~jOJ) l + I GAc2(l'oJ) l + I Cac3(joJ) I)IH(joJ)l

............

w. . . . . . . .

[

. . . . . . .

J ........

!. . . . .

!

. . . . .

~ . . . . . . . . .

L

.........

1 0 -1

1 0 -3 0

i 10

20

i 30

= 40 F r e q u e n c y

Figure 7. 25

50

60

(Hz)

Maximum limit-cycle amplitude at error signal, E

70

80

Aeroservoelasticity

273

The above theory has demonstrated that the maximum amplitude of the limit cycles within the system can be defined quickly using the p e r f o r m a n c e b o u n d a r y of the actuation systems and the gain response of the aircraft structure and flight control system. The ability to predict such limit-cycle amplitudes enables their effect on, and interaction with, other system elements to be assessed. In reality, the existence of limit cycles within the system would not be tolerated for long periods of time. Such conditions would have serious consequences both in terms o f the fatigue life o f the aircraft structure and in terms of the wear of actuator components. In addition, were a limit-cycling condition to arise, a large a m o u n t o f power would be dissipated within the flight control system in responding to it. As a result, it is vital to ensure that such limit-cycling conditions do not arise u n d e r normal flight operations.

7.4.1.3 Prevention of limit cycles Returning to the system of Section 7.2.4, the system as shown in Figure 7.16 has the characteristic equation: -1 G1(jw) G2(jo0 GF(jOJ) - Gn(Jw, E)

(7.30)

Consider now that the gain of the rate limiter, Gn(joo, E), which can never be greater than unity by definition. As a result, the magnitude of the right-hand side o f e q n 7.30 can never be less than unity. The result of this in terms of the Nyquist diagram is that the locus of the right-hand side of eqn 7.30 originates from the ( - 1,0) point and never enters the unit circle. In order to prevent a possible limit-cycle condition, it is therefore adequate to ensure that the locus of the lefthand side of eqn 7.30 remains within the unit circle. If this is achieved, then the two loci cannot intersect and no limit cycle can occur. This can be demonstrated graphically as shown on the Nyquist diagram of Figure 7.26. In this contrived example, the linear elements of the example system considered earlier have been attenuated by a gain sufficient to bring the response within the unit circle. Although the inclusion of such a gain in the system may not result in the required closed-loop response, it will ensure that a limit-cycling condition may not occur. Such a criterion may be satisfied in the case of the aircraft system even in the presence of phase uncertainty. Since the criterion only depends on the open-loop gain of the system, phase effects are unimportant. If phase information were available at certain structural frequencies, it may be possible to relax this requirement. For example, if reliable phase information was available for the 7 Hz structural mode, and it was found that it did not cross the locus of the rate-limiter describing function, then a limit cycle could not result.

274

Flight control systems 2

,

1.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1

..... 1

!

........

Unit Circle

. . . .

! n c r e g s m g (ii ........... :::.. i:..

0.5

.

.

.

.

.

:i"

i -1.5

,

. . . .

]

,

i

,. I . . . . . . . . . . . . . . . . . . .

. :_G_I G_2 G F (~,i 0 ) )

i . . . . . . . . . . . . . . .

: .......

: ....

I

i

-2 -

i -1.5

I i

-1

-0.5

0 Real

i

,

=

0.5

1

1.5

2

Figure 7.26 Nyquist diagram for arbitrary system In summary, provided that the open-loop gain of the system is less than unity, the Nyquist plot for the linear system cannot intersect the rate-limit describing function at any point. As a result, the existence of a limit cycle is not possible given the nature of this particular nonlinearity. As with the current clearance procedure, suitable filters introduced into the feedback path may be used to reduce the open-loop gain to the required level. It is i m p o r t a n t to note that, should the model of the aircraft be in error, then the nature of any potential limit cycle is predictable. In addition, if a limit cycle does occur, its effect in terms of actuator p e r f o m a n c e and h e n c e rigid-aircraft response can be quantified.

7. 4.1.4 Specification of an alternative clearance procedure T h e current clearance procedure as discussed earlier assumes that the aircraft system can be considered to be linear in the main. T h e result of this is that feedback filters are designed so as to ensure closed-loop stability by ensuring a m a x i m u m open-loop gain of - 9 dB for the majority of structural frequencies. This safety margin of 9 dB ensures, that even in the presence of significant modelling errors, closed-loop stability will be assured. This large safety margin was applied owing to uncertainty in the effect of an unstable structural m o d e on the aircraft as a whole. T h e previous sections have discussed in some detail the effect of the nonlinear nature of the actuation system on the structural-coupling problem. In particular, it has been d e m o n s t r a t e d that, owing to the existence of the rate-limiting function within the FCS, an unstable structural response may only result in a limit cycling condition. T h e criteria for the existence of such

Aeroservoelasticity

275

a limit cycle have been introduced earlier. In the presence of uncertainty of the phase response, however, it has been shown that limit-cycling conditions may arise wherever the open-loop gain of the system exceeds 0 dB. The effect of allowing limit cycles to exist in the nominal case has been discussed earlier, and as a result suitable filters should be incorporated into the system to give a maximum open-loop gain of less than 0 dB. The question that remains, however, is to what extent should the open-loop gain be attenuated below this level in order take account of possible modelling errors? Fortunately, in the event of modelling errors causing the open-loop gain to b e c o m e greater than unity, any resulting limit cycle can be predicted. For example, for the case of the system model being in error, any frequency at which the open-loop gain exceeds 0 dB may result in a limit cycle. Importantly however, the amplitude of such a limit cycle can be predicted and its effect on the satisfactory control of the rigid-body aircraft assessed. Suppose that the structural filters were designed so as to give a maximum open-loop gain of - 1 dB. As a result, the phase lag introduced by these filters will be significantly less than that introduced by the current - 9 dB filters. In the nominal case, these filters will ensure that a limit-cycling condition could not arise. One consequence of this action, however, would be that any error in the modelling of the system could result in a limit-cycling condition occurring. Consider a situation where an error in the modelling has indeed resulted in an in-flight limit-cycle condition. Such a condition would be more likely at high aircraft incidence where the FCS gains are highest. Provided that such a possibility has been investigated in terms of the limit-cycle amplitude and its effect on the actuator performance, rigid-body stability will be maintained. The aircraft incidence could then be safely reduced, whereupon the limitcycle would dissipate as a result of the reduction in FCS gain. If such an in-flight interaction were encountered, then it would be possible to correct the flexible aircraft model accordingly, redesigning the structural-mode filters so as to maintain the - 1 dB maximum open-loop gain for the nominal case. Provided that a suitable safety margin has been explored in terms of limitcycle amplitude and its effects, the implementation o f structural filters giving a - 1 dB open-loop gain should be free of risk to the aircraft. An alternative design procedure can be represented by the flow diagram given in Figure 7.27. The initial stages of the design process are identical to that currently employed. First, a flexible-aircraft model is developed, which when combined with a model of the flight control system allows the production of an envelope showing maximum open-loop gain against frequency. These results can be modified by actual ground-test data when available. As for the current design method, it is assumed that all the signal paths act in phase. The next stage in the design process is to design suitable structural-mode filters to meet the - 1 dB maximum open-loop gain requirement.

276

Flight control systems LinearModellingof FlexibleAircraftand FCS

"Nonl~ne~-M~odeHingof FCS

sumptions ~N~ Aliasing l In-Phaseadditionof I ignat paths 1 SU averaging] ZoH attenuation J

oxib,0Airora' o,FCS II O.ou.Stoao

1

~ ~ oUmVtions ~X ingleinput(worst[ ase) [ h signalwaveform[ o load /

Actuator/Rate/ [ActuatorBench LimitModellins~[ Test

Performancelimitsof [ ActuatorandRate Limit['--~ Combination 1

Envelopeof Maximun~ Open-LoopGain 1 versusFrequency[ Designfiltersto I InitiallyMeet-1 dB [ MaximumOpen-Loop Gain

MaximumPossible [ FilteredResponse(nominal) at Actuator/RateLimit

~[

NotchFilterDefinition I CheckBelowRate ] LimitThreshold

MaximumPossible [ FilteredResponse at Actuator/RateL mit Check Rigid-Body Stability-Margins

I

Figure 7.27 Proposed aeroservoelastic design and clearanceprocess In parallel with this work, the performance limit of the actuation systems is derived both from modelling and bench tests of the actual hardware. Once this has been obtained, it can be combined with the model o f the remaining

Aeroservoelasticity 277 elements within the system. This results in a specification of the maximum filtered-system response, assuming the system model to be correct. As a check that all is well at this stage, if the amplitude of the structural feedback signals at the rate limiter are calculated u n d e r these conditions, the rate limit should not be exceeded. The next stage in the design process is to consider the effect of any errors within the modelling of the system. This could be expressed in terms of an overall increase in gain, or a more specific increase in gain for each structural mode. For example, it may be felt that the system model might be in e r r o r by a certain factor. Alternatively, results from ground tests and where possible inflight tests, might lead to a greater confidence in the gain of particular structural modes. Once obtained, such an error model may be used to predict the maximum possible filtered-system response. This envelope will therefore permit the prediction of the amplitude of any limit cycle which may exist within the system. Assuming such a situation to be the case, the effect of these limit cycles on rigid-body performance can be assessed from a consideration of their effects on actuator performance. If it were found that none of the predicted limit cycles caused unsatisfactory rigid-body response, then it would be safe to proceed to flight testing. Alternatively, if it were found that a particular limit cycle had the potential for causing unsatisfactory rigid-body response, then the structural-mode filters should be compensated accordingly. Although in the presence of modelling errors the potential for limit cycles may exist, it is still not certain that they will occur. The discussion of the criterion for limit cycles made earlier in the chapter has highlighted the need for the correct phase response before a limit cycle occurs. Combining this requirement with the fact that the separate control paths will almost certainly not act in phase as is assumed makes the existence of an in-flight limit cycle a remote possibility. Such conditions for the actual occurrence of a limit cycle are highlighted within Figure 7.28. In the following section, the alternative design procedure is demonstrated using a typical aircraft-system model.

7.4.1.5 Demonstration of alternative clearanceprocedure on analogue aircraft system Design of structural-mode filters In order to design suitable structural-mode filters using the alternative design procedure, it is necessary to produce a model of the aircraft system as for the current design procedure. In order to prevent a limit-cycle condition arising, it has been discussed that it is sufficient to ensure that the open-loop gain of the system is less than unity. In order to achieve this, filters can be designed for implementation within the feedback path of the FCS. Although this is identical to the current design procedure, it is important to note, that in this case, filters are designed to give a maximum open-loop gain of - 1 dB. This

278

Flight control systems

Conservative Design Process

Notch Filters Designed to Meet -1 dB Maximum Open-Loop Gain for Nominal Model

_] o dBOp~n-~op Yes

v ] Gain not Exceeded

No No

limit-cycle Possible I

No limit-cycle Possible ]

No Yes No

limit-cycleDoes Not Occur ]

I limit-cycleOccurs I Frequency and Maximum ] Amplitude, Effect on Rigid [ Body Stability Predictable ]

In-Flight In Tests: ] Change I e Flight Condition to I FCj Gain and Dissipate Reduce FCS limit-cycle

Figure 7.28 Conditions for limit-cycle oscillation and implications is in contrast to the c u r r e n t design p r o c e d u r e which results in a m a x i m u m o p e n - l o o p gain o f - 9 dB. P r o d u c i n g the m a x i m u m o p e n - l o o p gain for the earlier aircraft m o d e l for all flight conditions results in a specification o f the structural-mode filter a t t e n u a t i o n as shown in Figure 7.29.

A eroservoelasticity

i: ::::::::i~,:::::

~-,~ ..... t ,~ |

: i

.~.

~

..........

::i:...... : .... .......... :',. ....

'

:

/

~

...........

i

gain requirement

............

............

.......................

I

-%

10

....... ~.... ::::i

.

/

~............

"......

20

30

279

............

I

40 50 Frequency (Hz)

60

70

80

Figure 7.29 Maximum open-loop modal response envelope for full flexible-aircraft system model

If suitable s t r u c t u r a l - m o d e filters are d e s i g n e d so as to m e e t t h e a t t e n u a t i o n r e q u i r e m e n t s d e f i n e d in F i g u r e 7.29, t h e r e s u l t a n t filters are: s2 + 0.90s + 2018 Gqa (s) = s2 + 2.7s + 1968

(7.31)

Gsf2 (s) =

s2 + 1.62s+ 10250 s2 + 2s+ 9990

(7.32)

G~f3(s) =

s2 + 1 . 4 9 s + 8636 s~ + 7s+ 8420

(7.33)

0.1648 (s2 + 5.3854s + 113290) (s 2 + 2.2307s + 19437)

Gsf4(s) =

(s2 + 274s+ 29821)(s2 + 50s+13131e4)

(7.31)

where

Gsjq(s)

is a n o t c h filter c e n t r e d o n 7.15 Hz;

Gsf2(s)

is a n o t c h filter c e n t r e d o n 16.1 Hz;

Gsf3(s)

is a n o t c h filter c e n t r e d o n 14.8 Hz;

G~f4(s)

is a low-pass filter d e s i g n e d to a t t e n u a t e t h e h i g h f r e q u e n c y

Flight control systems

280

.....

t ...... 1o-

~o

[ /

!

:

i

i

•

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i. . . . . .

i ........

:

:

'

i

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.

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................

a ~

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'

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..........

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"0

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Before filtering

I ~ - .

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..........

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: .........

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:

10

20

30 Frequency 40 (Hz)50

~

--

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7"

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. . . .

-4° [ .......... ................ ............ :............. : ............ i............ :........

0

--

:. . . . .

:

60

70

80

Figure 7.30 Maximum open-loopgain for aircraft system aflerfiltering modes. Applying these filters to the m a x i m u m open-loop gain as shown in Figure 7.29 results in the m a x i m u m open-loop gain for the filtered system as shown in Figure 7.30. Figure 7.30 demonstrates that the required level of attenuation has been achieved resulting in the m a x i m u m open-loop gain of the system being less than - 1 dB. As a result, inclusion of such filters into the aircraft system will ensure that a limitcycling condition cannot arise. As a demonstration of the significant reduction in phase lag obtained by applying such filters, the phase lag of the - 1 dB filters at a frequency of 3 Hz is - 18.0 degrees. This compares very favourably with a phase lag of - 32.4 degrees for - 9 dB filters at the same frequency. It can be seen that there is a significant advantage to be gained in applying a clearance r e q u i r e m e n t of - 1 dB for the structural modes. Such an advantage has however been achieved at the expense of system robustness to modelling errors. T h e ability of the - 1 dB filters to prevent a limit-cycle condition relies on the actual aircraft response being accurately modelled. Any increase in the system gain above that represented in Figure 7.29 may result in the open-loop gain o f the filtered system exceeding 0 dB. This could in turn result in a limitcycling condition. It is important therefore to assess what impact such a situation would have on rigid-body control. T h e ability to predict the possible outcome of an error in the modelling of the system is crucial to this alternative clearance procedure. For the linear system, it must be assumed that a structural m o d e for which the open-loop gain is greater than 0 dB, would result in an u n b o u n d e d structural oscillation in the closed loop. T h e nonlinear nature of the system allows the prediction

Aeroservoelasticity

281

100

~:::~::~:~:~:~:~::::::~:~::::~:!::::~i~:::i~ ~::: ~: ~:~:~:~ ...........

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::::::::::::::::::::::::::::::::::::::::::::::::::::::::

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10"

0

Figure 7.31

!!i!

~

I

I

i

10

20

30

:::::::

===================== ..........

!.

i

I

I

I

40

50

60

70

Frequency (Hz)

.!'!~/

80

Maximum limit-cycle amplitude at error signal for nominal model (broken line) and with - 1 dB filter (solid line)

o f any resulting limit cycle and its effects, allowing a confident reduction in the structural-mode clearance requirements. It should be noted that even if the gain of the open-loop system were to exceed 0 dB, the existence of a limit cycle is by no means certain. As has been discussed earlier, the existence of a limit cycle is governed by consideration o f both gain and phase. The consequence of this is that, if the gain is greater than 0 dB, a limit cycle will only occur if the phase response of the system is appropriate. In terms of a Nyquist diagram, even though the response of the linear elements may exceed the unit circle, it may still not cross the locus o f the describing function of the rate limiter at a compatible frequency.

Limit-cycle prediction in the presence of system modelling errors T h e results of earlier sections have shown how it is possible to predict the maximum amplitude of any possible limit cycles within a system. In this case, provided that the system gain is as modelled, then no limit cycles will occur owing to the presence of correctly designed structural-mode filters. In the presence of modelling errors, however, the amplitude of any limit cycle can be obtained and its effect on the rigid-body control assessed. Consider the nominal system model, with no structural-mode filters in the feedback path. The resulting maximum amplitude of any limit-cycle oscillation can be predicted as in Section 7.3. This results in the maximum amplitude envelope as shown in Figure 7.25. If the - 1 dB structural filters were now incorporated into the system, then the maximum amplitude of any resultant limit cycle could be predicted as shown in Figure 7.31.

282

Flight control systems 10°

:![[i!!!iii~'!i!i!i!!!!!!}!!!!!![!i!{!!!!!!!!!!'?i!i

!i!!! ':!!!! !!!!!!!'.!?!!!!ii!!i)!??!??!!??!

21112112111211112112552i2111121211227111111211112i121212122212;211211 ..........

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2111221:

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g lO-1 ~ 1 0 -=

~ 1 0 -~

10"

0

Figure 7.32

10

20

30

40

Frequency (Hz)

50

60

70

80

Maximum limit-cycle amplitude at error signal - 2* nominal model, - I dBfilters

Production of such an envelope in the case of the nominal model is purely an academic exercise. In reality, provided that the system gain is as modelled, then the - 1 dB filters will prevent limit cycling. Production of the maximumamplitude envelope for the nominal model does allow the effect of modelling errors to be quickly assessed, however. Suppose for example that the open-loop gain of the system was in e r r o r by a factor of two. From Figure 7.31, the amplitude of any possible limit cycle can easily be obtained. The resulting amplitude envelope is as shown in Figure 7.32. Although the system model is in error to such a degree, it is still only possible for limit cycles to occur where the open-loop gain of the system exceeds 0 dB. The open-loop gain response of such a system is as shown in Figure 7.33 where it is possible to identify those frequencies at which a limit cycle may occur as those at which the open-loop gain is greater than 0 dB. Incorporating these results on to the specification of the maximum limit-cycle amplitude results in a prediction of the possible limit-cycle frequencies and amplitudes when the system gain is twice that of the nominal model. Such a prediction is shown in Figure 7.34. It can be seen, therefore, that it is possible to predict both the frequency and amplitude of limit cycles which may exist within the system given a particular level of error in the modelling of the system. In this case, this e r r o r was chosen as being a twofold increase in the open-loop gain o f the structural modes. It is important to be able to assess the effect, if any, of such limit-cycling

Aeroservoelasticity lO

,

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Maximum open-loop gain for system with 2* nominal gain and - 1 dB filters in place

10 °

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i 20

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i 30

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; ............

i i 40 50 Frequency (Hz)

i ............

i 60

i. . . . . . . . . . . .

i 70

80

Predicted limit-cycle frequencies and amplitudes for system with 2* nominal gain and - 1 dB filters

284

Flightcontrol systems

conditions on the satisfactory rigid-body control of the aircraft. If it can be shown that satisfactory rigid-body control is maintained, then the - 1 dB filters can be applied as designed. In this way, the condition where the system model is significantly in error can be explored and the safety of the system ensured.

7. 4.2 Active control for rigid body and structural-mode stabilisation As was explained earlier in this chapter, fundamental interaction exists between the rigid-body FCS, unsteady aerodynamics and the airframe structural dynamics through the FCS motion sensors, control laws and aerodynamic control surfaces. This aeroservoelastic phenomenon presents the possibility for closed-loop instability, which is traditionally prevented by incorporating notch filters into the FCS; forming a passive structural-mode control system. This passive approach attenuates the modal feedback contribution of the control-surface actuation demands, but of course the additional FCS filters can be expected to degrade rigid-body stability through the phase lag introduced. Although this approach continues to be applied successfully, increasing difficulty and cost is now encountered with the trend in modern aircraft designs towards higher instability, higher FCS gains and more complex weapon systems. One alternative solution is to extend the use of the existing aerodynamic control surfaces to suppress the structural vibration, forming an active structural mode control. A recent study [17] has investigated the use of an asymptotic pseudoderivative feedback (PDF) structure for simultaneous control of the rigid-body dynamics and the structural vibration. In single-input single-output (SISO) PDF control [Phelan 26], a pseudoderivative term replaces the erroractuated proportional action of the well-known proportional-plus-integral (P+I) structure, leaving only integral action in the forward path. Through analysis and comparative studies with P+I control, Phelan demonstrated that PDF control reduces the peak demands to the actuating elements driving the plant, and is more readily conditioned in the event of nonlinear saturations. Multi-input, multi-output (MIMO) generalisations of the SISO PDF philosophy have been developed based on robust inverse dynamics estimate (RIDE) inner-loop compensation [26]. However, RIDE control has been shown to be incompatible with the active structural-vibration control system, leading to the development of asymptotic PDF [17] to provide an intuitive and multivariable design procedure which satisfies a demanding set of criteria for both the rigid-body and the structural modes.

7. 4.2.1 The agile combat aircraft (A CA)--case study design criteria The case study presented to illustrate the effectiveness of the controller design procedure is an open-loop unstable, generic agile combat aircraft (ACA), typical of the developing structural-control problem. The ACA is a canard--delta configuration with trailing-edge inboard and outboard elevons

Aeroservoelasticity 285 and with fuselage-mounted foreplanes for symmetric axis control. A set of design criteria in the time and frequency domains for simultaneous rigid-body and active structural-vibration control was proposed together with established requirements for rigid-body stability and handling qualities [27] and conservative aeroelastic stability margins [10]. These are: (i)

Rigid-body stability is assessed against a 6 dB/35 ° exclusion boundary on a Nichols plot. (ii) A pitch-rate command be tracked to produce an integrating pitchattitude response [27] in the time domain. (iii) Manoeuvre trimming must be achieved through the inboard and outboard flaps only. In order to reduce trim drag at the chosen flight condition, the steady-state foreplane deflection should be zero. The performance of the active-control strategy is to be measured by the increase in structural damping to reduce airframe fatigue [28,29]. The Nichols stability criterion is extended to the controlled structural modes, and the conventional aeroelastic gain margin applies for frequencies beyond these modes.

7. 4.2. 2 Plant and control law description Without loss of generality, if the open-loop plant dynamics and input, output and extra measurement vectors can always be decomposed into the set of firstorder modes [30] respectively:

Jc2(t) x3(t)

=

A21 A2z A23 LA31 A32 A33

y(t)=[C 1 0

C3][xl(t )

/x2(t)/ + Lx3(t)J

x2(t )

m(t) = [M 1 M 2 M3] [il (t)

u(t) B3

x3(t)] T

i2(/)

(7.36)

x3(/) ] T

(7.37)

(7.38)

and w(t)=[F l

F 2 F3][x](t)

x2(t)

x3(t)] T

(7.39)

where xa(t ) E~m, x2(t ) E~n-2m, X3(/) E~m, A22E~f~(n-2m)×(n-Zm), A23E~)](n-2m)×m' A31Eg] raxm,

A21E£(~(n-2m) xm, A 32 ~)~m×(n-2m), A33~f~m×m, B3E~ m×m, rank B~=m (i.e. invertible), C l e ~ m×'~, C 3 E ~ mXm M 1 E ~ mxm, Mz~)~mx(n-2m), M 3 ~ mxm, F1E~f~mxm, F2~)~mx(n-2m), F3E,~f~mXm, u ( t ) E~'~ m is the input vector, y(t) e,~ m is the output vector, m(t) E~f~m is the extra-measurement vector, w(t)E~)~ m is the feedback vector and rank F~B~= m. Defining the asymptotic PDF control law as: u(t) = g(Ki.ze(t ) -Kpw(t)) +K~(t)

(7.40)

where ge ~ +, K i e ~m× m, Kp E ~m× m, and with the feed-forward term defined

286

Flight control systems

by,

[.f1(t)l = [ O I m ][f,(t)]+[O ] v(t) [f2(t)_ ] &2 -2(I)l-I [_f2(t)J ~-~2

(7.41)

f(t) = [Im 0m][fl(t )

(7.42)

fz(t)] T

and introducing the extra integral-of-error action state relationship: Ze(t) =v(t) -w(t)

(7.43)

Furthermore, if the vector of extra plant measurements, re(t), is arranged such that:

[M1 M2 M3] =

R[ 0 0 Im] A21 A22 A2~

(7.44)

where R+ [diag~rl, r2. . . . . rm} Om×(n_2m)

(7.45)

then it follows from eqns 7.37 to 7.38 and eqn 7.44 that: [F l F 2 F3]=[C 1 0

(C~+diag~rlr2. . . . .

rm})]

(7.46)

Moreover, using eqn 7.36 under the necessary and sufficient condition that the closed-loop system is stable such that the steady-state relationship:

lirn

0 0 Im / x2(t) A21 A22 A2~ mxs(t)

=

(7.47)

is approached asymptotically, then from eqns 7.38, 7.44 and 7.47 it is clear that the extra measurements satisfy the necessary condition: lim (w(t)) = lim (y(t) +re(t)) =y(t)

(7.48)

and combining eqns 7.43 and 7.48, steady-state tracking in the sense of: lim (v(t) -y(t)) = 0

t~

(7.49)

will be satisfied using the control law governed by eqn 7.40. 7. 4.2.3 Asymptotic analysis of the closed-loop system

The set of closed-loop equations obtained by combining eqns 7.36 to 7.43 is not in a block-diagonal form. Thus decoupling of the multivariable system,

Aeroservoelasticity 287 required for the general control problem, would not be achieved and it would be difficult to generalise the characteristics of the system. Neglecting the feedforward term's contribution in eqn 7.40 to the closed-loop eigenvalues, the closed-loop system can be partitioned into distinct infinite and finite eigenvalue sets being amenable to fast and slow-mode block diagonalisation [31]. Thus, as the scalar gain parameter, g, tends to infinity and neglecting higher-order terms, the asymptotic closed-loop structure assumes the blockdiagonal form: I

[7"n~(/) ] Lz.i(t )

=

- Kp 1Ki F 3 1 g ; 1gi A23F~-.1K-1Ki 0

0

0

~

0

- F~-IF1 0 I 0 A21-A23F~_lF1 A22- _.l _ _ 0_ _ 0

0

O0

_

* - gB 3KpF~

(7.50)

v(t)

[Z,f(t)

- F~- 1Kp 1Ki

and,

y(t) = [CaF~-~Kp1Ki

C I-CaF~-IF,

0 C a]

Z,,] kzvJ

(7.51)

where the closed-loop states, Zn, and Z n . are associated with the asymptotic slow and fast modes respectively [17,31]~ It is immediately obvious from eqn 7.50 that the set of slow modes, Pl, is given by Pl = Zl U z2 U z3 , where:

Z1 = {Se C: SIm+Ki~ 1Ki=0 }

(7.52)

7.2 = {SE C: sI m+ F 31F 1=0}

(7.53)

z3 ={sE C: sI,_2m-A22 = 0}

(7.54)

and,

together with the set of 'fast' modes, P2, given by P2 = z4, where:

Z4 = {$E C: slm+ gB3KpF s = 0}

(7.55)

It should be apparent from the above system definitions that the closed-loop poles, z2, will always be stable and decoupled and the poles z~ will approach the set of transmission zeros relating the control input vector, u(t), to plant output, y(t). Thus, stability of the asymptotic closed-loop system is guaranteed if Pl U P2 C C-, where C- represents the open left-half complex plane, and provided that the open-loop plant is minimum phase. Therefore, using eqns 7.52 and 7.55, closed-loop stability and non-interacting multivariable control

288

Flight control systems

can be arranged by defining: Kp = (F~B3)- 1 •

(7.56)

Ki=Kp~

(7.57)

where = diag~o-1, O-2. . . . .

O'm}, O - i ~ +

(7.58)

= diagtpl, P2. . . . .

Pm}, Pi ~'~+

(7.59)

The feedback gain definitions given by eqns 7.56 and 7.57 are in agreement with previous decoupling methodologies [33], high-gain control [33-35] and RIDE control [26], each of which established the conditions for excellent command tracking and disturbance rejection. The separation of the fast and slow modes as g--* ~, and the resultant blockdiagonal structure of eqns 7.50 and 7.51, gives rise to the asymptotic transfer function described by: (7.60)

FT(S ) = Fn~(S ) + Fn/(s )

where, Fns(S) = C3F~- 1Kp- 1Ki(sI m+ Kp- lKi) - 1 + (C 1 - C~F3-1F1) (sI," + F~-1Fl) -1F~-lKp- 1Ki-(sI m+ Kp- lKi.) -1 (7.61) and Fnf(S) = _ C3F31 ($I," + gF3m3gp)- 1Kp- 1Ki.

(7.62)

It is of some significance that the slow modes corresponding to z~ become asymptotically unobservable and uncontrollable and consequently do not appear in the tracking modes, eqns 7.61 and 7.62). Moreover, as g--* o0, the fast modes become increasingly negligible and eqns 7.60, will approach the asymptotic form: FT(S) -----F~ (s),

as g---, oo

(7.63)

7. 4.2. 4 Deterministic controller parameter selection

Previous work [36] has highlighted the link between singular perturbation analysis of high-gain control systems and the sliding modes of variable structure control [37] (VSC). A review of this work and other literature [38] has recently been done to emphasise the role of the equivalent control [39] with application to multivariable servomechanisms including integral-of-error action. It can be shown that for a controllable state-space plant governed by eqn 7.35 and defining m regulating switching planes: s(t) = [S 1 S 2 S3] [Xl (t)

x2(t )

x3(t) ] T

(7.64)

where S 1~ fil m× m, $2 ~ film× (n- 2,.) and S~ ~ ,q~,. m, then from the sliding-mode

Aeroservoelasticity

289

condition, s(t).~(t)~