Industrial servo control systems: fundamentals and applications

INDUSTRIAL SERVO CONTROL SYSTEMS Fundamentals and Applications Second Edition, Revised and Expanded GEORGE W. YOUNKIN ...

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INDUSTRIAL SERVO CONTROL SYSTEMS Fundamentals and Applications

Second Edition, Revised and Expanded

GEORGE W. YOUNKIN Industrial Controls Consulting, Inc. Fond du Lac, Wisconsin, U.S.A.

Copyright 2003 by Marcel Dekker, Inc. All Rights Reserved

Marcel Dekker, Inc.

New York • Basel

TM

Copyright © 2002 by Marcel Dekker, Inc. All Rights Reserved.

Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the Library of Congress. ISBN 0-8247-0836-9 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-260-6300; fax: 41-61-260-6333 World Wide Wed http://www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright # 2003 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA


FLUID POWER AND CONTROL A Series of Textbooks and Reference Books FOUNDING EDITOR

Frank Yeaple President TEF Engineering Allendale, New Jersey

1. Hydraulic Pumps and Motors: Selection and Application for Hydraulic Power Control Systems, Raymond P. Lambeck 2. Designing Pneumatic Control Circuits: Efficient Techniques for Practical Application, Bruce E. McCord 3. Fluid Power Troubleshooting, Anton H. Hehn 4. Hydraulic Valves and Controls: Selection and Application, John J. Pippenger 5. Fluid Power Design Handbook, Frank Yeaple 6. Industrial Pneumatic Control, Z. J. Lansky and Lawrence F. Schrader, Jr. 7. Controlling Electrohydraulic Systems, Wayne Anderson 8. Noise Control of Hydraulic Machinery, Stan Skaistis 9. Interfacing Microprocessors in Hydraulic Systems, Alan Kleman 10. Fluid Power Design Handbook: Second Edition, Revised and Expanded, Frank Yeaple 11. Fluid Power Troubleshooting: Second Edition, Revised and Expanded, Anton H. Hehn 12. Fluid Power Design Handbook: Third Edition, Revised and Expanded, Frank Yeaple 13. Industrial Servo Control Systems: Fundamentals and Applications, George W. Younkin 14. Fluid Power Maintenance Basics and Troubleshooting, Richard J. Mitchell and John J. Pippenger ADDITIONAL VOLUMES IN PREPARATION


Preface

In this second edition of Industrial Servo Control Systems, the chapters have been updated and expanded and a new chapter has been added on servo compensating techniques. The book continues to be dedicated to the practicing engineer making the transition from academic theory to the realworld solution of engineering problems related to the application of servo drives to industrial machines. Part I focuses on the evolution and classification of servos, with descriptions of servo drive actuators, amplifiers, feedback transducers, performance, and troubleshooting techniques. Part II discusses system analogs and vectors, with a review of differential equations. The concept of transfer functions for the representation of differential equations is discussed in preparation for block diagram concepts. Discussion of the mathematical equations for electric servo motors has been expanded to include both DC and brushless DC servo motors. The equations for mechanical and electrical time constants are derived with additional analysis on the effects of temperature on these time constants. The representation of servo drive components by their transfer function is followed by the combination of these servo drive building blocks into system block diagrams. Frequency response techniques are introduced because of their usefulness in determining proper servo compensation. Also included are practical formulas for calculating inertia and examples that show how machine components reflect inertia to the


servo drive motor. Torque-to-inertia ratios for electric servomotors are discussed along with calculations of the reflected inertias for various machine configurations. These reflected inertias are critical when sizing the drive and motor and when determining time constants for a stability analysis. Servo drive analysis and servo compensation techniques include the use of lag and lead compensation for analog-type servo drive amplifiers. This discussion is followed by a description of proportional, integral, and differential compensation, which is very popular with digital-type amplifiers. To classify practical servo performance criteria, the use of servo indexes of performance is discussed for both electrical and hydraulic servo drives. The chapter on servo plant compensation techniques addresses the continuing problems of structural dynamics and resonances in industrial machinery. This type of compensation is different from feedback control compensation in that it uses special electrical devices and software algorithms to correct for machine nonlinearities and mechanical resonance problems. Nonlinearities of dead zone and change-in-gain to overcome such machine problems as stiction and cogging of the servo drive at low velocities are covered. The topic of simple and practical notch networks used to compensate for machine mechanical resonances has been expanded to include frequency selective feedback with suggestions for software implementation. This edition also includes a discussion on the use of a control technique known as feedforward control to minimize the position errors of machine axes with widely varying dynamics. Chapters on servo drive stiffness and drive resolution are an integral part of the analysis of industrial servo drives. Coverage of speed and acceleration has been broadened to include the derivation and application of ‘‘S’’ type acceleration. Machine considerations for ball screw resonances have been expanded to include ball screw critical speed, axial, and torsional resonance calculations, and drive ratio considerations have been expanded to include worm/wheel gear boxes. Friction considerations include the three types of friction and their relation to servo drives on industrial machines. One important aspect of selecting a servo for a given application is sizing the drive, because the servo must be large enough to meet the load requirements. Manual drive sizing forms for both electric and hydraulic servo drives are included in this book. The electric drive sizing forms have been expanded to include both DC and brushless DC drives. Chapter 14 is entirely new and reviews the process of compensating an electric servo drive. It is assumed that this industrial servo drive has a brushless DC motor with a current loop. An example is given for the case in which the motor and current loop are closed with a position loop, and also with a velocity and a position loop. The application of proportional plus


integral compensation is used throughout Chapter 14 and detailed in the inclusion of machine structural resonances in the position servo loop. Once a servo drive has been properly sized for a given machine, it is necessary to determine whether the machine and servo drive will be stable. There are many classical engineering methods that can be used, but it is also possible to use high-speed computer iterative techniques to simulate the control–servo drive–machine combination. Transient step responses in input are used in this simulation since it is readily possible to duplicate them on an actual machine and compare the results. Machine simulation is used to predict performance before the machine is built. Machine simulation includes the significant parameters of the servo drive: the nonlinearities of feedback; coulomb, static, and viscous friction; machine structural resonance; and machine mass. A number of examples are presented with case histories for comparing simulated response with actual response. My contemporaries encouraged me to pull together a lifetime of servo drive experience and write the first edition of this book. The second edition updates, expands, and increases the usefulness of this book to the practicing engineer. I am sincerely grateful to Dr. Thomas Higgins for providing me, as a student, with the academic tools needed in the field of feedback control. I am also grateful to Dr. John Bollinger and Dr. Robert Lorenz from the University of Wisconsin, for their help over the last 45 years in researching, teaching, and applying principles that have been critical in improving the performance of servo drives. Tom Rehm, my friend of 40 years and a fellow software ‘‘hacker,’’ has been a great help in software technology. In addition, I would like to thank the Giddings and Lewis Machine Tool Company for providing the atmosphere for study and research in the field of industrial servo drives, and my family for their long years of patience as my career progressed. George W. Younkin


Contents

Preface I

BASICS OF INDUSTRIAL SERVO DRIVES 1 The What and Why of a Machine Servo Just What Are Some of the Benefits of a Servo System? 2 Types of Servos 2.1 Evolution of Servo Drives 2.2 Classification of Drives 3 Components of Servos 3.1 Hydraulic/Electric Circuit Equations 3.2 Actuators—Electric 3.3 Actuators—Hydraulic 3.4 Amplifiers—Electric 3.5 Amplifiers—Hydraulic 3.6 Transducers (Feedback) 4 Machine Servo Drives 4.1 Types of Drives 4.2 Feed Drive Performance


5

Troubleshooting Techniques 5.1 Techniques by Drive 5.2 Problems: Their Causes and Cures

6

Conclusion: Machine Feed Drives—An Integral Part of a Machine Control System 6.1 Advances in Technology 6.2 Parameters for Making Application Choices

II

ADVANCED APPLICATION OF INDUSTRIAL SERVO DRIVES

7

Background 7.1 Introduction 7.2 Physical System Analogs, Quantities, and Vectors 7.3 Differential Equations for Physical Systems 7.4 Electric Servo Motor Transfer Functions and Time Constants 7.5 Transport Lag Transfer Function 7.6 Servo Valve Transfer Function 7.7 Hydraulic Servo Motor Characteristics 7.8 General Transfer Characteristics

8

Generalized Control Theory 8.1 Servo Block Diagrams 8.2 Frequency-Response Characteristics and Construction of Approximate (Bode) Frequency Charts 8.3 Nichols Charts 8.4 Servo Analysis Techniques 8.5 Servo Compensation

9

Indexes of Performance 9.1 Definition of Indexes of Performance for Servo Drives 9.2 Indexes of Performance for Electric and Hydraulic Drives Summary

10

Performance Criteria 10.1 Percent Regulation 10.2 Servo System Responses


Contents

11 Servo 11.1 11.2 11.3 11.4 11.5

Plant Compensation Techniques Dead-Zone Nonlinearity Change-in-Gain Nonlinearity Structural Resonances Frequency Selective Feedback Feedforward Control

12 Machine Considerations 12.1 Machine Feedback Drive Considerations 12.2 Ball Screw Mechanical Resonances and Reflected Inertias for Machine Drives 12.3 Drive Stiffness 12.4 Drive Resolution 12.5 Drive Acceleration 12.6 Drive Speed Considerations 12.7 Drive Ratio Considerations 12.8 Drive Thrust/Torque and Friction Considerations 12.9 Drive Duty Cycles 13 Drive 13.1 13.2 13.3

Sizing Considerations Introduction Hydraulic Drive Sizing Electric Drive Sizing

14 Adjusting Servo Drive Compensation 14.1 Motor and Current Loop 14.2 Motor/Current Loop and Position Loop 14.3 Motor/Current Loop with a Velocity Loop 14.4 PI Compensation 14.5 Position Servo Loop Compensation 15 Machine Simulation 15.1 Introduction 15.2 Simulation Fundamentals 15.3 Machine Simulation Techniques to Predict Performance 15.4 Other Simulation Software 16 Conclusion Glossary Key Constants and Variables


Appendix: Hydraulic Drive and Electric Drive-Sizing Forms Bibliography


I BASICS OF INDUSTRIAL SERVO DRIVES


1 The What and Why of a Machine Servo

The control user should be familiar with servos. The user will understand what a servo is and why it is required in so many applications. This discussion will answer these two basic questions: What is a servo? Why use a servo? Any discussion of servos will have to employ the term ‘‘feedback.’’ Thousands of times every day we require information to be ‘‘fed back’’ to us so that we can perform normal activities. When controlling a car down a highway, feedback is provided to our brain by the gift of sight. How terrifying it would be if we were traveling at 70 mph and we lost the ability to see. Our brain, which is the center of our control system, would have little feedback to help it decide what corrective actions need to be taken to maintain a proper path. The poorer feedback channels still available would be the senses of hearing and touch, which would allow us to ride the shoulder. The result would be a lower speed, poorer control, a very irregular path, and a greater chance for an accident. Inferior feedback on a machine blinds the operator or the control just as it does a driver. When using numerical control and servos, poor feedback can result in inferior parts, poor productivity, and high costs. Essentially, feedback is the retrieval of information about the process being controlled. It verifies that the machine is doing as commanded. There are two types of feedback—negative and


positive. Positive feedback, used for instance in radios, is not discussed here. Negative feedback, required to make a servo work properly, subtracts from commands given to the servo so that a discrepancy or error between output and input can be detected. This discrepancy initiates an action that will cause that discrepancy to approach zero. A perfect example of a negative feedback system is a wall thermostat and furnace, as depicted in Figure 1. If, in a 658F room, we set the thermostat for 728F, then 728F can be considered the command. The 658F of the room feeds back, subtracts from the 728F command, and results in a 78F discrepancy or error that instructs the furnace to supply heat. The furnace supplies heat until the negative feedback is sufficient to cancel the command so that no discrepancy exists and no further heat is required. A servo or servomechanism is a system that works on the negative feedback principle to induce an action to cause the output to be slaved to the input. Our thermostat/furnace example was one of a servo which induced the generation of heat. Any servo has two basic elements. These are a summing network and an amplifier. The summing network, as shown in Figure 2, is simply a device that sums the negative feedback (F) with the command (C) to generate an error discrepancy (E). Our driver’s summing network (Figure 3) was his brain. The command would be to keep the car in the right-hand lane. If he was straddling the center line, the feedback through his eyes to his mind would so indicate. If he subtracts this feedback information from the

Fig. 1 Thermostat example.


Fig. 2 Summing network.

command, he will deduce that an error exists, which can be corrected by moving 2 ft to the right. A machine feed axis drive example (Figure 4) would be to have a command of þ10 in. If, as the machine was executing the command, we took a snapshot of the summing network when the machine reached þ9 in., we would see a command of þ10 in., a feedback of þ9 in., and a resulting error of þ1 in. The error would be the amount of further movement required for the feedback to equal the command. The second main element (see Figure 5) is the amplifier. This is simply a power device that takes a small error (E) and multiplies it by an amplification factor, which is a measure of the muscle or power available to drive the output and thus the feedback device (F). The amplification factor is what is normally referred to as the gain of the system.

Fig. 3

Feedback.


Fig. 4

Summing network for positioning.

Our driver (Figure 6) mentally computed an error (E) requiring that the car be moved 2 ft to the right. This instruction traveled from his brain through nerves to the muscles in his arms and hands, which turned the steering wheel and with the muscle in his power steering caused the car to move into the right-hand lane. In the machine feed axis example (Figure 7) the error of þ1 in would be in the form of a small voltage, which would cause the servo motor to turn, and axis positioning motion would result. If we connect the two elements together, as shown in Figure 8, a basic closedloop servo system results. A new command will generate an error (E), which will activate the muscle until sufficient movement has caused the feedback (F) to be coincident with the command (C), at which point the error (E) is zero and motion is no longer instructed. The term ‘‘closed loop’’ suggests that after entering a command, signals traveled around the loop until equilibrium is attained.

Fig. 5

Amplifier.


Fig. 6

Human muscle.

Our automobile and driver (Figure 9) are now a servo system with a command to stay in the right-hand lane. The servo is shown above and the position of the car to the centerline is shown below. When the car is actually straddling the white line, an error is mentally computed, which instructs the driver’s muscle and the car’s muscle to take a corrective action. When this corrective action is taken, the position of the car corresponds to the command, no further error is detected, and no further action is taken. Our snapshot of the machine axis servo feed (Figure 10) showed a command of þ10 in., from which the þ9-in. feedback was substracted. The þ1-in. error instructed the axis to continue moving. As the axis continues on, the error will get smaller and smaller until the feedback indicates that the axis is in position with no resulting error. The earliest axis feed systems used the operator as the summing network that closed the servo loop. The command was located on a part drawing, and the operator’s mind was the summing network. The operator read the scale on the machine, subtracted it from the desired command, and

Fig. 7

Servomotor.


Fig. 8

Closed-loop servo.

came up with an error. The operator instructed the machine’s muscle by shifting the appropriate levers to engage motion. As the machine neared the commanded point, the error indicated the need to slow down to one or more intermediate geared speeds. Creep speed was used to accurately reach final position. A repeat performance on a second and third axis would complete the operation.

Fig. 9

Car example.


Fig. 10

Closed-loop position servo.

JUST WHAT ARE SOME OF THE BENEFITS OF A SERVO SYSTEM? Here are six benefits of a machine axis feed servo drive. 1. Shorter positioning time: The servo operates at maximum positioning rate until the ideal time to decelerate, at which point it slows down uniformly to the end point with no hesitation at intermediate feeds. Since it dynamically searches for zero error, variations in machine conditions are compensated for. Positioning time is thus minimized. 2. Higher accuracy: A servo continually homes to the final position so that on January mornings it will continually strive to push the axis toward the end point, whereas on the Fourth of July when the machine might have a tendency to overshoot, the servo error will reverse and force the machine back into position. 3. Better reliability: An outstanding feature of servos is the ability to control acceleration and deceleration so that the mechanical hardware will hold its specification tolerance much longer. 4. Improved repeatability: Repetitive moves to a particular commanded point will show much better consistency. The result is more consistency of parts that are intended for interchangeability. 5. Coordinated movements: Since all axes are closed-loop servos, they are continually responding to the command at all feed rates. Coordinated movements thus require the generation of coordinated commands through employing interpolators with the control. 6. Servo clamping: There is no longer a dependency on mechanical clamps for servoed axes because of the continuous position-


holding capability of a servo. The stiffness of the servo must be relied on for any contouring movements requiring that both axes be in motion. Properly designed, the servo can also hold the axis very stiffly at a standstill.


2 Types of Servos

2.1

EVOLUTION OF SERVO DRIVES

The word ‘‘servo’’ is a learned borrowing from Latin where it meant ‘‘slave.’’ Industrial servos had their real beginning during World War II. Some applications were in military gun control and steering control. The evolution of speed and positioning drives since the war is shown in Figure 1. Industrial servos can be classified in four different ways as follows: By use: Cranes and hoists Winders Steering Refrigeration Heating Combustion Machine tool feed and speed Process control Power Guidance By variables controlled: Force


Fig. 1

Evolution of industrial servo drives.

Tension Level Speed Position Mixture Temperature and humidity Voltage and current Volume Density By type: Chemical: gasoline, paint, etc. Electronic: AFC (automatic frequency control), AVC (automatic volume control), color synchronization Electric drives Hydraulic drives By feedback: Regulators (Type 0) Servomechanisms (Type 1) Acceleration (Type 2)

2.2

CLASSIFICATION OF DRIVES

For purposes of this book, industrial machine feed and speed servo drives are addressed. Machine drives can be classified further as shown in Figure 2.


Fig. 2 Classification of machine drives.

Mechanical drives are not considered as servo drives, but they are included here as one of the three types of machine drives. Hydraulic servo valve drives have been used extensively as machine servo drives. With hydraulic servo drives it is very important to minimize the trapped oil volume to maintain a stable servo drive. In general the hydraulic resonance of the trapped oil volume should be greater than 200 radians/sec. Thus the servo valve type of hydraulic drive will be used because the trapped oil volume will be minimized by joining the servo valve and motor close together with a manifold. The result will be an increased hydraulic resonance and a more stable servo drive. Servo pump hydraulic drives, on the other hand, have a large volume of trapped oil between the pump and actuator, thus lowering the hydraulic resonance and creating possible stability problems. Hydraulic stepping motor drives had reliability problems and were not used extensively.


Electric drives are shown in Figure 2 with four of the many types available. The motor starter drives are not servo drives, but they are in the majority since they are used extensively in industrial applications and consumer products such as appliances. Stepping motor drives are used in low-torque, high-speed applications such as tape transports. Direct current (DC) drives have numerous industrial applications. The majority of these drives use a power amplifier and motor. The amplifiers were initially of the Ward–Leonard type using a rotary amplifier. These drives were rugged but had very slow response with frequency responses of a few hertz. The thyratron was a form of an electrical switch that was not reliable and had noticeably large dead times or transport lag. The static amplifier has been used extensively in industrial servo drives. The magnetic amplifier was highly reliable and rugged but was also very slow in response. The silicon controlled rectifier (SCR) is the solid-state version of the thyratron. The SCR is highly reliable and is available in very large current ratings. It has been used extensively in industrial servo drives, both for speed and positioning or feed drives. Like the thyratron, the SCR has a dead time where no current flows. This dead time is described as transport lag causing amplifier phase lag and limiting the DC SCR drive to low servo response. Maximum torque ratings are about 400% of rated, which can be used for forcing (acceleration). For very-high-horsepower industrial servo drives, in the hundreds of horsepower, for example, the DC motor was at one time driven from separately excited generators. These drives have largely been replaced by the SCR drive. Alternating current (AC) industrial servo drives have a number of forms. Those discussed in this chapter are shown in Figure 2. The adjustable-frequency motor drives are used in industrial applications where positioning is not a requirement. An example would be a high-horsepower fan drive. The two-phase AC servo drive has been used in fractionalhorsepower instrument-type servos. For many lower horsepower positioning servo drives the synchronous AC (brushless DC) servo drive is being used extensively. These drives are available in a class of about 30 HP or less. Many of these brushless DC drives are used for positioning or feed drives on industrial machines. These AC drives can be treated as DC drives in the servo application—hence the name ‘‘brushless DC drive.’’ This drive uses transistors in the servo amplifier. The result is a higher performance drive (servo bandwidths of 30– 40 Hz are possible on large machine applications). The disadvantage is that the torque ratings of the drive are limited by the transistor ratings in the amplifier. Characteristically these drives have a 200% maximum torque rating for drive forcing (acceleration). The drive motors have maximum


torque ratings of about 400%, but the amplifier limits the overall torque rating to about 200% because of the current rating of the transistors. These ratings have been increased with the introduction of the insulated-gate bipolar transistor (IGBT). For high-horsepower servo drive applications, the induction motor with vector control is being used in both speed and positioning drives. These drive amplifiers use transistors which have current limitations. By using IGBTs the horsepower ratings are available upward of 500 HP. These drive classifications are those that will be discussed in Parts I and II of this book. There are other types of drives, but these classifications have been selected for their numerous industrial drive applications.


3 Components of Servos

3.1

HYDRAULIC/ELECTRIC CIRCUIT EQUATIONS

From a basic hardware point of view it is important to understand the steady-state equations of a hydraulic and electric actuator. The majority of hydraulic positioning or machine feed drives use a rotary actuator with a servo valve attached to the motor to minimize the amount of trapped oil under compression. By minimizing the volume of oil that is trapped between the servo motor and servo valve, the hydraulic resonance will be increased and the drive made more stable. The hydraulic flow equations for a fixed displacement servo motor are shown in Figure 1. The steady-state direct current (DC) motor equations are also shown in Figure 1. The voltage and torque equations include the motor back emf constant (Ke) and the torque constant (KT). These motor constants are used throughout the basic and advanced portions of this book. Therefore it is important to know where to find them and how they are used in the forthcoming servo calculations.

3.2

ACTUATORS—ELECTRIC

It is important from the hardware point of view to be familiar with manufacturers’ motor specifications to find the design parameters such as


Fig. 1

Hydraulic and electric motor circuits.

the voltage constant and torque constants that are required for servo drive calculations. Sample electric drive manufacturer specifications are included for DC and alternating current (AC) servo drives. DC motor specifications for Gettys motors are shown in Figure 2. AC (brushless DC) Allen-Bradley motor specifications are shown in Figure 3. The motor voltage and torque constants are included in these specifications. For all drive calculations the torque constants for a hot motor (408C) should be used wherever possible.


Fig. 2 Gettys DC motor data. (Courtesy of Gettys Corp.)


Fig. 3

Allen-Bradley AC motor data. (Courtesy of Rockwell Automation/Allen-Bradley.)


In addition to the motor specifications, it is important to be familiar with the speed/torque characteristics of a given drive motor. These characteristics show how much torque can be developed at a given speed to stay within the rating of the drive. It should be noted that the speed torque ratings are for the motor/amplifier combination. The speed torque characteristics for two Gettys DC motors are shown in Figure 4. As the operating point moves to the right (higher torque) the motor will develop increasing sparking at the brushes and thus the drive must be derated. These other operating zones can be used intermittently for drive forcing and acceleration. If the required torque moves further to the right, beyond the operating zones, the motor will be damaged. To prevent this from happening, all commercial servo amplifiers use ‘‘current limit.’’ Speed/torque characteristics for two Allen-Bradley brushless DC motors are shown in Figure 5. These AC motors do not have the commutation limits of the DC motors and therefore can be operated at higher speeds for rated torque conditions. While the DC drive (amplifier and motor) can use 450% rated torque intermittently, for drive forcing, the AC drive package can only operate at about 200% rated torque for drive forcing. As the state of the art in drive amplifiers advances, this 200% limit for the AC (brushless DC) drive should increase.

3.3

ACTUATORS—HYDRAULIC

Most industrial hydraulic servos are of the servo valve classification. Hydraulic servo pump designs usually have a large amount of trapped oil, which results in a low hydraulic resonance and stability problems. Hydraulic servo valve designs using a piston actuator can also have large amounts of trapped oil volume for the longer stroke designs. Therefore most industrial hydraulic positioning or feed drives use rotary actuators. Like electric motors, the hydraulic servo motors have manufacturer specifications. These motors also have a torque constant with units of so many inch-pounds per 100 psi pressure. Hydraulic rotary actuators are generally of the piston type motor or the roll-vane type of motor. A typical specification sheet for a Hartman roll-vane motor is shown in Figure 6. The advantage of the hydraulic servo is the large amount of torque that can be produced. They also have a disadvantage of oil contamination requiring oil filtration of 10 mm. The oil viscosity can change with operating temperature, which can affect the stability of the servo. Oil temperature should be held below 1308F. If the operating temperature exceeds 1408F for


Fig. 4

Gettys DC motor speed/torque data. (Courtesy of Gettys Corp.)


Fig. 5 Allen-Bradley AC motor speed/torque data. (Courtesy of Rockwell Automation/Allen-Bradley.)


Fig. 6

Hartman hydraulic motor data. (Courtesy of Hartmann Controls Inc.)

a long period of time the oil can start to break down, causing the servo valve spool to stick, resulting in a stall or runaway condition. Hydraulic pump noise can also be an annoying condition. From the government Walsh– Healy act, hydraulic pump noise must be limited to 90 dB on the A scale.


3.4

AMPLIFIERS—ELECTRIC

In Figure 2 for the classification of drives, three classes of amplifiers were shown: rotary amplifiers, electronic amplifiers, and static amplifiers. Of these three types of amplifiers the static solid-state amplifier is predominant. The silicon controlled rectifier (SCR) has been used extensively in industrial applications. The SCR is the solid-state version of a thyratron. As an amplifier component the SCR is very rugged and available in very high current ratings, but by itself it is just a switch that conducts for a part of a half cycle of the AC power. Therefore, for part of the conduction half cycle no current flows. The period where no current is flowing is called the off time of the SCR, which is referred to as the transport lag of the amplifier and is discussed further in Part II. SCR amplifiers are designed in various circuit configurations, with the most popular circuit being the three-phase, half-wave amplifier. For reference, this circuit design for a Gettys DC drive is shown in Figure 7. Each circuit design for the SCR has an efficiency rating, represented by the form factor, which is a measure of the amount of ripple current in its output relative to the average DC value of its output. Thus the form factor is equal to Irms/Idc. For DC SCR amplifiers it is necessary to derate the drive rated torque. The rated torque is divided by the form factor. The derating form factor for various SCR amplifier designs are listed as follows: SCR amplifiers Single-phase, full-wave Single-phase, full-wave/inductor Three-phase, half-wave Three-phase, half-wave/ inductor Pulse width modulation or brushless DC amplifiers

Derating form factor 1.66 1.2 1.25 1.05 1.0

Another class of DC static amplifiers uses pulse width modulation (PWM) techniques. These amplifiers use transistors for current control to the motor. While the PWM amplifier has a high switching rate, allowing for much higher servo performance, it has much lower current ratings than DCSCR drives. In general, these drives have a maximum rating of 200% rated current. The form factor of these drives is one, so no derating is required. A typical block diagram of an Allen-Bradley DC pulse width modulation amplifier is shown in Figure 8. While these drives have a servo bandwidth of about 40 Hz, they are limited in velocity because of the mechanical commutator in the DC motor.


Fig. 7

Gettys DC SCR electric drive diagram. (Courtesy of Gettys Corp.)


Fig. 8 Allen-Bradley DC PWM electric drive diagram. (Courtesy of Rockwell Automation/Allen-Bradley.)


Lastly, the brushless DC drives offer higher speeds and higher performance. Most industrial versions of this drive use a synchronous AC motor. A position transducer in the motor measures the armature position and provides a signal to the amplifier to commutate the three-phase armature currents. Thus the motors can rotate at higher velocities than the DC motors. Speeds of 3000–5000 rpm are common. The brushless DC transistor amplifier also has a high switching rate with a 200% limit of rated torque. The amplifier and motor can be treated as a DC drive. A typical block diagram for an Allen-Bradley digital brushless DC drive is shown in Figure 9.

Fig. 9 Allen-Bradley brushless DC block diagram. (Courtesy of Rockwell Automation/Allen-Bradley.)


3.5

AMPLIFIERS—HYDRAULIC

Hydraulic servo drive amplifiers take the form of a servo valve. Servo pump drives are not being considered. For reasons stated in Section 2.2, to maintain a minimum of trapped oil volume, the servo valve is mounted to the actuator with a manifold. Oil is supplied to the servo valve from a pump through a filter, which usually has a rating of 10 mm. Based on maximum power transfer, the hydraulic pressure at the servo motor through a servo valve is equal to two-thirds of the pressure at the input to the servo valve. In general it is assumed there is approximately a 300 psi line loss between the pump and the servo valve. When selecting a servo valve based on motor speed and required flow, it is important to allow additional oil flow to compensate for system leakage. As an index of performance, 30% more oil flow than required should be used in selecting the flow rating of the servo valve. The typical servo valve force motor (or torque motor) is shown in schematic form in Figure 10. The armature and drive arm are suspended on the flexure tube, which acts as a pivot point and also provides a spring force tending to keep the armature on center between the poles of the ‘‘C’’ section. The force motor has two symmetrical flux paths as shown by the dotted lines. Assuming an electrical current is applied to coil ‘‘A,’’ magnetic flux will be produced in air gap ‘‘a,’’ which tends to draw the armature toward that pole. The armature will move a distance such that the restoring force of the spring suspension (flexure tube) equals the magnetic pull. Thus, the greater the current in the coil, the greater the magnetic pull, and the further the stroke. Since the flexure tube acts as a pivot, the tip of the drive arm strokes in the opposite direction as the armature. The motion at the tip of the drive arm (also known as the flapper) is the force motor output. In summary, the force motor produces a displacement output proportional to differential current. If the coil currents are not the same, then the pull on one side will be greater and the armature will stroke an amount proportional to the difference in the two currents. As the flapper strokes one way, the nozzle pressures A and B will be unbalanced. This causes the spool to move in a direction to reestablish a balance of pressure at the nozzles. As the valve spool moves to a new point of equilibrium, oil will flow through the valve to the motor. Therefore the servo valve can be considered as a positioning servo where the spool is being positioned to allow oil flow. Servo valve spools can be made with overlap (creating a dead zone in output flow), underlap (which can cause system instability), and critical or zero lap. For most hydraulic servo drive applications, a very small overlap is used on the spool. Since the 1970s, advances have been made in hydraulic servo valve and actuator designs to include feedback transducers such as linear differential transducers (LDT).


Fig. 10

Pegasus hydraulic servo valve diagram. (Courtesy of Schenck Pegasus.)


3.6

TRANSDUCERS (FEEDBACK)

One of the important, if not the most important, elements of an industrial servo drive is the measuring device. One of the purposes of the feedback device is to accurately place a tool or workpiece at some desired location, prior to some machine operation. For the control system to know where the tool or workpiece is located, some measuring device must be used to provide this information in a language the control will understand. Measuring devices in general can be called transducers, a device used to transform one form of energy to another form of energy. A simple thermostat is an example of a transducer, where temperature is registered as a physical bending in a bimetallic strip. For some specified deflection of the bimetallic strip as the result of a temperature change, an electric circuit will be activated to run a furnace in the case of a heating control, or a compressor in the case of a refrigerator. There are many examples of transducers in the average home, but the type used with numerical control systems will convert position information from the motion of a machine drive screw or element into electrical signals. These electrical signals are the feedback information

Fig. 11

Feedback devices.


to the control system in a language the control can understand. A classification of feedback devices is shown in Figure 11. There are two basic types of feedback signals, which also define the control system as to the data information used within the system. The first type of signal is called analog, and the control is usually referred to as an analog system. Analog signals have two characteristic features. They directly represent some physical quantity and are continually varied. A tachometer is an example of an analog measuring device where the output voltage is directly proportional to the velocity of input shaft rotation. The second type of signal is called digital, and the control system is usually referred to as a digital system. Physical quantities are represented through the medium of digits or numbers, which would be discrete electrical pulses in the digital control system. Digital signals or information can be further defined as of two types: incremental and absolute. Incremental signals are merely a train of pulses where each pulse has a specific weighted value such as 0.01 in per pulse. The absolute digital information will take the form of a pattern of pulses. The pattern can have the form of a binary numbering code or some special coding. There are many commercial versions of transducers available. Perhaps the best known device is the tachometer, which is a small generator, sometimes producing AC output voltage but more often a DC output voltage. Tachometers are used to a large extent with velocity regulators. With brushless DC drives, the velocity feedback is synthetically generated. Since these drives have a position transducer as part of the motor (used for commutating motor currents in the amplifier), the position signal is differentiated in the amplifier creating a synthetic velocity signal to close a velocity servo loop. The velocity regulator may not be the complete control system, but it is quite often part of a positioning system. Transducers used for positioning systems have two basic forms as analog devices. Probably the simplest analog device for positioning systems is the potentiometer. As a feedback measuring device, the potentiometer can be a single-turn or a multiturn device. One of the most common forms of feedback measuring devices is the synchro, an AC electromechanical device providing a mechanical indication of its shaft position for some electrical input, or providing some electrical output that is some function of the angular position of its rotor shaft. Another electromechanical feedback device often used is the resolver. The device is similar in appearance to the synchro, but the electrical construction is not the same. Both types are a form of variable transformer, with more or less decoupling between the rotor and stator windings as the armature rotates. A linear version of the resolver is known as the Inductosyn. These devices are discussed later in more detail.


The synchro construction has a single winding on the rotor with three windings on the stator. The stator windings are wound, so that induced AC voltages in each of three windings from the rotor winding are 1208 apart. In application, these units are used as a transmitter or receiver in the transmission of data in position-type servos. A variation of the usual type synchro is the differential synchro. This device has a set of three windings on both the stator and rotor. The differential is used to add another mechanical input to the data transmission system of servo drives. The resolver is a precision induction-type device acting like a variable transformer, with the amount of coupling varying as the sine and cosine of the angular position of its rotor shaft. In control systems, the resolver is used for coordinate transformation in analog computer applications, in position servos as applied to industrial controls, and in other control applications where rectangular conversions to polar coordinate or vice versa are desired. The rotor and stator have two windings, which are wound at 90 electrical degrees with respect to each other. As with the synchro, the resolver can be used as a data transmitter or receiver. The resolver has the advantage that it can transmit data either side of zero degrees (operate in all four quadrants) whereas the synchro can only operate in quadrant one. In addition, the same resolver used to transmit or receive AC signals can be used as a differential unit. An electrical drawing of a resolver is shown in Figure 12. The resolver could be considered as a variable coupling transformer, with the amount of coupling dependent on the angle of the rotor shaft. Considering voltages V1 and V2 as primary voltages, the secondary voltages would be Vr1 and Vr2. Each secondary voltage would be a function of both primary voltages V1 and V2, plus the angle of the rotor shaft. Therefore, the two secondary

Fig. 12

Resolver circuit.


voltages Vr1 and Vr2 would have the following mathematical relationship to the primary voltages V1 and V2 : Vr1 ¼ V1 cos ya þ V2 sin ya Vr2 ¼ V1 sin ya V2 cos ya where: ya ¼ actual angle of the rotor shaft in degrees Since the resolver is a rectilinear to polar coordinate transforming device, the voltages V1 and V2 are also a function of the desired rotor angle as follows: V1 ¼ E sin yd V2 ¼ E cos yd where: yd ¼ Desired angle of the rotor shaft in degrees E ¼ rms value of an alternating sinusoidal voltage of a specified frequency When the resolver is used as a measuring device in a continuous positioning system, the position of the rotor shaft is a measure of where the machine element being positioned actually is. The resolver shaft is connected to the movable machine element through a gear train to the drive screw or sometimes by a precision rack and pinion. Therefore, the angular position of the rotor shaft of the resolver is a measure of the linear position of the machine element. A block diagram of the resolver used as a measuring device in a positioning system is shown in Figure 13.

Fig. 13

Servo drive with resolver feedback.


The difference between the actual angle ya and the desired angle yd is the position error. However, the input and output of the resolver windings are electrical voltages, not angles. The input voltages can be a function of the desired angle, as from the equations for V1 and V2 . The output rotor voltage is a function of the difference between the actual angle ya and the desired angle yd . When ya ¼ yd the voltage Vr1 is zero, which is the same as saying the machine slide is in position. This fact can be determined from the preceding equations when yd and ya ¼ 0 : Vr1 ¼ 0 cos 0 þ Eð0Þ ¼ 0 Vr2 ¼ 0ð0Þ E cos 0 ¼ E

ðnot usedÞ

Note: Only one resolver rotor winding is used. Thus Vr1 satisfies the condition of zero output when yd ¼ ya and it is therefore used; Vr2 is not used. It should be apparent that Vr1 can be made zero (the positioning system null position) by varying either the rotor shaft ya or varying V1 and V2 as functions of the desired angle yd . Most of the resolver devices are used as measuring devices coupled to a machine drive screw. With most industrial machines, the drive screw will have some backlash between its angular position and the position of the element it is driving—a machine slide, for example. For this reason, there has been difficulty in obtaining accurate positioning when measuring from the machine drive screw. Some manufacturers have designed their controls so positioning will always occur from the same direction. In general, measuring from the machine drive screw is not ideal. A considerable effort has gone forth to create a linear measuring device that can be used right at the moving machine slide rather than through a drive screw. These devices are called linear transducers (e.g., Inductosyn) and take the commercial forms of linear resolvers. With the linear analog measuring devices, either the stator or rotor is mounted on the moving part, and the other part is mounted on the stationary machine element. There is an associated attenuation with these devices, and amplification is required. The linear digital measuring devices have taken the form of optical grating devices, and some are magnetic coupling devices that generate a series of pulses, with each pulse being equal to some given distance. Some manufacturers have used precision gear racks on the moving machine element with a rotary measuring device fastened to the stationary element. This technique obviously is better than measuring off the machine drive screw. Each of the three methods of measuring—from the machine drive screw, a precision rack, or a linear transducer—has advantages and disadvantages in cases of application to a machine. In general, accuracy


improvements of a factor of 10 can be obtained between measuring from a machine drive screw and a linear transducer. Measuring at the drive screw can provide accuracies of one thousandth of an inch when using a good ballbearing screw. Both analog and digital systems are in use, and equally good results have been obtained with both. Most process-type control systems and numerical contouring systems use a single measuring device. It is characteristic of these types of control systems for the actual position to vary with the varying command position such as to make the position error of the control system very small. A plot of a resolver output voltage vs the rotor shaft angle is shown in Figure 14. With a continuously varying control voltage (V1 and V2 ) the resolver output voltage seldom gets more than a few degrees away from the resolver null position. Digital feedback is used extensively in many industrial servos. The digital feedback transducers can provide improved accuracy over the analog resolver or Inductosyn if the resolution of the pulses count per revolution is high enough (e.g., 500,000 pulses per revolution). For short-travel machine slides, the absolute digital feedback is practical, but in general most digital feedback devices used are incremental pulse generators. For maximizing the accuracy of positioning, the transducer is mounted on the machine slide.

Fig. 14

Resolver output voltage.


Fig. 15

Feedback devices.

Therefore for short-travel machine slides there are many linear digital incremental feedback devices that can be used. These linear devices are costly and must be justified. Examples of some of the feedback devices are shown in Figure 15.


4 Machine Servo Drives

4.1

TYPES OF DRIVES

Positioning systems in general have their most basic form, and also the most complex, in the human being. The brain serves as the summing network that accepts the command for a desired motion or position, the musculatory system serves as the power source or prime mover to cause motion to take place, and the sensory system, such as the eyes, determines the present position. In general, these three things—the brain, the muscles, and the eyes—are analogues to the three basic parts of any positioning system. The brain accepts the command, or reference as it is sometimes called, and compares it to the feedback to answer the question, ‘‘How do we get to where we want to be?’’ The eyes are the feedback device, sometimes called a measuring system, which answers the question, ‘‘Where are we?’’ The difference between the command or the desired position and the actual position (determined from the feedback device) is referred to as the position error. It is this error that makes the prime mover cause motion to take place, resulting in the actual position equaling the desired position and the position error being reduced to zero. Applying these definitions to a position control system, we have three basic parts of a position system, shown in block diagram form in Figure 1. The ‘‘desired position’’ must take the form of a piece of equipment to


Fig. 1

Machine servo-drive block diagram.

convert from the language of dimensions to the language of the prime mover. The input may be a calibrated scale in the dimension of inches or degrees with a pointer and handle. The output will usually be some voltage. The ‘‘actual position’’ is usually determined with some measuring device that is generally referred to as a transducer. The output language of the measuring or feedback device must be the same language as the command since the feedback is subtracted from the command signal. The answer is the position error signal. Thus the three basic parts of the servo are the drive, feedback device, and summing junction. The prime mover is usually the ‘‘drive’’ for the positioning system. The position error signal is the input to the drive. When there is a position error, the drive will cause motion to take place. Thus far, the discussion has been around positioning systems. In this discussion there are three types of feedback control systems in common usage. These are referred to as type 0, type 1, and type 2 servomechanisms. The type number refers to the net number of integrators around the loop. A type 0 servomechanism has a constant value of the output, such as speed, and requires a constant error signal under steady-state conditions. One form of a type 0 servo is a regulator, which implies that something is being controlled to produce a desired output, such as speed, despite disturbance conditions. The block diagram of Figure 2 shows a drive used in a speed regulating system where the controlled output is speed. Desired output speed is controlled by the reference input voltage to the drive. The system becomes a regulator when a feedback signal is added with a tachometer generator to measure output speed. As the tachometer input shaft rotates, an output voltage is generated that is proportional to the speed of the tachometer. A summing circuit at the input of the drive will subtract tachometer feedback voltage from the reference input voltage. The resultant


Fig. 2 Speed regulating system.

voltage will be a constant error voltage to the drive under steady-state conditions. An external disturbance, such as loading, or a change in the amount of reference input will cause the regulator to compensate for loading and maintain its original speed or change its original output speed to some new speed if the reference input voltage is varied. For either case, the regulator is acting under transient conditions, and the time required to again reach the steady-state condition, or a new steady-state condition, is the response time. There are times when the reference input is continuously varied, and the regulator output will attempt to follow the change in reference input. A sinusoidal reference input voltage is often used to test the ability of the regulator to follow a changing reference input. As the frequency of the sinusoidal voltage increases, the regulator output will follow the changing reference input until a frequency is reached where the regulator output can no longer follow the varying input. The frequency at which the regulator ceases to follow the sinusoidal reference input is referred to as the cutoff frequency of the servo-drive frequency response. With appropriate compensation (an integrator), a type 0 regulator can be converted to a type 1 system. A type 1 servomechanism will have zero error for any constant value of the controlled output. A constant rate of change of position (velocity) requires a constant error signal under steady-state conditions. This error is usually referred to as the following error in a type 1 positioning system. The positioning machine servo drive is an example of a type 1 servo. Such a feedback control system may include a speed regulator as shown in Figure 3. The feedback signal for this type of servomechanism is an integrated measure of speed (position). Some type of measuring device is used to provide a feedback voltage proportional to position (a resolver for example). The third type of servomechanism is referred to as a type 2 servomechanism, sometimes referred to as a ‘‘zero-velocity error’’ servo.


Fig. 3

Positioning servomechanism.

The type 2 servomechanism has a zero error for a constant value of controlled variable (position). These drives also have zero error for a constant controlled variable of speed. A constant rate of change of speed (acceleration) requires a constant error. The type 2 servo drive requires compensation, which results in its being conditionally stable. Changing gains or compensation time constants can produce an unstable drive.

4.2

FEED DRIVE PERFORMANCE

Servo-drive performance is a measure of how well a servo can make rapid changes in velocity, path, etc. and maintain required accuracy in the controlled variable (position). The frequency-response bandwidth is one way to define the performance of an industrial servo drive. To understand the relevance of servo loop bandwidth to servo performance it is necessary to define what is meant by servo bandwidth. ‘‘Bandwidth’’ is a term describing the frequency-response characteristic of a servo drive. In its simplest definition, the frequency response is a measure of how well an output of a servo follows the input as a sinusoidal input driving frequency increases. At low frequencies the output of a servo faithfully follows the input, so the ratio of output to input is 1. This is often referred to as the flat part of the response. At high frequencies, the output of a servo no longer follows the input. The higher the servo bandwidth, the greater the capability of the servo to follow rapid changes in the commanded input. For example, in a machine contouring system, the performance of a servo to make rapid changes in the path (square corners, etc.) is directly related to the servo bandwidth.


As the frequency increases beyond the flat part of the response, the servo output begins to lag behind the input driving signal. There is a phase lag and an amplitude attenuation between the output and input. When the phase lag reaches 180 degrees the servo is unstable. Thus it is a requirement to establish some performance specification to state how much phase lag is acceptable before instability occurs. Most industrial axis servo drives use a velocity servo inside a positioning servo system. It is critical that the position servo drive have an open-loop phase lag less the 180 degrees to avoid instability of the servo. As an index of performance (IP), a maximum of 135 degrees phase lag has been used as a criterion. This means there are 45 degrees phase lag left before instability occurs, and this 45 degrees is referred to as the phase margin before the servo goes unstable. Thus, the total acceptable phase lag of the internal velocity loop and other components cannot be more than 135 degrees phase lag. In any positioning servo system with an internal velocity servo there will be a required integration of the velocity output of the velocity servo to the position output of the position loop. This integration component takes place in the motor and is measured by the position transducer (often a resolver). Any integration component has a fixed 90 degree phase lag at all frequencies. Thus the total allowable phase lag of 135 degrees for the velocity servo and integration is now reduced to 45 degrees (135790) for the closed-loop velocity servo. Therefore the useful velocity servo bandwidth occurs at a frequency where the closed-loop velocity servo has a phase lag of 45 degrees (often stated as the 45 degree phase-shift frequency). A typical frequency response for a brushless DC servo drive with a load inertia equal to the motor armature is shown in Figure 4. The useful velocity servo bandwidth is 20 Hz. A term to define the performance criteria of a position servo is referred to as the position-loop gain or velocity constant. This gain is actually the open position-loop gain. Referring to Figure 5, the block diagram for a position servo, the open-loop gain is a parameter that represents the product of the individual gains in the position servo loop without the feedback being closed. The closed position-loop gain for this example is position output/ position command. Without the feedback being closed, a position command will cause the drive to have motion. The ratio of output/input will therefore be in units of velocity/position. As an example, if the input command has the units of inches, the open position loop output will be inches per second. Thus the open position-loop gain is Kv ¼ (in.)/(in.-sec) ¼ 1/sec. A position-loop gain, in units of 1/sec, does not have a practical meaning to many machine control people working in industry. By making a units


Fig. 4 Machine servo frequency response.

conversion of Kv ¼

1 60 sec in: 1 inches per minute 6 6 ¼ 60:06 ¼ sec min 1000 mils sec mil

or ðinches per minute=milÞ616:67 ¼ ð1=secÞ Thus the open position loop gain expressed as some velocity (inches per minute, ipm) divided by distance (mils) has a practical significance.

Fig. 5 Machine servo-drive block diagram.


Typical measured velocity servo frequency response bandwidths for some commercial servo drives are shown in Figure 6. The servo bandwidths are shown versus increasing inertia loads. The Gettys DC silicon controlled rectifier (SCR) drive is a typical three-phase, half-wave DC SCR servo drive. As inertia load is added to the motor, the drop in servo bandwidth is minimal since the motor inertia is 0.437 lb-in.-sec2 compared to the inertia load being added. However, the servo bandwidth is limited since it is a function of the transport lag (dead time in the SCR firing), which contributes phase shift to the servo drive. The DC SCR drive has a forcing capability of 400%, which is an advantage over the transistor type servo amplifiers. If the same DC motor is used with a transistor-type pulse-width modulation (PWM) amplifier (General Electric HI-AK), the servo bandwidth characteristics are much higher since there is no transport lag in the servo amplifier. However, the forcing capability (for acceleration) is limited to 200% because of the transistor current capability. As time passes, newer transistor technology will improve the current capability. With an AC drive (brushless DC Indramat drive) the servo performance is comparable to the DC PWM servo drive and has the same

Fig. 6 Loading effects on servo performance.


current capacity limitations. The AC (brushless DC) synchronous motor shown has an inertia about half (0.2 lb-in.-sec2) that of the DC motor. The hydraulic (Hartman) servo drive has an armature of about 0.015 lb-in.-sec2. Thus at no load, the performance is over 60 Hz. As a coupling and load inertia are added to the motor shaft, the servo performance drops rapidly. The frequency response is a powerful analytical tool that can be used for design or diagnostic procedures. Industrial servo drives are connected to machines. Since machines can have nonlinearities of backlash, stiction, etc. and mechanical resonances, the frequency response of the servo drive and machine can be used to identify these nonlinearities and structural resonances. An example of a frequency response of a machine slide that has a 40-Hz resonance inside the position loop is shown in Figure 7. The resonant peak is about 25 dB, which results from a structural compliance and an underdamped machine slide (roller bearings). These applications of the frequency response are discussed in further depth in Part II. In addition to the frequency-response method to measure performance of an industrial drive, the transient step response can be used. Measuring the frequency response requires a servo analyzer, which may not always be

Fig. 7 Machine servo frequency response with a resonance.


Fig. 8

Second-order transient response.

readily available. A transient step response can readily be made with a simple battery circuit. The step response is used extensively in testing, diagnosing, etc. of industrial machines in the field. A typical transient response for a second-order system is shown in Figure 8. For velocity servo drives an index of performance exists, which recommends that the transient response have one overshoot. Likewise, for positioning servo drives (especially contouring drives) there should not be any overshoot (critically damped).


5 Troubleshooting Techniques

The time is gone when machines, controls, and drives were ‘‘add-ons,’’ as shown in Figure 1. Early machines used add-on drives. These drives had one thing in common: There was no interaction among the control, drive, and machine. To a large extent these machines were open loop. Today’s numerically controlled machines are tightly integrated machine systems. There is a great deal of interaction between the machine, drive, and control. It is this interaction that results in problems with stability, surface finish on the work part, and accuracy. The actual block diagram for today’s machine systems looks more like the block diagram shown in Figure 2.

5.1

TECHNIQUES BY DRIVE

The primary difference between the machine drives of yesteryear and those of today lies in the number and type of feedback signals that occur with modern control systems. It is true that early drives had load forces fed back to the drive, and these forces could cause a droop in the feed rate with load (called load regulation). Nonlinearities (stiction, lost motion, etc.) would not affect the stability because they were outside the servo loop, but they could cause inaccuracies. By and large, drives were ‘‘hooked’’ onto a machine and in spite of resonances in the mechanical drive, stick-slip, lost motion, etc.,


Fig. 1

Machine control system block diagram.

the machines performed with less than acceptable accuracy by today’s standards. With the ever-increasing demand for more accurate machines, more and more of the machine was included in the control/drive feedback loops. Today the machine, control, and drive are an integrated machining system. The existence of resonances between the drive motor and machine slide can make the drive unstable. A stick-slip condition on the machine slide can cause a null hunt (discussed in the next section) in the drive. Poor surface finish can result where load forces are fed back to a drive that has poor servo stiffness. A contouring drive with poor resolution also demonstrates poor low feed characteristics affecting the surface finish. Electrical noise feedback into transducer cables, as the result of poor shielding and isolation, can cause stability and accuracy problems. With just about everything in the machine system being a variable that can affect machine accuracy and stability, where does the technician start to look for the cause of a machine that will not perform properly? It is virtually impossible to diagnose the trouble of a malfunctioning machine with all the control loops closed. Therefore, the control and machine should be

Fig. 2

Machine control system block diagram with nonlinearities.


separated. With a hydraulic drive the separation should be at the servo valve connector. With a DC electric drive the separation should be at the input to the electric motor. With brushless DC drives the battery box should be connected to the drive amplifier input. The troubleshooting should now proceed in the following sequence.

Closed Velocity Loop The next logical step in the ‘‘setting up’’ or troubleshooting of the servo drive is to close the tachometer or velocity loop and check the performance.

Hydraulic Drive The velocity loop performance can be checked by closing the servo loop external to the control. A battery box connected to the velocity drive input can be used to operate the servo drive independently of the control. By operating the velocity drive back and forth and putting step changes in input voltage to the drive, the servo performance can be observed for stability. Any unacceptable performance must be corrected before proceeding further.

Electric Drive Setup instructions for the electric drive are provided by the drive supplier. This type of drive can also be controlled by a separate variable DC voltage applied to the drive amplifier input terminals. Likewise, by moving the machine slide back and forth and putting step changes in input voltage to the drive, the servo performance can be observed for stability. Unacceptable performance must be corrected before proceeding to close the position loop. In either the hydraulic or electric drive the performance of the velocity loop should be checked with an external DC voltage source. The numerical control voltage sources such as the feed-forward voltage should not be used for trouble shooting. The most obvious test to make with the velocity loop is to make sure the drive can be controlled from standstill to the traverse rate. Whether the feed rates are smooth or jerky, especially at the lower feed rates, should be observed. With either electric or hydraulic drives the velocity loop gain should be set at its highest possible setting. The velocity loop performance is directly related to the gain. With too low a gain the drive will be sluggish and exhibit a speed droop with applied load. One of the prime reasons for poor surface finish with numerically controlled machines is a velocity loop with too low a gain (thus also poor performance and bandwidth). There are engineering evaluation tests that can be used to


ascertain the servo loop performance. However, these tests should only be made by a trained analyst. For general use the gain setting can be made by raising the velocity loop gain until the drive goes unstable and oscillates. The oscillation is usually observed as an audible rumble often called ‘‘tachometer growl.’’ When this condition occurs the gain should be reduced until the ‘‘growl’’ ceases. The gain should then be reduced slightly further to allow some margin in reliability of the gain setting. With electric drives the gain setting is often a component part of the setup instructions.

Hydraulic Drives Machine piping should be checked to assure that all return lines run directly to the ‘‘tank.’’ The drain lines should have a loop at the motor to be higher than the motor. Any restriction in the drain line can blow out a motor seal. A blown seal is obvious with a puddle of oil on the floor. Hydraulic pressure and return line pressure can be checked at the servo valve as a rapid way to determine if a piping problem exists. Return line pressure at the motor should be less than 100 psi when the motor is rotating.

Electric Drive Wiring for electric drives does not pose the same problems as hydraulic drives. However, motor armature cables carry currents with very fast rise times from pulse-width modulation (PWM) DC drives and brushless DC drives. These cables should be isolated as much as possible from tachometer feedback cables and position transducer (resolver or Inductosyn scales) cables.

Open Loop Battery boxes can be used for both hydraulic and electric drives.

Hydraulic Drive The battery box connected to the servo valve can be used to move the machine slide back and forth. A normal machine slide will move (break away) with about þ0.004 A or less. This current may not necessarily be symmetrical around zero. The servo valve mechanical null adjustment may cause a slight servo shift if it is not centered.


Electric Drive For DC electric motors, the breakaway current should be approximately less than one-half the rated current. Excessive breakaway currents in either drive indicate a sticking or binding machine slide. Vanes or pistons in a hydraulic motor and armature winding slots in electric motors will cause a cogging effect when these motors are operated as an open loop. The cogging is noticeable at low speeds. It is normal and should not be a cause for alarm. A properly operating tachometer loop will smooth the open-loop cogging action. Machine slide stick-slip can be observed with a battery box in cases of friction slides. With antifriction slides (hydrostatic or roller bearing) stick-slip should not be a problem. In the case of friction slides a breakaway current two or more times the run current can cause a position loop null hunt if the stick-slip is inside the position loop. Hydraulic drives usually have some amount of internal leakage. This leakage is a form of damping for the hydraulic resonance in the drive. It will be of some benefit in damping and will permit higher gains to be used. When the leakage becomes excessive and variable, the low feed rates may become jerky. This is the same resultant effect obtained from varying loads on a lowgain velocity servo loop. The cure is the same for both situations. The velocity loop gain (and thus the bandwidth) should be set to its highest feasible setting. With some hydraulic motors the leakage has been found to be excessive and the motor should be replaced. Some control suppliers make an unnecessary practice of adding cross-port leakage to all hydraulic motors. Cross-port leakage in the form of a drilled set-screw plug in the servo valve manifold should only be used if needed. Cross-port leakage reduces the sensitivity of a drive and if required should be kept as small as possible. The diameter of the drilled plug should be about 0.001 in. With the larger hydraulic motors, experience has shown that a 0.0025- to 0.003-in. diameter orifice will suffice. In general the setup and troubleshooting of electric drives has been found to be simple and reliable. The numerous variables associated with hydraulic drives have proven to be challenging at times.

Closed Position Loop Each control manufacturer will probably have a different technique for closing the position loop. The one thing in common to all controls is that the position loop gain must be set at a predetermined value. The techniques vary for setting this gain. It is quite common to set the gain by measuring the position lag (command position7actual position, called the following error)


at some given speed. In other cases the output position responses to a step input position may be measured and recorded on a chart recorder. The position-loop gain is then adjusted until the desired response is observed on the chart recorder. Whatever the techniques used to set the position-loop gain, the control manufacturer will have a step-by-step procedure for these adjustments. Once the position-loop gain is set to the prescribed value, the servodriven axis may not perform properly for a variety of reasons. These are some symptoms of faulty position loops: 1. The servo drive may be unstable or it may null hunt at a low frequency. 2. The feed rates may not be smooth. 3. The drive may not be stiff enough. 4. The drive may not position accurately. To relate all the possible faults to the symptoms would result in endless discussion. The next section attempts to relate different kinds of problems to their possible causes.

5.2

PROBLEMS: THEIR CAUSES AND CURES

Table 1 illustrates the causes of problems.

Poor Surface Finish Causes: Other than tooling problems, a poor surface finish can result from a poor low-feed contouring control. If the low-feed-rate contouring control does not operate smoothly it can be defined as a drive with poor drive resolution (the difference between breakaway error and run error is too large). The smaller the control signal required to cause the drive to move, the smoother is the drive and the better the surface finish. The surface finish is also related to the bandwidth of the velocity loop and the position loop. Poor surface finish is very often the end result of a low gain (and thus low bandwidth) tachometer loop. Stiction and high-friction machine ways can also contribute to poor surface finish. A machine way is the surface area where a machine slide makes contact with the structure of the machine. Nonlinearities such as nonuniform leakage, as found in hydraulic motors, can definitely cause surface finish problems. Cures: It is recommended that all feed drives use the highest tachometer loop bandwidth (highest gain) possible. A wide bandwidth


Table 1

Causes of Problems Problem

Possible causes 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Mechanical backlash Stick-slip Low spring rate Undamped hydraulic resonance Too much hydraulic leakage Too much friction Tach loop gain too low Tach loop gain too high Position loop gain too high Position loop gain too low

Note: X, Definite cause; p, possible cause.


Poor surface finish

Unstable position loop

Null hunt

p p p p X p X p p X

X

X X

Tach loop growl

X X p

X X

Feed rate not smooth

Low stiffness

Insufficient accuracy

p p p p X p X p p X

X

p p p

p p X X

X p X

X

X

tachometer loop will minimize the nonlinear effects of hydraulic motor leakage. The machine slide should have no lost motion (backlash) in the mechanical drive train, and the machine ways should be antifriction (roller bearings, hydrostatic, Rulon way liners, etc.).

Unstable Position Loop Causes: There are several causes for an unstable position loop, with the most obvious being too high a position-loop gain for a given system. When resolver feedback is used at the drive motor, the nonlinear mechanical problems such as lost motion, stiction, and low spring rates will not affect the stability of the drive. However, when direct slide feedback is used (using Inductosyn scales) these mechanical nonlinearities are inside the position loop. Cures: For contouring servo drives the position-loop gain should be in the ‘‘soft servo’’ range (0–2 ipm/mil). The machine dynamic problems can be minimized by using a low position-loop gain when direct machine slide position feedback is used. Some control manufacturers use 0.6 ipm/mil position-loop gain on all axes. In general, most large machines with direct feedback should have position-loop gains of about 1 ipm/mil. It is very important that lost motion (backlash) be absent from drives with machine slide feedback. If a wound-up gear train should lose its windup it will probably result in an unstable position loop.

Null Hunt Causes: A null hunt is a form of instability. A null hunt is a very-lowfrequency oscillation sometimes called a limit cyle oscillation. Lost motion (backlash) can cause a null-hunt condition when combined with large friction forces. Usually a backlash condition inside a position loop results in an unstable drive. The fact that the period of oscillation may be fast or slow is not significant. Stick-slip on a machine slide can definitely cause a null hunt. In general, a null hunt is possible when the breakaway friction is at least twice the running friction. The null hunt associated with stick-slip can also be aggravated by a spring (unstiff drive screw) inside the position loop. With hydraulic drives, excess leakage will cause an unstable position loop, which will oscillate at a low frequency and appear as a null hunt. Cures: For most cases of null hunt caused by backlash, antibacklash gearing (wound-up gearboxes) should be used. When the windup is lost in a wound-up gearbox the position loop is almost guaranteed to be unstable. Friction-type slides should be avoided. For machine ways using roller


bearings, hydrostatic ways, or Rulon way liners, null hunt from stick-slip should not be a problem. Excessive cross-port leakage on hydraulic servo drives will cause a null hunt, and care should be taken that if an orifice is required for hydraulic damping the orifice is in place. There have been cases where the orifice was omitted. The orifice is located in the servo valve manifold. Hartman motors have enough internal leakage and do not require additional cross-port leakage.

Tachometer Loop Growl Cause: The instability of a velocity loop will cause an oscillation at a frequency high enough to be audible, thus the term ‘‘tach loop growl.’’ The most significant cause is trying to set the loop gain too high for the existing parameters. Cures: The most obvious cure for an unstable tachometer loop is to lower the loop gain. However, if the loop gain must be lowered the total contouring drive will have reduced performance.

Feed Rate Not Smooth Causes: There are numerous causes for an unsmooth feed rate. Excessive and varying hydraulic leakage can also cause a varying low feed rate in hydraulic drives. Other things, such as the drive nonlinearities of stick-slip, lost motion, low mechanical resonances can affect the drive smoothness. Cures: A prime consideration is to maintain as high a tachometer loop gain (thus bandwidth) as possible assuming other restrictions, such as underdamped hydraulic resonances and mechanical resonances, have been dealt with.

Low Stiffness Cause: Stiffness as referred to here is the servo drive loop stiffness. It is a measure of how many lb–in. of torque is required to rotate the motor shaft a given number of degrees. Too much leakage will reduce the stiffness of a hydraulic drive. On a machine, the stiffness measured at the motor increases by the square of the drive ratio. The stiffness can also be measured at the machine slide where the stiffness increases by the square of the ratio/lead. Drive stiffness is discussed in depth in Part II.


Cures: To maintain adequate stiffness the design of the drive must include the proper sizing. After the drive is assembled the only variables left to adjust are the loop gains.


6 Conclusion: Machine Feed Drives—An Integral Part of a Machine Control System

6.1

ADVANCES IN TECHNOLOGY

In the post–World War II years, machine and control builders were still provincially minded in building controls and machines as separate entities, believing that a control could be ‘‘hung’’ on a machine with few problems. Advances in technology have shown that the separate elements of control, drive, and machine must be integrated into the total system concept. Each of these elements is dependent on the others. It is the purpose of this discussion to illustrate how feed drives serve the purpose of system interface and prime mover through three areas, namely, selection of the drive, sizing the drive, and finally, evaluating the performance of the drive and total system. In selecting the feed drive, it is appropriate to ask the question, which drive—electrical or hydraulic? In the process of selecting a drive, it is worthwhile to classify the various types of feed drives. Electric drives can be classified into three main types, namely, the DC drive, the pulse-width modulation (PWM) DC drive, and the brushless DC drive. One of the most popular drives has been the hydraulic drive. The greatest share of these drives have been the servo-valve drives, because of the minimal trapped oil volume and lower hydraulic resonance than in hydraulic servo pump drives.


The electric and hydraulic drives have the greatest application for servo drives. A natural question might be, why a servo drive at all? Some of the reasons are: 1. A servo drive will be required for numerical control applications. 2. The servo drive will result in improved drive resolution. 3. Improved drive stiffness will be realized with servo drives, eliminating the need for auxiliary clamps. 4. Positioning time will be greatly reduced. 5. Acceleration can be controlled with the servo drive. 6. The servo drive is easier to apply in different applications because of its modular design. Some historical background would be appropriate prior to discussing specific comparisons in the selection process. In the post World War II era machine feed servo drives were motor-generator electric drives such as the Amplidyne, Rototrol, and Metadyne. On large machines, these drives were limited in performance. Advanced hydraulic drives using high torque-to-inertia ratio servo motors and high-response servo valves quickly overshadowed the rotary electric servo drive. The outstanding advantage of the hydraulic drive was its higher performance, although it had other advantages such as a large motor torque capacity in a small package. As the state of the art of numerical control advanced, with its ever-increasing demands for feed drive performance and accuracy, hydraulic drives seemed to fit the specifications best. Improved hydraulic motors were developed, with less breakaway torque and more uniform low-speed characteristics. In addition, servo valves showed improved reliability in industrial environments. However, the machine user was becoming dissatisfied with fluid maintenance and with the noise problems associated with hydraulic drives. One of the most frequent complaints from the user of hydraulic drives was the noise problem. It grew to such magnitude that enforcement standards were imposed on suppliers to reduce the noise level of hydraulic servo systems. The Walsh–Healy Public Contracts Act, which became effective May 20, 1969, established an upper limit on noise level as a stimulus to noise abatement efforts. The noise problem was probably the greatest deterrent to the use of hydraulic drives. Despite these problems with hydraulic drives, the electric drives’ apparent lack of performance capability made them take a back seat for a considerable time. With the appearance in the 1960s of the low-inertia slotless-armature DC electric drive, however, it looked like electric drives might be due for a revival. These motors had high torque, excellent lowspeed characteristics, and high performance. However, their high torque was


thermally limited to a 1-sec rating. Performance of the low-inertia drive motors was comparative with their hydraulic counterparts. After several years of evaluation throughout industry, it appeared that the low-inertia DC motor had advantages for machine feed drive applications that require high-performance situations, where many rapid accelerations of low mass loads are the mode of operation. These motors were used briefly on medium-size machines. For the large machine, however, the low-inertia DC servo drives did not provide sufficient feed thrust. The low-inertia DC motor also provided a peak torque at high acceleration rates, which, if not compensated for, could destroy the mechanical components of the feed drive. Therefore, controlled acceleration had to be provided with these drives. Accordingly, it appeared that a DC electric drive with ample torque capacity and less performance than the low-inertia slotless-armature DC electric drive would better suit the machine feed drive market. These motors were referred to as high-torque, low-speed DC motors. Subsequently, during the 1970s and to the present, the silicon controlled rectifier (SCR) DC drive, the PWM DC drive, and the brushless DC drive were introduced to the machine drive market. With this revival of electric drives, making the proper choice for a specific application required detailed knowledge about some of the more important requisites of feed drives and about some of the significant advances in drive motors, amplifiers, and control techniques. Such knowledge can be obtained from a comparative study of a number of the newer types of drive motors. They are compared here for rated torque, maximum torque, inertia, acceleration characteristics, drive stiffness, and thrust requirements.

6.2

PARAMETERS FOR MAKING APPLICATION CHOICES

Rated torques for the drive motors are compared in Figure 1, which shows the difference between several high-torque, low-speed DC and brushless DC electric motors, and several hydraulic motors. The hydraulic motor torque rating is limited by the hydraulic pressure, and these ratings are also continuous. Electric motors have a continuous rating and a higher thermally limited rating. In addition, the electric motors have an absolute maximum rating, which is available for short-duration forcing torques needed in acceleration and deceleration. Relative inertias are compared in Figure 2. The low inertia is directly related to the performances capabilities of drive motors. It is important to note in Figure 3 that performance capabilities are modified as a load inertia


Fig. 1

Torque characteristics comparison.

is connected to the drive motor. There is a varying reduction in performance capability for a given load, as illustrated. The electric motors have two performance limitations, electrical and mechanical, with the latter being reduced with increased inertia load. Hydraulic drives also have a performance limitation related to load inertia, which is referred to as the

Fig. 2

Inertia characteristics comparison.


Fig. 3

Loading effects.

hydraulic resonance. The reduction in performance with load, however, is much more pronounced with the hydraulic motors. Therefore, the advantage of high performance with the low-inertia drive motor can only be realized if the motor does not see large reflected inertias at the rotor. As performance improves, the acceleration capacity also increases. Maximum motor acceleration is directly related to the performance and the maximum velocity. Acceptable acceleration rates vary with the application. Some machine builders limit the acceleration to 0.1 G (gravity) or 0.2 G, which is equivalent to a rate of 2320 ipm/sec and 4640 ipm/sec, respectively. If a large machine has a 100,000-lb load, for example, that is being accelerated at 0.1 G or at the rate of 2320 ipm in 1 sec, it is not too difficult to imagine the excessive forces involved. Therefore, feed drives must have some form of controlled acceleration. For the soft servo with low gain and extended error-control features, acceleration is limited. With the highperformance, high-gain feed drives referred to as hard servos, the acceleration must be limited through programming or control techniques. A further requirement is that machine feed drives should have sufficient static stiffness to be insensitive to load disturbances. In addition, a feed drive in a numerical control system must remain stationary or clamped when not in motion. Also, during the standstill period, the axis at rest must resist the load disturbances caused by the reaction forces of the other axes. Relative feed drive stiffnesses are compared in Figure 4, which represents the relative amount of torque that will be developed at the machine drive


Fig. 4

Drive stiffness comparison.

screw for a load disturbance on the drive screw resulting in an angular deflection of 1 radian (rad). The presence of a high-gain tachometer minor loop adds greatly to the drive stiffness, since the static stiffness is the product of the position loop gain, the velocity loop gain, and the square of the gear ratio when a gearbox is used. A very important part of sizing a feed drive properly is selecting a motor rating large enough to provide the required feed force. For drilling applications, feed forces of 10,000 lb-force are not uncommon. With a surface feed per minute (sfm) of 30, the suggested feed force should be 1000 lb per usable cutting horsepower. The most frequent questions asked by the machine builder concerning drives relate to the choice between hydraulic, DC SCR, DC PWM, or brushless DC electric drives. With the new electric drive motors (DC or brushless DC) it is possible to meet all the requirements of performance and load with electric drives, provided sufficient engineering expertise is brought to bear on the problem. The important criteria in selecting the type of drive is the application of the drive. There are a number of factors the system designer should consider in selecting a drive. Drive motor size may be important. The machine designer may object to the larger physical space requirements of the electric motor. Weight can also play an important role in the selection of a drive motor. Heavy drive motors could be a detrimental factor in the area of machine structural dynamics. Hydraulic motors can operate at a maximum


torque continuously, whereas DC electric motors operated from SCR amplifiers must be derated. In general, DC motors must be derated 60% of their rating when used with full-wave, single SCR amplifiers, and 80% of their rating with three-phase, half-wave SCR amplifiers. Brushless DC motors can operate at their rated torque continuously. The DC SCR drive has a 400% rating for forcing or acceleration, while the brushless DC drive has an equivalent 200% rating. Another consideration in selecting a drive is the effects of noise. There are two kinds of noise to consider. While audible noise is generally associated with hydraulic drives, electric noise is an important consideration with PWM DC and brushless DC electric drives. Government regulations have initiated an attack on audible noise pollution, and to meet and surpass these requirements, quiet hydraulic power supplies are available. Electrical noise can cause loss of operation and possible catastrophic failures with digital control systems. Next to diathermy machines, the PWM DC and the brushless DC amplifier are electrical noise generators of the worst kind, and special isolation practices must be incorporated. Standards for the installation of electrical control systems are available from the Institute of Electrical and Electronic engineers (IEEE Std. 518-1982). In addition to the power duration requirements for electric drives, both types of drives have performance limitations. Hydraulic drive performance is usually limited by the hydraulic resonance where the resonance is a function of motor inertial load, motor size, and oil under compression. Electric drives using SCR amplifiers have an on–off timing function. With SCR switching on and off, dead time exists in each cycle of AC power where no power will be applied to the motor from each of the silicon controlled rectifiers. The on–off switching function of the SCR amplifier is referred to as the transport lag of the amplifier and adds phase shift to the servo drive. In addition to the inertial time constant limitation of the DC motor, the transport lag of the SCR amplifier will also limit the performance of the DC drive to about 10 Hz on large machines. The brushless DC drive is not limited by current switching and therefore has performance bandwidths of about 30 Hz on large machines. The DC SCR drive has a current and torque rating of about 400% for the purpose of forcing (acceleration). The brushless DC drive and the PWM-DC drive have an amplifier with transistors, which limits the overall drive to about 200% of rated torque. The second area under consideration is the sizing of the drive. Once the drive has been selected, it is necessary to size the drive properly, and criteria for sizing are based on the proper performance and feed thrust. Sizing a drive requires the expertise of a system analyst; however, the


technology involved has been reduced to simple computerized programs to be used by design engineers. In summarizing, it would be appropriate to recap some of the more significant points discussed. Today’s industrial machines should be considered as a machine system comprised of a control, drive, and machine. The selection of the type of servo drive should be based on the application. Evaluation of the low-inertia slotless-armature DC motors proved inadequate for industrial servo machine applications. Low-inertia brushless DC motors (e.g., neodymium iron boron or samarium cobolt armatures) have many industrial applications for high-performance applications where it is recommended that the motor armature be matched to the reflected load inertia through a ratio. For an inertia mismatch of up to about four to one (reflected load inertia to motor armature), ceramic magnet armature motors are recommended. Advances in the area of electric drives continue with improvements in amplifiers and motors. The introduction of the insulatedgate bipolar transistor (IGBT) to brushless DC drives and vector-controlled AC drives has increased the torque capacity of these drives by about 50%. New innovations will continue unabated.


II ADVANCED APPLICATION OF INDUSTRIAL SERVO DRIVES


7 Background

7.1 INTRODUCTION Part I discussed the basics of industrial servo drives from a hardware point of view. Physical parameters and practical applications were discussed. Part II repeats some of the things in Part I but from a mathematical point of view. The advanced application of industrial servo drives requires the use of differential equations to describe mechanical, electrical, and fluid systems. As applied to servo drives there are numerous academic techniques to analyze these systems (e.g., root locus, Nyquist diagrams, etc.). In working with industrial machinery we live in a sinusoidal world with such things as structural machine resonances. Thus frequency analysis is used in Part II to describe and analyze industrial servo systems. To solve the differential equations describing the physical systems of servo drives, transformation calculus is used to obtain the required transfer functions for the components of servo drives and in analyzing the servo system. There are a multitude of academic textbooks and university courses dealing with feedback control. It is the purpose of Part II to show how the fundamentals of servo drives described in the many academic sources are applied in practice.


7.2

PHYSICAL SYSTEM ANALOGS, QUANTITIES, AND VECTORS

As a beginning, analogous parameters for an electrical system, a linear mechanical system, and a rotary mechanical system are compared for future reference. In all physical systems there are scalar quantities and vector quantities. Vector quantities can be represented as complex numbers on a complex plane, in polar form, or in exponential form as in Eq. (7.2-1) to (7.2-12).

Scalar Quantities (a) Magnitude only (b) Examples: length of a line, mass, volume

Vector Quantities (a) Magnitude and direction (b) Examples: force, voltage, weight, velocity

Complex Numbers A vector can be represented by its rectilinear components.

Fy Fx cos y ¼ F F Fy ¼ F sin y Fx ¼ F cos y qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jFj ¼ ðFx Þ2 þ ðFy Þ2 sin y ¼

Fy y ¼ tan1 Fx qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fy ;F ¼ ðF cos yÞ2 þ ðF sin yÞ2 ffy ¼ tan1 Fx A vector can also be represented on a complex plane.


(7.2-1) (7.2-2) (7.2-3) (7.2-4) (7.2-5)

F ¼ Fx þ jFy F ¼ ðjFj cos yÞ þ jðjFj sin yÞ pffiffiffiffiffiffiffi j ¼ 1

(7.2-6) (7.2-7) (7.2-8)

A vector can be represented in polar form. F ¼ jFjffy qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Fy F ¼ ðFx Þ2 þ ðFy Þ2 ffy ¼ tan1 Fx

(7.2-9) (7.2-10)

A vector can be represented in exponential form. F ¼ jFje jy

y ¼ tan1

Fy Fx

(7.2-11)

Thus: Rectangular F cos y þ jF sin y ¼

7.3

Polar jFjffy

¼

Exponential jFje+jy

(7.2-12)

DIFFERENTIAL EQUATIONS FOR PHYSICAL SYSTEMS

The differential equations for physical systems can be written for individual servo components such as motors and amplifiers or for complete multiloop servo drives. In actual practice servo drive block diagrams can be put together with a combination of individual transfer functions representing the differential equation of the separate servo drive components. These individual transfer characteristics can, in general, be represented by singleorder or second-order blocks in the overall servo block diagram. A singleorder differential equation or transfer characteristic results from a circuit having a single time-varying parameter. Likewise, a second-order transfer characteristic results from a circuit (mechanical, electrical, or fluid) having two time-varying parameters. Most servo drive components can be represented by either a first-order transfer characteristic (or transfer function) or a second-order transfer function. A transfer function is, by definition, the ratio of the Laplace transform of the output to the Laplace transform of the input. In general a transfer function is a shorthand solution for solving differential equations. The derivation of a single-order electrical circuit transfer function having an inductor as a single time-varying parameter is shown in Figure 1. The steady-state equations for the output voltage, based on a sinusoidal


Fig. 1 (a) Inductive/resistive circuit. (b) Circle diagram.

input voltage, are 7.3-1 to 7.3-17. Replacing the jo term by the differential operator p or the Laplace transform operator s changes Eq. (7.3-10) to the transform function of Eq. (7.3-19). This transform function can be represented in the frequency response of Figure 2. To illustrate a second-order circuit, the circuit of Figure 3 with two time-varying parameters has the differential equation of Eq. (7.3-20). The output voltage for the unique case of a sinusoidal input voltage is Eq. (7.325). A second-order mechanical circuit for linear translation is shown in Figure 4. Eq. (7.3-30) is the differential equation for this circuit. Assuming a sinusoidal input, the output displacement is Eq. (7.3-35). Lastly, a rotary mechanical circuit is shown in Figure 5. The output angular motion is Eq. (7.3-44). These examples of single-order and second-order circuits are to illustrate that individual servo drive components can be represented mathematically by differential equations, transfer functions, or the absolute case for a sinusoidal input driving source. The circuit shown in Figure 1 is further described for three cases of absolute, vector, or differential analysis followed by the response of this circuit to a step input and a ramp input. ei ¼ iRe þ iXL

(7.3-1)

ei ¼ iZ

(7.3-2)

XL ¼ 2pf ffoL Zffy ¼ Zðcos y þ j sin yÞ

(7.3-3) (7.3-4)


Fig. 2

Single-order frequency response.


Fig. 3

Inductive/capacitive/resistive circuit.

Fig. 4 Spring/mass diagram (linear).

Fig. 5 Spring/mass diagram (rotary).

Note: a þ jb ¼ cffy: Z

Re XL þj ¼ Re þ jXL Z Z

(7.3-5)

ei ¼ iðRe þ jXL Þ ¼ iðRe þ joL Þ ei ei i¼ ¼ Re þ joL Re 1 þ joL L Re


(7.3-6) (7.3-7)

L ¼ T1 (7.3-8) R

(7.3-8)

ei ei ¼ Re ð1 þ joT1 Þ Z ei eo ¼ R e i ¼ ð1 þ joT1 Þ

i¼

(7.3-9) (7.3-10)

For 1 þ joT1 ¼ Z eo 1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ei 1 þ ðoT1 Þ2 ffy ¼ tan1

(7.3-11) (7.3-12) oT1 1

eo 1 oT1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ff y ¼ tan1 ei 1 2 1 þ ðoT1 Þ T1 ¼

1 o1

eo 1 1 o ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ffi ff y ¼ tan o1 ei o 1þ o 1

(7.3-13)

(7.3-14) (7.3-15)

For o ¼ o1 ; ;y ¼ 45 : 1 Amplitude ratio ¼ pffiffiffi ¼ 0:707 2 eo ; ¼ 0:707ff 45 ei An example of a complex plane plot is:


(7.3-16) (7.3-17)

eo ¼ Ki ¼

Re e i ei ei ¼ ¼ Re þ pLi 1 þ RLi p 1 þ RLi s e e

eo 1 ¼ ei ð1 þ tsÞ Z di i dt ei ¼ Re i þ Li þ dt Ca Z d 1 ¼p ðf Þt dt ¼ dt p

(7.3-18) (7.3-19) (7.3-20) (7.3-21)

For sinusoidal input, p ¼ jo ei ¼ i Re þ joLi þ

1 joCa

ei ei joCa ¼ 1 R þ joLi þ joC ½jRoCa þ ðjoÞ2 LCa þ 1 a ei joRCa eo ¼ 2 ½ðjoÞ Li Ca þ joRCa þ 1

i¼

ðjoÞ2 2d Quadratic : þ jo þ 1 2 o sffiffiffiffiffiffiffiffiffiffi o 1 o¼ Li Ca dx dt d2x dx Ma 2 ¼ F kx c dt dt d2x dx Ma 2 þ c þ kx ¼ F dt dt

SF ¼ Ma ¼ F kx c

(7.3-22) (7.3-23) (7.3-24) (7.3-25) (7.3-26) (7.3-27) (7.3-28) (7.3-29) (7.3-30)

For f ¼ F sin ot, the differential d ¼ jo ¼ p dt


(7.3-31)

where p is the differential operator. Ma p2 x þ cpx þ kx ¼ F 2

ðMa p þ cp þ kÞx ¼ F 2

½Ma ðjoÞ þ cjo þ kx ¼ F F F=k x¼ ¼ 2 2 ðjoÞ c ðjoÞ Ma þ joc þ k k=Ma þ jo k þ 1

(7.3-32) (7.3-33) (7.3-34) (7.3-35)

For quadratic: "

# ðjoÞ2 2d þ jo þ 1 o2 o sffiffiffiffiffiffiffi k 2d on ¼ ¼ c=k Ma o c o d¼ k 2 ST ¼ Ja ST ¼ J

d 2 y0 dy0 ¼ GT ðy1 y0 Þ b 2 dt dt

d ¼ p Differential operator dt Jp2 y þ bpy0 þ GT y0 ¼ GT y1 2

½Jp þ bp þ GT y0 ¼ GT y1

(7.3-36)

(7.3-37) (7.3-38)

(7.3-39) (7.3-40) (7.3-41) (7.3-42)

For: y1 ¼ y1 sin ot p ¼ jo ½JðjoÞ2 þ bjo þ GT y0 ¼ GT y1 GT y1 y1 ¼ y0 ¼ 2 2 ðjoÞ b ðjoÞ J þ job þ GT ðGT =JÞ þ GT jo þ 1


(7.3-43) (7.3-44)

For quadratic: "

# ðjoÞ2 2d þ þ1 o2 o rffiffiffiffiffiffiffi GT 2d b o¼ ¼ J o GT b o d¼ GT 2

(7.3-45) (7.3-46) (7.3-47)

Absolute

Vector

jei j ¼ Ri þ xL i

ei ¼ Ri þ jxL i

jei j ¼ jijðRi þ xL Þ jei j ¼ jijðR þ 2pfL Þ

ei ¼ iðR þ jxL Þ ei ¼ iðR þ 2pfL Þ

jei j jij ¼ ðRþoLÞ

ei i ¼ RþjoL

jei j jij ¼ jZj

i ¼ Zei

jei j ffi jij ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2

Rffi i ¼ pi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2

Rjei j ffi jeo j ¼ jijR ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2

R ei eo ¼ iR ¼ RþjoL

jei j jeo j ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 ð1Þ2 þðoRLÞ

eo ¼

di eiðtÞ ¼ Ri þ ff dt d p ¼ dt eiðtÞ ¼ iðtÞ ðR þ LpÞ e

iðtÞ iðtÞ ¼ ðRþLpÞ

e fftan1 XL

R þðoLÞ

R þðoLÞ

R þðoLÞ

L R

Differential

ei

ð1þjoRLÞ

Re

iðtÞ eoðtÞ ¼ iðtÞ R ¼ ðRþLpÞ

eoðtÞ ¼

eiðtÞ

ð1þRLpÞ

¼ T1

jei j jeo j ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðT1 oÞ þð1Þ

iðtÞ eoðtÞ ¼ ðT1 pþ1Þ

eo ¼ ð j oeiþ1Þ

eoðsÞ ¼ ðT1iðsÞ sþ1Þ

o1


e

ei eo ¼ ðT1 joþ1Þ

e

Examples Absolute Case ei ¼ 10 V at 60 Hz R ¼ 5O L ¼ 0:2 H ei 1065 50 50 jeo j ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ ¼ 0:66 V 25 þ 5679 7513 52 þ ð377Þ2 R2 þ ð2pfLÞ2 ei 10 10 10 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi jeo j ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ r ¼ 0:66 V ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ¼ 2 15:1 227 þ 1 0:262pf ðT1 oÞ2 þ 1 þ1 R

Vector Case ei ¼ 10ffy V R ¼ 5O L ¼ 0:2 H f ¼ 60 Hz ei 6R eo ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi R2 þ ðoLÞ2 ff tan1 eo ¼

¼ oL R

10ff0 65 ¼ 0:66ff 86 75:3ff86

10ff0 10ff0 10ff0 ei ¼L ¼ ¼ ¼ 0:66ff 86 T1 jo þ 1 R 2pfj þ 1 15j þ 1 15:1ff86

Differential Case R ¼ 5O L ¼ 0:2 H eiðsÞ eiðsÞ eiðsÞ ¼ ¼ 0:2 eoðsÞ ¼ ðT1 s þ 1Þ ð0:04 s þ 1Þ 5 sþ1


For the Case of Sinusoidal Input eiðtÞ ¼ E sin ot E ¼ 10 V Eo eiðsÞ ¼ 2 ðs þ o2 Þ Eo 25610o eoðsÞ ¼ 2 ¼ ðs þ o2 Þð0:04 s þ 1Þ ðs2 þ o2 Þðs þ 25Þ " # e25t sinðot yÞ eoðtÞ ¼ 250o þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð25Þ2 þ o2 o ð25Þ2 þ o2 o ¼ 377

e25t sinðot yÞ eoðtÞ ¼ 2506377 þ 142;750 142;440 1 o Phase ¼ y ¼ tan 25 y ¼ 86

E 25t

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