ellis, g. (2002). observers in control systems - a practical guide

Observers in Control Systems Observers in Control Systems A Practical Guide George Ellis Danaher Corporation Amsterdam Boston London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo This book is printed on acid-free paper. Copyright 2002, Elsevier Science (USA). All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Requests for permission to make copies of any part of the work should be mailed to the following address: Permissions Department, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida, 32887-6777. ACADEMIC PRESS An imprint of Elsevier Science 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA http://www.academicpress.com Academic Press 84 Theobald’s Road, London WC1X 8RR, UK http://www.academicpress.com Library of Congress Control Number: 2002104256 International Standard Book Number: 0-12-237472-X Printed in the United States of America 020304050607MB987654321 To LeeAnn, my loving wife, and our daughter Gretchen, who makes us both proud. Observers in Control Systems ? Acknowledgments xi Safety xiii 1 Control Systems and the Role of Observers 1 1.1 Overview 1 1.2 Preview of Observers 2 1.3 Summary of the Book 4 2 Control-System Background 5 2.1 Control-System Structures 5 2.2 Goals of Control Systems 13 2.3 Visual ModelQ Simulation Environment 17 2.4 Software Experiments: Introduction to Visual ModelQ 18 2.5 Exercises 39 3 Review of the Frequency Domain 41 3.1 Overview of the s-Domain 41 3.2 Overview of the z-Domain 54 3.3 The Open-Loop Method 59 3.4 A Zone-Based Tuning Procedure 62 3.5 Exercises 66 4 The Luenberger Observer: Correcting Sensor Problems 67 4.1 What Is a Luenberger Observer? 67 4.2 Experiments 4A-4C: Enhancing Stability with an Observer 72 4.3 Predictor-Corrector Form of the Luenberger Observer 77 4.4 Filter Form of the Luenberger Observer 78 4.5 Designing a Luenberger Observer 82 4.6 Introduction to Tuning an Observer Compensator 90 4.7 Exercises 95 5 The Luenberger Observer and Model Inaccuracy 97 5.1 Model Inaccuracy 97 5.2 Effects of Model Inaccuracy 100 5.3 Experimental Evaluation 102 5.4 Exercises 114 6 The Luenberger Observer and Disturbances 115 6.1 Disturbances 115 6.2 Disturbance Response 123 6.3 Disturbance Decoupling 129 6.4 Exercises 138 7 Noise in the Luenberger Observer 141 7.1 Noise in Control Systems 141 7.2 Sensor Noise and the Luenberger Observer 145 7.3 Noise Sensitivity when Using Disturbance Decoupling 156 7.4 Reducing Noise Susceptibility in Observer-Based Systems 161 7.5 Exercises 170 8 Using the Luenberger Observer in Motion Control 173 8.1 The Luenberger Observers in Motion Systems 173 8.2 Observing Velocity to Reduce Phase Lag 185 8.3 Using Observers to Improve Disturbance Response 202 8.4 Exercises 212 References 213 A Observer-Based Resolver Conversion in Industrial Servo Systems1 217 B Cures for Mechanical Resonance in Industrial Servo Systems1 227 Introduction 227 Two-Part Transfer Function 228 Low-Frequency Resonance 229 Velocity Control Law 230 Methods of Correction Applied to Low-Frequency Resonance 231 Conclusion 235 Acknowledgments 235 References 235 C European Symbols for Block Diagrams 237 Part I: Linear Functions 237 Part II: Nonlinear Functions 238 D Development of the Bilinear Transformation 241 Bilinear Transformation 241 Prewarping 242 Factoring Polynomials 243 Phase Advancing 243 Solutions to Exercises 245 Chapter 2 245 Chapter 3 245 Chapter 4 246 Chapter 5 246 Chapter 6 247 Chapter 7 248 Chapter 8 249 Index 251 Acknowledgments xi Writing a book is a large task and requires support from numerous people, and those people deserve thanks. First, I thank LeeAnn, my devoted wife of more than 20 years. She has been an unflagging fan, a counselor, and a demanding editor. She taught me much of what I have managed to learn about how to express a thought in ink. Thanks to my mother who was sure I would grow into someone in whom she would be proud when facts should have dissuaded her. Thanks also to my father for his insistence that I obtain a college education; that privilege was denied to him, an intelligent man born into a family of modest means. I am grateful for the education provided by Virginia Tech. Go Hokies. The basics of electrical engineering imparted to me over my years at school allowed me to grasp the concepts I apply regularly today. I am grateful to Mr. Emory Pace, a tough professor who led me through numerous calculus courses and, in doing so, gave me the confidence on which I would rely throughout my college career and beyond. I am especially grateful to Dr. Charles Nunnally; having arrived at university from a successful career in industry, he provided my earliest exposure to the practical application of the material I strove to learn. I also thank Dr. Robert Lorenz of the University of Wisconsin at Madison, who introduced me to observers some years ago. His instruction has been enlightening and practical. Several of his university courses are available in video format and are recommended for those who would like to extend their knowledge of controls. In particular, readers should consider ME 746, which presents observers and numerous other subjects. I thank those who reviewed the manuscript for this book. Special thanks goes to Dan Carlson for his contributions to almost every chapter contained herein. Thanks also to Eric Berg for his numerous insights. Thanks to the people of Kollmorgen Corporation (now, Danaher Corporation), my long-time employer, for their continu- ing support in writing this book. Finally, thanks to Academic Press, especially to Joel Claypool, my editor, for the opportunity to write this edition and for editing, print- ing, distributing, and performing the myriad other tasks required to publish a book. [...]... can be an effective way to simultaneously increase system reliability and reduce cost 2.2.3 Stability Control systems should remain stable in all operating conditions The results of unstable operation are unpredictable; certainly, it is never desirable and in many cases, people may be injured or equipment damaged In addition to maintaining absolute stability, systems must maintain reasonable margins of... is a measure of how well a system maintains its performance when system parameters vary The most common variations occur in the plant As examples, the capacitance of a power supply storage capacitor may vary over time, the rotational 2.3 VISUAL MODELQ SIMULATION ENVIRONMENT inertia of a mechanism may vary during different stages of machine operation, and the amount of fluid in a fluid bath may vary and... temperature change of 5° by generating oscillatory changes of 5° or 10° that die out only after minutes of ringing Such a system may meet an abstract definition of stability, but it would be unacceptable in most industrial applications Margins of stability must be maintained so that performance can be predictable Two common measures of stability, phase margin and gain margin, will be discussed in Chapter... stability; control- law gains often must be reduced to compensate Since margins of stability must be maintained at an acceptable level, the end effect is that filtering often forces control- law gains down Observers can exacerbate problems with sensor-generated noise One reason is that one of the primary benefits of observers is supporting increased control- law gains through the reduction of phase lag... occur Accidents can cause personal injury to you, your co-workers, and other people Accidents can also damage or destroy equipment By operating control systems safely, you decrease the likelihood that an accident will occur Always operate control systems safely! You can enhance the safety of control- system operation by taking the following steps: 1 Allow only people trained in safety-related work practices... stabilize The result is often that system gains must be reduced to maintain stability in order to accommodate slow sensors Reducing gains is usually undesirable because both command and disturbance response degrade Cyclical error is the repeatable error that is induced by sensor imperfections For example, a strain gauge measures strain by monitoring the change in electrical parameters of the gauge material... example, value could be increased by providing a more reliable feedback signal or a more accurate feedback signal that will lead to improved performance Those readers who are leading their companies in the use of observers should expect that they will have to demonstrate the practical advantages of observers if they want the methods to be adopted Bear in mind that observers often produce undesirable characteristics,... material that is seen when the material is deformed The behavior of these parameters for ideal materials is well known However, there are slight differences between an ideal strain gauge and any sample Those differences result in small, repeatable errors in measuring strain Since cyclical errors are deterministic, they can be compensated out in a process where individual samples of sensors are characterized... author developed Visual ModelQ, a stand-alone, graphical, PC-based simulation environment, as a companion to this book The environment provides time-domain and frequency-domain analysis of analog and digital control systems Visual ModelQ is an enhancement of the original ModelQ in that Visual ModelQ allows readers to view and build models graphically More than two dozen Visual ModelQ models were developed... above, observers can increase margins of stability and thus allow incrementally higher gains in the control law 2.2.5 Disturbance Rejection Disturbance rejection is a measure of how well a control system resists the effect of disturbances As with command response, higher gains help the system reject disturbances, but they reduce margins of stability Again, tuning control- law gains requires a compromise . Observers in Control Systems Observers in Control Systems A Practical Guide George Ellis Danaher Corporation Amsterdam Boston London New York Oxford Paris San Diego San Francisco Singapore. feedback signal to generate an error signal. This error signal is fed into a control law such as a proportional-integral (PI) control to generate an excitation command. The excitation command. Observers offer designers an inviting alternative to adding new sensors or upgrading existing ones. This book is written as a guide for the selection and installation of observers in control systems. It