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 02 03 04 05 06 07 MB 9 8 7 6 5 4 3 2 1 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 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. xi