Observers in Control Systems: A Practical Guide

264 Pages·2002·5.504 MB·English

by  George Ellis

Observers in
Control Systems

Observers in
Control Systems
A Practical Guide
George Ellis
Danaher Corporation
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Copyright 2002,Elsevier Science (USA).
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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.
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