Adaptive Inverse Control A Signal Processing Approach

by Widrow, Bernard; Walach, Eugene

• ISBN13: 9780470226094
• ISBN10: 0470226099
• Edition: 1st
• Format: Hardcover
• Copyright: 2007-11-02
• Publisher: Wiley-IEEE Press

Summary

A self-contained introduction to adaptive inverse control Now featuring a revised preface that emphasizes the coverage of both control systems and signal processing, this reissued edition of Adaptive Inverse Control takes a novel approach that is not available in any other book. Written by two pioneers in the field, Adaptive Inverse Control presents methods of adaptive signal processing that are borrowed from the field of digital signal processing to solve problems in dynamic systems control. This unique approach allows engineers in both fields to share tools and techniques. Clearly and intuitively written, Adaptive Inverse Control illuminates theory with an emphasis on practical applications and commonsense understanding. It covers: the adaptive inverse control concept; Weiner filters; adaptive LMS filters; adaptive modeling; inverse plant modeling; adaptive inverse control; other configurations for adaptive inverse control; plant disturbance canceling; system integration; Multiple-Input Multiple-Output (MIMO) adaptive inverse control systems; nonlinear adaptive inverse control systems; and more. Complete with a glossary, an index, and chapter summaries that consolidate the information presented, Adaptive Inverse Control is appropriate as a textbook for advanced undergraduate- and graduate-level courses on adaptive control and also serves as a valuable resource for practitioners in the fields of control systems and signal processing.

Author Biography

Bernard Widrow, PhD, has been Professor of Electrical Engineering at Stanford University for forty years. Together with M.E. Hoff, Jr., Dr. Widrow invented the LMS algorithm, which is now the world's most widely used learning algorithm. He is the recipient of numerous industry awards and holds twenty U.S. or foreign patents. Dr. Widrow has published nearly 200 papers, two of which became Citation Classics.

Eugene Walach, PhD, is Director and Senior Researcher of R&D Management at IBM Haifa (Israel) Research Labs. His research areas include industrial vision-based applications, low-level image analysis, and signal processing. He and Dr. Widrow developed their system of adaptive inverse control.

Table of Contents

Preface	p. xv
The Adaptive Inverse Control Concept	p. 1
Introduction	p. 1
Inverse Control	p. 2
Sample Applications of Adaptive Inverse Control	p. 7
An Outline or Road Map for This Book	p. 22
Bibliography	p. 33
Wiener Filters	p. 40
Introduction	p. 40
Digital Filters, Correlation Functions, z-Transforms	p. 40
Two-Sided (Unconstrained) Wiener Filters	p. 45
Shannon-Bode Realization of Causal Wiener Filters	p. 51
Summary	p. 57
Bibliography	p. 57
Adaptive LMS Filters	p. 59
Introduction	p. 59
An Adaptive Filter	p. 60
The Performance Surface	p. 61
The Gradient and the Wiener Solution	p. 62
The Method of Steepest Descent	p. 64
The LMS Algorithm	p. 65
The Learning Curve and Its Time Constants	p. 67
Gradient and Weight-Vector Noise	p. 67
Misadjustment Due to Gradient Noise	p. 69
A Design Example: Choosing Number of Filter Weights for an Adaptive Predictor	p. 71
The Efficiency of Adaptive Algorithms	p. 74
Adaptive Noise Canceling: A Practical Application for Adaptive Filtering	p. 77
Summary	p. 81
Bibliography	p. 84
Adaptive Modeling	p. 88
Introduction	p. 88
Idealized Modeling Performance	p. 90
Mismatch Due to Use of FIR Models	p. 91
Mismatch Due to Inadequacies in the Input Signal Statistics; Use of Dither Signals	p. 93
Adaptive Modeling Simulations	p. 97
Summary	p. 102
Bibliography	p. 108
Inverse Plant Modeling	p. 111
Introduction	p. 111
Inverses of Minimum-Phase Plants	p. 111
Inverses of Nonminimum-Phase Plants	p. 113
Model-Reference Inverses	p. 117
Inverses of Plants with Disturbances	p. 120
Effects of Modeling Signal Characteristics on the Inverse Solution	p. 126
Inverse Modeling Error	p. 126
Control System Error Due to Inverse Modeling Error	p. 128
A Computer Simulation	p. 130
Examples of Offline Inverse Modeling of Nonminimum-Phase Plants	p. 131
Summary	p. 136
Adaptive Inverse Control	p. 138
Introduction	p. 138
Analysis	p. 141
Computer Simulation of an Adaptive Inverse Control System	p. 144
Simulated Inverse Control Examples	p. 147
Application to Real-Time Blood Pressure Control	p. 154
Summary	p. 159
Bibliography	p. 159
Other Configurations for Adaptive Inverse Control	p. 160
Introduction	p. 160
The Filtered-X LMS Algorithm	p. 160
The Filtered-[epsilon] LMS Algorithm	p. 165
Analysis of Stability, Rate of Convergence, and Noise in the Weights for the Filtered-[epsilon] LMS Algorithm	p. 170
Simulation of an Adaptive Inverse Control System Based on the Filtered-[epsilon] LMS Algorithm	p. 175
Evaluation and Simulation of the Filtered-X LMS Algorithm	p. 180
A Practical Example: Adaptive Inverse Control for Noise-Canceling Earphones	p. 183
An Example of Filtered-X Inverse Control of a Minimum-Phase Plant	p. 186
Some Problems in Doing Inverse Control with the Filtered-X LMS Algorithm	p. 188
Inverse Control with the Filtered-X Algorithm Based on DCT/LMS	p. 194
Inverse Control with the Filtered-[epsilon] Algorithm Based on DCT/LMS	p. 197
Summary	p. 201
Bibliography	p. 208
Plant Disturbance Canceling	p. 209
Introduction	p. 209
The Functioning of the Adaptive Plant Disturbance Canceler	p. 211
Proof of Optimality for the Adaptive Plant Disturbance Canceler	p. 212
Power of Uncanceled Plant Disturbance	p. 215
Offline Computation of Q[subscript k](z)	p. 215
Simultaneous Plant Modeling and Plant Disturbance Canceling	p. 216
Heuristic Analysis of Stability of a Plant Modeling and Disturbance Canceling System	p. 223
Analysis of Plant Modeling and Disturbance Canceling System Performance	p. 226
Computer Simulation of Plant Modeling and Disturbance Canceling System	p. 229
Application to Aircraft Vibrational Control	p. 234
Application to Earphone Noise Suppression	p. 236
Canceling Plant Disturbance for a Stabilized Minimum-Phase Plant	p. 237
Comments Regarding the Offline Process for Finding Q(z)	p. 248
Canceling Plant Disturbance for a Stabilized Nonminimum-Phase Plant	p. 249
Insensitivity of Performance of Adaptive Disturbance Canceler to Design of Feedback Stabilization	p. 254
Summary	p. 255
System Integration	p. 258
Introduction	p. 258
Output Error and Speed of Convergence	p. 258
Simulation of an Adaptive Inverse Control System	p. 261
Simulation of Adaptive Inverse Control Systems for Minimum-Phase and Nonminimum-Phase Plants	p. 266
Summary	p. 268
Multiple-Input Multiple-Output (MIMO) Adaptive Inverse Control Systems	p. 270
Introduction	p. 270
Representation and Analysis of MIMO Systems	p. 270
Adaptive Modeling of MIMO Systems	p. 274
Adaptive Inverse Control for MIMO Systems	p. 285
Plant Disturbance Canceling in MIMO Systems	p. 290
System Integration for Control of the MIMO Plant	p. 292
A MIMO Control and Signal Processing Example	p. 296
Summary	p. 301
Nonlinear Adaptive Inverse Control	p. 303
Introduction	p. 303
Nonlinear Adaptive Filters	p. 303
Modeling a Nonlinear Plant	p. 307
Nonlinear Adaptive Inverse Control	p. 311
Nonlinear Plant Disturbance Canceling	p. 319
An Integrated Nonlinear MIMO Inverse Control System Incorporating Plant Disturbance Canceling	p. 321
Experiments with Adaptive Nonlinear Plant Modeling	p. 323
Summary	p. 326
Bibliography	p. 329
Pleasant Surprises	p. 330
Stability and Misadjustment of the LMS Adaptive Filter	p. 339
Time Constants and Stability of the Mean of the Weight Vector	p. 339
Convergence of the Variance of the Weight Vector and Analysis of Misadjustment	p. 342
A Simplified Heuristic Derivation of Misadjustment and Stability Conditions	p. 346
Bibliography	p. 347
Comparative Analyses of Dither Modeling Schemes A, B, and C	p. 349
Analysis of Scheme A	p. 350
Analysis of Scheme B	p. 351
Analysis of Scheme C	p. 352
A Simplified Heuristic Derivation of Misadjustment and Stability Conditions for Scheme C	p. 356
A Simulation of a Plant Modeling Process Based on Scheme C	p. 358
Summary	p. 359
Bibliography	p. 362
A Comparison of the Self-Tuning Regulator of Astrom and Wittemnark with the Techniques of Adaptive Inverse Control	p. 363
Designing a Self-Tuning Regulator to Behave like an Adaptive Inverse Control System	p. 364
Some Examples	p. 366
Summary	p. 367
Bibliography	p. 368
Adaptive Inverse Control for Unstable Linear SISO Plants	p. 369
Dynamic Control of Stabilized Plant	p. 370
Adaptive Disturbance Canceling for the Stabilized Plant	p. 372
A Simulation Study of Plant Disturbance Canceling: An Unstable Plant with Stabilization Feedback	p. 378
Stabilization in Systems Having Both Discrete and Continuous Parts	p. 382
Summary	p. 382
Orthogonalizing Adaptive Algorithms: RLS, DFT/LMS, and DCT/LMS	p. 383
The Recursive Least Squares Algorithm (RLS)	p. 384
The DFT/LMS and DCT/LMS Algorithms	p. 386
Bibliography	p. 394
A MIMO Application: An Adaptive Noise-Canceling System Used for Beam Control at the Stanford Linear Accelerator Center	p. 396
Introduction	p. 396
A General Description of the Accelerator	p. 396
Trajectory Control	p. 399
Steering Feedback	p. 400
Addition of a MIMO Adaptive Noise Canceler to Fast Feedback	p. 402
Adaptive Calculation	p. 404
Experience on the Real Accelerator	p. 406
Acknowledgements	p. 407
Bibliography	p. 407
Thirty Years of Adaptive Neural Networks: Perceptron, Madaline, and Backpropagation	p. 409
Introduction	p. 409
Fundamental Concepts	p. 412
Adaptation - The Minimal Disturbance Principle	p. 428
Error Correction Rules - Single Threshold Element	p. 428
Error Correction Rules - Multi-Element Networks	p. 434
Steepest-Descent Rules - Single Threshold Element	p. 437
Steepest-Descent Rules - Multi-Element Networks	p. 451
Summary	p. 462
Bibliography	p. 464
Neural Control Systems	p. 475
A Nonlinear Adaptive Filter Based on Neural Networks	p. 475
A MIMO Nonlinear Adaptive Filter	p. 475
A Cascade of Linear Adaptive Filters	p. 479
A Cascade of Nonlinear Adaptive Filters	p. 479
Nonlinear Inverse Control Systems Based on Neural Networks	p. 480
The Truck Backer-Upper	p. 484
Applications to Steel Making	p. 487
Applications of Neural Networks in the Chemical Process Industry	p. 491
Bibliography	p. 493
Glossary	p. 495
Index	p. 503
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