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Summary
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 Notes
Eugene Walach is Director and Senior Researcher of R&D Management at IBM Haifa (Israel) Research Labs.
Table of Contents
Preface | p. xv |
1 The Adaptive Inverse Control Concept | p. 1 |
1.0 Introduction | p. 1 |
1.1 Inverse Control | p. 2 |
1.2 Sample Applications of Adaptive Inverse Control | p. 7 |
1.3 An Outline or Road Map for This Book | p. 22 |
Bibliography | p. 33 |
2 Wiener Filters | p. 40 |
2.0 Introduction | p. 40 |
2.1 Digital Filters, Correlation Functions, z-Transforms | p. 40 |
2.2 Two-Sided (Unconstrained) Wiener Filters | p. 45 |
2.3 Shannon-Bode Realization of Causal Wiener Filters | p. 51 |
2.4 Summary | p. 57 |
Bibliography | p. 57 |
3 Adaptive LMS Filters | p. 59 |
3.0 Introduction | p. 59 |
3.1 An Adaptive Filter | p. 60 |
3.2 The Performance Surface | p. 61 |
3.3 The Gradient and the Wiener Solution | p. 62 |
3.4 The Method of Steepest Descent | p. 64 |
3.5 The LMS Algorithm | p. 65 |
3.6 The Learning Curve and Its Time Constants | p. 67 |
3.7 Gradient and Weight-Vector Noise | p. 67 |
3.8 Misadjustment Due to Gradient Noise | p. 69 |
3.9 A Design Example: Choosing Number of Filter Weights for an Adaptive Predictor | p. 71 |
3.10 The Efficiency of Adaptive Algorithms | p. 74 |
3.11 Adaptive Noise Canceling: A Practical Application for Adaptive Filtering | p. 77 |
3.12 Summary | p. 81 |
Bibliography | p. 84 |
4 Adaptive Modeling | p. 88 |
4.0 Introduction | p. 88 |
4.1 Idealized Modeling Performance | p. 90 |
4.2 Mismatch Due to Use of FIR Models | p. 91 |
4.3 Mismatch Due to Inadequacies in the Input Signal Statistics; Use of Dither Signals | p. 93 |
4.4 Adaptive Modeling Simulations | p. 97 |
4.5 Summary | p. 102 |
Bibliography | p. 108 |
5 Inverse Plant Modeling | p. 111 |
5.0 Introduction | p. 111 |
5.1 Inverses of Minimum-Phase Plants | p. 111 |
5.2 Inverses of Nonminimum-Phase Plants | p. 113 |
5.3 Model-Reference Inverses | p. 117 |
5.4 Inverses of Plants with Disturbances | p. 120 |
5.5 Effects of Modeling Signal Characteristics on the Inverse Solution | p. 126 |
5.6 Inverse Modeling Error | p. 126 |
5.7 Control System Error Due to Inverse Modeling Error | p. 128 |
5.8 A Computer Simulation | p. 130 |
5.9 Examples of Offline Inverse Modeling of Nonminimum-Phase Plants | p. 131 |
5.10 Summary | p. 136 |
6 Adaptive Inverse Control | p. 138 |
6.0 Introduction | p. 138 |
6.1 Analysis | p. 141 |
6.2 Computer Simulation of an Adaptive Inverse Control System | p. 144 |
6.3 Simulated Inverse Control Examples | p. 147 |
6.4 Application to Real-Time Blood Pressure Control | p. 154 |
6.5 Summary | p. 159 |
Bibliography | p. 159 |
7 Other Configurations for Adaptive Inverse Control | p. 160 |
7.0 Introduction | p. 160 |
7.1 The Filtered-X LMS Algorithm | p. 160 |
7.2 The Filtered-[epsilon] LMS Algorithm | p. 165 |
7.3 Analysis of Stability, Rate of Convergence, and Noise in the Weights for the Filtered-[epsilon] LMS Algorithm | p. 170 |
7.4 Simulation of an Adaptive Inverse Control System Based on the Filtered-[epsilon] LMS Algorithm | p. 175 |
7.5 Evaluation and Simulation of the Filtered-X LMS Algorithm | p. 180 |
7.6 A Practical Example: Adaptive Inverse Control for Noise-Canceling Earphones | p. 183 |
7.7 An Example of Filtered-X Inverse Control of a Minimum-Phase Plant | p. 186 |
7.8 Some Problems in Doing Inverse Control with the Filtered-X LMS Algorithm | p. 188 |
7.9 Inverse Control with the Filtered-X Algorithm Based on DCT/LMS | p. 194 |
7.10 Inverse Control with the Filtered-[epsilon] Algorithm Based on DCT/LMS | p. 197 |
7.11 Summary | p. 201 |
Bibliography | p. 208 |
8 Plant Disturbance Canceling | p. 209 |
8.0 Introduction | p. 209 |
8.1 The Functioning of the Adaptive Plant Disturbance Canceler | p. 211 |
8.2 Proof of Optimality for the Adaptive Plant Disturbance Canceler | p. 212 |
8.3 Power of Uncanceled Plant Disturbance | p. 215 |
8.4 Offline Computation of Q[subscript k](z) | p. 215 |
8.5 Simultaneous Plant Modeling and Plant Disturbance Canceling | p. 216 |
8.6 Heuristic Analysis of Stability of a Plant Modeling and Disturbance Canceling System | p. 223 |
8.7 Analysis of Plant Modeling and Disturbance Canceling System Performance | p. 226 |
8.8 Computer Simulation of Plant Modeling and Disturbance Canceling System | p. 229 |
8.9 Application to Aircraft Vibrational Control | p. 234 |
8.10 Application to Earphone Noise Suppression | p. 236 |
8.11 Canceling Plant Disturbance for a Stabilized Minimum-Phase Plant | p. 237 |
8.12 Comments Regarding the Offline Process for Finding Q(z) | p. 248 |
8.13 Canceling Plant Disturbance for a Stabilized Nonminimum-Phase Plant | p. 249 |
8.14 Insensitivity of Performance of Adaptive Disturbance Canceler to Design of Feedback Stabilization | p. 254 |
8.15 Summary | p. 255 |
9 System Integration | p. 258 |
9.0 Introduction | p. 258 |
9.1 Output Error and Speed of Convergence | p. 258 |
9.2 Simulation of an Adaptive Inverse Control System | p. 261 |
9.3 Simulation of Adaptive Inverse Control Systems for Minimum-Phase and Nonminimum-Phase Plants | p. 266 |
9.4 Summary | p. 268 |
10 Multiple-Input Multiple-Output (MIMO) Adaptive Inverse Control Systems | p. 270 |
10.0 Introduction | p. 270 |
10.1 Representation and Analysis of MIMO Systems | p. 270 |
10.2 Adaptive Modeling of MIMO Systems | p. 274 |
10.3 Adaptive Inverse Control for MIMO Systems | p. 285 |
10.4 Plant Disturbance Canceling in MIMO Systems | p. 290 |
10.5 System Integration for Control of the MIMO Plant | p. 292 |
10.6 A MIMO Control and Signal Processing Example | p. 296 |
10.7 Summary | p. 301 |
11 Nonlinear Adaptive Inverse Control | p. 303 |
11.0 Introduction | p. 303 |
11.1 Nonlinear Adaptive Filters | p. 303 |
11.2 Modeling a Nonlinear Plant | p. 307 |
11.3 Nonlinear Adaptive Inverse Control | p. 311 |
11.4 Nonlinear Plant Disturbance Canceling | p. 319 |
11.5 An Integrated Nonlinear MIMO Inverse Control System Incorporating Plant Disturbance Canceling | p. 321 |
11.6 Experiments with Adaptive Nonlinear Plant Modeling | p. 323 |
11.7 Summary | p. 326 |
Bibliography | p. 329 |
12 Pleasant Surprises | p. 330 |
A Stability and Misadjustment of the LMS Adaptive Filter | p. 339 |
A.1 Time Constants and Stability of the Mean of the Weight Vector | p. 339 |
A.2 Convergence of the Variance of the Weight Vector and Analysis of Misadjustment | p. 342 |
A.3 A Simplified Heuristic Derivation of Misadjustment and Stability Conditions | p. 346 |
Bibliography | p. 347 |
B Comparative Analyses of Dither Modeling Schemes A, B, and C | p. 349 |
B.1 Analysis of Scheme A | p. 350 |
B.2 Analysis of Scheme B | p. 351 |
B.3 Analysis of Scheme C | p. 352 |
B.4 A Simplified Heuristic Derivation of Misadjustment and Stability Conditions for Scheme C | p. 356 |
B.5 A Simulation of a Plant Modeling Process Based on Scheme C | p. 358 |
B.6 Summary | p. 359 |
Bibliography | p. 362 |
C A Comparison of the Self-Tuning Regulator of Astrom and Wittemnark with the Techniques of Adaptive Inverse Control | p. 363 |
C.1 Designing a Self-Tuning Regulator to Behave like an Adaptive Inverse Control System | p. 364 |
C.2 Some Examples | p. 366 |
C.3 Summary | p. 367 |
Bibliography | p. 368 |
D Adaptive Inverse Control for Unstable Linear SISO Plants | p. 369 |
D.1 Dynamic Control of Stabilized Plant | p. 370 |
D.2 Adaptive Disturbance Canceling for the Stabilized Plant | p. 372 |
D.3 A Simulation Study of Plant Disturbance Canceling: An Unstable Plant with Stabilization Feedback | p. 378 |
D.4 Stabilization in Systems Having Both Discrete and Continuous Parts | p. 382 |
D.5 Summary | p. 382 |
E Orthogonalizing Adaptive Algorithms: RLS, DFT/LMS, and DCT/LMS | p. 383 |
E.1 The Recursive Least Squares Algorithm (RLS) | p. 384 |
E.2 The DFT/LMS and DCT/LMS Algorithms | p. 386 |
Bibliography | p. 394 |
F A MIMO Application: An Adaptive Noise-Canceling System Used for Beam Control at the Stanford Linear Accelerator Center | p. 396 |
F.1 Introduction | p. 396 |
F.2 A General Description of the Accelerator | p. 396 |
F.3 Trajectory Control | p. 399 |
F.4 Steering Feedback | p. 400 |
F.5 Addition of a MIMO Adaptive Noise Canceler to Fast Feedback | p. 402 |
F.6 Adaptive Calculation | p. 404 |
F.7 Experience on the Real Accelerator | p. 406 |
F.8 Acknowledgements | p. 407 |
Bibliography | p. 407 |
G Thirty Years of Adaptive Neural Networks: Perceptron, Madaline, and Backpropagation | p. 409 |
G.1 Introduction | p. 409 |
G.2 Fundamental Concepts | p. 412 |
G.3 Adaptation - The Minimal Disturbance Principle | p. 428 |
G.4 Error Correction Rules - Single Threshold Element | p. 428 |
G.5 Error Correction Rules - Multi-Element Networks | p. 434 |
G.6 Steepest-Descent Rules - Single Threshold Element | p. 437 |
G.7 Steepest-Descent Rules - Multi-Element Networks | p. 451 |
G.8 Summary | p. 462 |
Bibliography | p. 464 |
H Neural Control Systems | p. 475 |
H.1 A Nonlinear Adaptive Filter Based on Neural Networks | p. 475 |
H.2 A MIMO Nonlinear Adaptive Filter | p. 475 |
H.3 A Cascade of Linear Adaptive Filters | p. 479 |
H.4 A Cascade of Nonlinear Adaptive Filters | p. 479 |
H.5 Nonlinear Inverse Control Systems Based on Neural Networks | p. 480 |
H.6 The Truck Backer-Upper | p. 484 |
H.7 Applications to Steel Making | p. 487 |
H.8 Applications of Neural Networks in the Chemical Process Industry | p. 491 |
Bibliography | p. 493 |
Glossary | p. 495 |
Index | p. 503 |