Adaptive Inverse Control: A Signal Processing Approach 0470226099, 9780470226094

Table of contents :
Adaptive Inverse Control: A Signal Processing Approach......Page 0
Contents......Page 5
Preface......Page 10
1.0 Introduction......Page 12
1.1 Inverse Control......Page 13
1.2 Sample Applications of Adaptive Inverse Control......Page 18
1.3 An Outline or Road Map for This Book......Page 33
Bibliography......Page 44
2.1 Digital Filters, Correlation Functions, z-Transforms......Page 51
2.2 Two-sided (Unconstrained) Wiener Filters......Page 56
2.3 Shannon-Bode Realization of Causal Wiener Filters......Page 62
2.4 Summary......Page 68
Bibliography......Page 69
3.0 Introduction......Page 70
3.1 An Adaptive Filter......Page 71
3.2 The Performance Surface......Page 72
3.3 The Gradient and the Wiener Solution......Page 73
3.4 The Method of Steepest Descent......Page 75
3.5 The LMS Algorithm......Page 76
3.7 Gradient and Weight-Vector Noise......Page 78
3.8 Misadjustment Due to Gradient Noise......Page 80
3.9 A Design Example: Choosing Number of Filter Weights for an Adaptive Predictor......Page 82
3.10 The Efficiency of Adaptive Algorithms......Page 85
3.11 Adaptive Noise Canceling: A Practical Application for Adaptive Filtering......Page 88
3.12 Summary......Page 92
Bibliography......Page 95
4.0 Introduction......Page 99
4.1 Idealized Modeling Performance......Page 101
4.2 Mismatch Due to Use of FIR Models......Page 102
4.3 Mismatch Due to Inadequacies in the Input Signal Statistics; Use of Dither Signals......Page 104
4.4 Adaptive Modeling Simulations......Page 108
4.5 Summary......Page 113
Bibliography......Page 119
5.1 Inverses of Minimum-Phase Plants......Page 122
5.2 Inverses of Nonminimum-Phase Plants......Page 124
5.3 Model-Reference Inverses......Page 128
5.4 Inverses of Plants with Disturbances......Page 131
5.6 Inverse Modeling Error......Page 137
5.7 Control System Error Due to Inverse Modeling Error......Page 139
5.8 A Computer Simulation......Page 141
5.9 Examples of Offline Inverse Modeling of Nonminimum-Phase Plants......Page 142
5.10 Summary......Page 147
6.0 Introduction......Page 149
6.1 Analysis......Page 152
6.2 Computer Simulation of an Adaptive Inverse Control System......Page 155
6.3 Simulated Inverse Control Examples......Page 158
6.4 Application to Real-Time Blood Pressure Control......Page 165
Bibliography......Page 170
7.1 The Filtered-X LMS Algorithm......Page 171
7.2 The Filtered-ε LMS Algorithm......Page 176
7.3 Analysis of Stability, Rate of Convergence, and Noise in the Weights for the Filtered-e LMS Algorithm......Page 181
7.4 Simulation of an Adaptive Inverse Control System Based on the Filtered-ε LMS Algorithm......Page 186
7.5 Evaluation and Simulation of the Filtered-X LMS Algorithm......Page 191
7.6 A Practical Example: Adaptive Inverse Control for Noise-Canceling Earphones......Page 194
7.7 An Example of Filtered-X Inverse Control of a Minimum-Phase Plant......Page 197
7.8 Some Problems in Doing Inverse Control with the Filtered-X LMS Algorithm......Page 199
7.9 Inverse Control with the Filtered-X Algorithm Based on DCT/LMS......Page 205
7.10 Inverse Control with the Filtered-ε Algorithm Based on DCT/LMS......Page 208
7.11 Summary......Page 212
Bibliography......Page 219
8.0 Introduction......Page 220
8.1 The Functioning of the Adaptive Plant Disturbance Canceler......Page 222
8.2 Proof of Optimality for the Adaptive Plant Disturbance Canceler......Page 223
8.4 Offline Computation of Qk(z)......Page 226
8.5 Simultaneous Plant Modeling and Plant Disturbance Canceling......Page 227
8.6 Heuristic Analysis of Stability of a Plant Modeling and Disturbance Canceling System......Page 234
8.7 Analysis of Plant Modeling and Disturbance Canceling System Performance......Page 237
8.8 Computer Simulation of Plant Modeling and Disturbance Canceling System......Page 240
8.9 Application to Aircraft Vibrational Control......Page 245
8.10 Application to Earphone Noise Suppression......Page 247
8.11 Canceling Plant Disturbance for a Stabilized Minimum-Phase Plant......Page 248
8.12 Comments Regarding the Offline Process for Finding Q(z)......Page 259
8.13 Canceling Plant Disturbance for a Stabilized Nonminimum-Phase Plant......Page 260
8.14 Insensitivity of Performance of Adaptive Disturbance Canceler to Design of Feedback Stabilization......Page 265
8.15 Summary......Page 266
9.1 Output Error and Speed of Convergence......Page 269
9.2 Simulation of an Adaptive Inverse Control System......Page 272
9.3 Simulation of Adaptive Inverse Control Systems for Minimum-Phase and Nonminimum-Phase Plants......Page 277
9.4 Summary......Page 279
10.1 Representation and Analysis of MIMO Systems......Page 281
10.2 Adaptive Modeling of MIMO Systems......Page 285
10.3 Adaptive Inverse Control for MIMO Systems......Page 296
10.4 Plant Disturbance Canceling in MIMO Systems......Page 301
10.5 System Integration for Control of the MIMO Plant......Page 303
10.6 A MIMO Control and Signal Processing Example......Page 307
10.7 Summary......Page 312
11.1 Nonlinear Adaptive Filters......Page 314
11.2 Modeling a Nonlinear Plant......Page 318
11.3 Nonlinear Adaptive Inverse Control......Page 322
11.4 Nonlinear Plant Disturbance Canceling......Page 330
11.5 An Integrated Nonlinear MIMO Inverse Control System Incorporating Plant Disturbance Canceling......Page 332
11.6 Experiments with Adaptive Nonlinear Plant Modeling......Page 334
11.7 Summary......Page 337
Bibliography......Page 340
12 Pleasant Surprises......Page 341
A.1 Time Constants and Stability of the Mean of the Weight Vector......Page 350
A.2 Convergence of the Variance of the Weight Vector and Analysis of Misadjustment......Page 353
A.3 A Simplified Heuristic Derivation of Misadjustment and Stability Conditions......Page 357
Bibliography......Page 358
B Comparative Analyses of Dither Modeling Schemes A, B, and C......Page 360
B.1 Analysis of Scheme A......Page 361
B.2 Analysis of Scheme B......Page 362
B.3 Analysis of Scheme C......Page 363
B.4 A Simplified Heuristic Derivation of Misadjustment and Stability Conditions for Scheme C......Page 367
B.5 A Simulation of a Plant Modeling Process Based on Scheme C......Page 369
B.6 Summary......Page 370
Bibliography......Page 373
C A Comparison of the Self-Tuning Regulator of Åström and Wittenmark with the Techniques of Adaptive Inverse Control......Page 374
C.1 Designing a Self-Tuning Regulator to Behave like an Adaptive Inverse Control System......Page 375
C.2 Some Examples......Page 377
C.3 Summary......Page 378
Bibliography......Page 379
D Adaptive Inverse Control for Unstable Linear SISO Plants......Page 380
D.1 Dynamic Control of Stabilized Plant......Page 381
D.2 Adaptive Disturbance Canceling for the Stabilized Plant......Page 383
D.3 A Simulation Study of Plant Disturbance Canceling: An Unstable Plant with Stabilization Feedback......Page 389
D.5 Summary......Page 393
E Orthogonalizing Adaptive Algorithms: RLS, DFT/LMS, and DCT/LMS......Page 394
E.1 The Recursive Least Squares Algorithm (RLS)......Page 395
E.2 The DRT/LMS and DCT/LMS Algorithms......Page 397
Bibliography......Page 405
F.2 A General Description of the Accelerator......Page 407
F.3 Trajectory Control......Page 410
F.4 Steering Feedback......Page 411
F.5 Addition of a MIMO Adaptive Noise Canceler to Fast Feedback......Page 413
F.6 Adaptive Calculation......Page 415
F.7 Experience on the Real Accelerator......Page 417
Bibliography......Page 418
G.1 Introduction......Page 420
G.2 Fundamental Concepts......Page 423
G.4 Error Correction Rules — Single Threshold Element......Page 439
G.5 Error Correction Rules — Multi-Element Networks......Page 445
G.6 Steepest-Descent Rules — Single Threshold Element......Page 448
G.7 Steepest-Descent Rules — Multi-Element Networks......Page 462
G.8 Summary......Page 473
Bibliography......Page 475
H.2 A MIMO Nonlinear Adaptive Filter......Page 486
H.4 A Cascade of Nonlinear Adaptive Filters......Page 490
H.5 Nonlinear Inverse Control Systems Based on Neural Networks......Page 491
H.6 The Truck Backer-Upper......Page 495
H.7 Applications to Steel Making......Page 498
H.8 Applications of Neural Networks in the Chemical Process Industry......Page 502
Bibliography......Page 504
Glossary......Page 506
Index......Page 513