Landau / Tomizuka / Auslander Adaptive Systems in Control and Signal Processing 1983

Proceedings of the IFAC Workshop, San Francisco, USA, 20-22 June 1983
1. Auflage 2014
ISBN: 978-1-4831-9065-5
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 388 Seiten

Adaptive Systems in Control and Signal Processing 1983 is a compendium of papers presented at the International Federation of Automatic Control in San Francisco on June 20-22, 1983. One paper addresses the results through comparative alternative algorithms in adaptive control of linear time invariant and time varying systems. Another paper presents a method in computer simulation of a wide range of stable plants to achieve an alternative approach in designing an adaptive control system. The book also compares the stability and the sensitivity approach involving the design of model-reference adaptive systems. The authors involved explain that the sensitivity concept determines the 'dynamic speed of adaptation,' while the stability concept focuses on finding a linear compensator for any deviant signal. One paper proposes an indirect adaptive control algorithm for MIMO square full rank minimum phase systems, while another paper discusses the application of the discrete time multivariable adaptive control system, to non-minimum phase plants with an unknown dead time. This book can prove valuable to engineers and researchers of electrical, computer, and mechanical engineering. It can also be helpful for technicians and students dealing with automatic control and telecontrol.

Autoren/Hrsg.

Landau, I. D.

Tomizuka, M.

Auslander, D. M.

Inhaltsverzeichnis

1;Front Cover;1
2;Adaptive Systems in Control and Signal Processing 1983;4
3;Copyright Page;5
4;Table of Contents;8
5;IFAC WORKSHOP ON ADAPTIVE SYSTEMSIN CONTROL AND SIGNAL PROCESSING 1983;6
6;FOREWORD;7
7;PART 1: PLENARY SESSION 1;14
7.1;CHAPTER 1. ADAPTIVE CONTROL OF A CLASS OF LINEAR TIME VARYING SYSTEMS;14
7.1.1;1. INTRODUCTION;14
7.1.2;2. A NEW PERSISTENCY OF EXCITATION CONDITION;15
7.1.3;3. CONVERGENCE OF A POLE ASSIGNMENT ALGORITHM IN THE TIME INVARIANT CASE;16
7.1.4;4. JUMP PARAMETERS;17
7.1.5;5. DRIFT PARAMETERS;18
7.1.6;6. SIMULATION STUDIES;18
7.1.7;7. CONCLUSIONS;18
7.1.8;REFERENCES;19
7.2;CHAPTER 2. ADAPTIVE SIGNAL PROCESSING FOR ADAPTIVE CONTROL;20
7.2.1;INTRODUCTION;20
7.2.2;ADAPTIVE FILTERING;21
7.2.3;PLANT MODELING;21
7.2.4;PLANT INVERSE MODELING;21
7.2.5;INVERSE MODELING OFNONMINIMUM PHASE PLANTS;21
7.2.6;ADAPTIVE INVERSE CONTROL SCHEME;21
7.2.7;MODEL REFERENCE ADAPTIVE CONTROL SYSTEM;22
7.2.8;OFF-LINE MODEL REFERENCE INVERSE CONTROL;22
7.2.9;CONCLUSION;22
7.2.10;REFERENCES;23
7.3;CHAPTER 3. ROBUSTNESS ISSUES IN ADAPTIVE CONTROL;26
7.3.1;1. INTRODUCTION;26
7.3.2;2. GENERAL FRAMEWORK;27
7.3.3;3. ADAPTIVE ERROR MODEL;28
7.3.4;4. CONDITIONS FOR GLOBAL STABILITY;29
7.3.5;5. CONDITIONS FOR LOCAL STABILITY;30
7.3.6;6. CONCLUDING REMARKS;30
7.3.7;REFERENCES;31
7.4;CHAPTER 4. ROBUST REDESIGN OF ADAPTIVE CONTROL IN THE PRESENCE OF DISTURBANCES AND UNMODELED DYNAMICS;32
7.4.1;Abstract;32
7.4.2;Introduction;32
7.4.3;I. A Scalar Adaptive Control Problem;32
7.4.4;II. Adaptive Control with Unmodeled Dynamics and Disturbances;35
7.4.5;Acknowledgement;37
7.4.6;References;37
7.5;CHAPTER 5. MODEL REFERENCE ADAPTIVE CONTROL OF MECHANICAL MANIPULATORS;40
7.5.1;INTRODUCTION;40
7.5.2;MANIPULATOR MODEL;40
7.5.3;APPLICATION OF CONTINUOUS TIME MRAC;41
7.5.4;APPLICATION OF DISCRETE TIME MRAC;41
7.5.5;CONCLUSIONS;44
7.5.6;ACKNOWLEDGEMENT;44
7.5.7;REFERENCES;44
8;PART 2: ROBUSTNESS OF ADAPTIVE CONTROL ALGORITHMS;46
8.1;CHAPTER 6. DISTURBANCE CANCELLATION AND DRIFT OF ADAPTIVE GAINS;46
8.1.1;1. Introduction;46
8.1.2;2. Drift of Controller Gains;46
8.1.3;3. Simulation;47
8.1.4;References;47
8.2;CHAPTER 7. ON THE MODEL-PROCESS MISMATCH TOLERANCE OF VARIOUS PARAMETER ADAPTATION ALGORITHMS IN DIRECT CONTROL SCHEMES: A SECTORICITY APPROACH;48
8.2.1;INTRODUCTION;48
8.2.2;PARAMETER ADAPTATION ALGORITHMS: SECTOR PROPERTIE;51
8.2.3;CONCLUSIONS;53
8.2.4;REFERENCE;53
8.3;CHAPTER 8. A FREQUENCY DOMAIN ANALYSIS OF DIRECT ADAPTIVE POLE PLACEMENT ALGORITHMS IN THE PRESENCE OF UNMODELLED DYNAMICS;56
8.3.1;I. INTRODUCTION;56
8.3.2;II. PROBLEM FORMULATION AND BACKGROUND;56
8.3.3;III. FIXED CONTROL AND UNMODELLED DYNAMICS;58
8.3.4;VI. IDENTIFICATION MODELS AND UNMODELLED DYNAMICS;59
8.3.5;V. PARAMETER ESTIMATION AND UNMODELLED DYNAMICS;60
8.3.6;VI. CONCLUDING REMARKS;60
8.3.7;REFERENCES;61
8.4;CHAPTER 9. ANALYSIS OF ROBUSTNESS OF THE INEXACT MODEL MATCHING STRUCTURE TO REDUCED ORDER MODELLING;62
8.4.1;I. INTRODUCTION;62
8.4.2;II. DESCRIPTION OF THE PROBLEM;64
8.4.3;III. MATHEMATICAL DESCRIPTION OF THE SYSTEM;64
8.4.4;IV. PROOF OF STABILITY;65
8.4.5;V. CONCLUSIONS;67
8.4.6;REFERENCES;67
8.5;CHAPTER 10. ROBUSTNESS OF INDIRECT ADAPTIVE CONTROL BASED ON POLE PLACEMENT DESIGN;68
8.5.1;INTRODUCTION;68
8.5.2;ROBUSTNESS PROBLEM STATEMENT;68
8.5.3;ADAPTIVE CONTROL;69
8.5.4;CONCLUSION;70
8.5.5;REFERENCES;71
8.6;CHAPTER 11. AN ON-LINE METHOD FOR IMPROVEMENT OF THE ADAPTATION TRANSIENTS IN ADAPTIVE CONTROL;74
8.6.1;INTRODUCTION;74
8.6.2;DERIVATION OF THE ES;74
8.6.3;OPTIMIZATION OF THE ES AND CORRECTING ACTION THE c(.)-AP;76
8.6.4;CONCLUSION;77
8.6.5;ACKNOWLEDGMENTS;78
8.6.6;REFERENCES;78
9;PART 3: POSTER SESSION;80
9.1;CHAPTER 12. DESIGN OF MODEL-REFERENCE ADAPTIVE SYSTEMS — A COMPARISON OF THE STABILITY AND THE SENSITIVITY APPROACH;80
9.1.1;ABSTRACT;80
9.1.2;1. INTRODUCTION;80
9.1.3;2. THE SENSITIVITY APPROACH;80
9.1.4;3. THE STABILITY APPROACH;81
9.1.5;4. SIMULATIONS;81
9.1.6;5. CONCLUSIONS;81
9.1.7;6. REFERENCES;81
9.2;CHAPTER 13. ADAPTIVE MODEL REFERENCE PARAMETER TRACKING TECHNIQUE FOR AIRCRAFT;82
9.2.1;INTRODUCTION;82
9.2.2;PROPOSED ADAPTATION TECHNIQUE;82
9.2.3;MATHEMATICAL MODEL OF AIRCRAFT SYSTEM;84
9.2.4;ADAPTIVE PROPOSAL FOR THE AIRCRAFT SYSTEM;85
9.2.5;CONCLUSION;85
9.2.6;REFERENCES;85
9.3;CHAPTER 14. REDUCED CONTROL EFFORT FOR SELF-TUNING REGULATORS VIA AN INPUT WINDOW;88
9.3.1;INTRODUCTION;88
9.3.2;THE SELF-TUNING REGULATOR;88
9.3.3;INPUT WINDOW CONTROL;89
9.3.4;SIMULATION RESULTS;90
9.3.5;CONCLUSIONS;90
9.3.6;REFERENCES;90
9.4;CHAPTER 15. ADAPTIVE CONTROL WITH FEEDFORWARD COMPENSATION AND REDUCED REFERENC EMODEL;92
9.4.1;INTRODUCTION;92
9.4.2;THE PROPOSED CONTROL ALGORITHM;92
9.4.3;CONCLUSIONS;93
9.4.4;REFERENCES;93
9.5;CHAPTER 16. ON A CLASS OF ADAPTIVE PID REGULATORS;94
9.5.1;INTRODUCTION;94
9.5.2;CONCLUSION;95
9.5.3;REFERENCES;95
9.6;CHAPTER 17. ROBUST DESIGN OF ADAPTIVE OBSERVERS IN THE PRESENCE OF PARASITICS;96
9.6.1;INTRODUCTION;96
9.6.2;PROBLEM FORMULATION;96
9.6.3;REDUCED OKDEK PLANT MODEL;97
9.6.4;ADAPTIVE OBSERVER DESIGN;97
9.6.5;NUMERICAL SIMULATION RESULTS;99
9.6.6;CONCLUSIONS;100
9.6.7;ACKNOWLEDGEMENT;100
9.6.8;REFERENCES;100
9.7;CHAPTER 18. IDENTIFICATION OF A pH PROCESS REPRESENTED BY A NONLINEAR WIENER MODEL;104
9.7.1;INTRODUCTION;104
9.7.2;PROBLEM FORMULATION;104
9.7.3;IDENTIFICATION SCHEME;105
9.7.4;SIMULATION RESULTS;106
9.7.5;EXPERIMENTAL RESULTS;107
9.7.6;CONCLUSIONS;107
9.7.7;REFERENCES;108
9.8;CHAPTER 19. DEADBEAT ADAPTIVE CONTROL IN FEEDBACK;110
9.8.1;PROBLEM DESCRIPTION;110
9.8.2;ADAPTIVE CONTROL AND SYSTEM OBSERVER;110
9.8.3;NUMERICAL EXAMPLES;111
9.8.4;REFERENCES;111
9.9;CHAPTER 20. INFORMATION-THEORETIC ASPECTS OF PARAMETER ESTIMATION;112
9.9.1;INTRODUCTION;112
9.9.2;NOTATION AND DEFINITIONS;112
9.9.3;SOME BAYESIAN ESTIMATION ALGORITHMS;113
9.9.4;RESULTS;114
9.9.5;REFERENCES;115
9.10;CHAPTER 21. MODEL UPDATING IMPROVES PERFORMANCE OF AN MRAC DESIGN;116
9.10.1;INTRODUCTION;116
9.10.2;UPDATE CRITERIA;116
9.10.3;APPLICATION;117
9.10.4;REFERENCES;117
9.11;CHAPTER 22. ADAPTIVE CONTROL FOR A NONLINEAR FERMENTATION PROCESS;118
9.11.1;INTRODUCTION;118
9.11.2;LINEARIZATION VIA O.C;118
9.11.3;ADAPTIVE CONTROL;119
9.11.4;FERMENTATION PROCESS MODEL;119
9.11.5;EXPERIMENTAL RESULTS;120
9.11.6;COMMENTS;120
9.11.7;CONCLUSION;120
9.11.8;REFERENCES;121
9.12;CHAPTER 23. ADAPTIVE MULTIVARIABLE CONTROL APPLIED TO A BINARY DISTILLATION COLUMN;122
9.12.1;INTRODUCTION;122
9.12.2;PROCESS DESCRIPTION;123
9.12.3;ALGORITHMS;123
9.12.4;CONTROL IMPLEMENTATION;124
9.12.5;CONCLUSIONS;125
9.12.6;ACKNOWLEDGEMENT;125
9.12.7;REFERENCES;125
9.13;CHAPTER 24. MINIMUM VARIANCE CONTROL FOR MULTIVARIABLE SYSTEMS WITH DIFFERENT DEADTIMES IN INDIVIDUAL LOOPS;128
9.13.1;INTRODUCTION;128
9.13.2;DERIVATION OF GENERALIZED MINIMUM VARIANCE CONTROLLER;129
9.13.3;REFERENCES;130
9.14;CHAPTER 25. SOME RESULTS ON INFINITE HORIZON LQG ADAPTIVE CONTROL;132
9.14.1;INTRODUCTION AND DEVELOPMENT OF THE SYSTEM IMPLICIT MODEL;132
9.14.2;THE ADAPTIVE CONTROL ALGORITHM;133
9.14.3;ACKNOWLEDGMENT;134
9.14.4;REFERENCES;134
9.15;CHAPTER 26. MODEL REFERENCE ADAPTIVE CONTROL SYSTEM OF A CATALYTIC FLUIDIZED BED REACTOR;136
9.15.1;INTRODUCTION;136
9.15.2;PROCESS DESCRIPTION;136
9.15.3;MODEL REFERENCE ADAPTATIVE SCHEME;137
9.15.4;CONTROL HARDWARE AND SOFTWARE;138
9.15.5;REAL TIME CONTROL EXPERIMENTS;138
9.15.6;CONCLUSION;139
9.15.7;REFERENCES;139
9.16;CHAPTER 27. ODE METHOD VERSUS MARTINGALE CONVERGENCE THEORY;140
9.16.1;Introduction;140
9.16.2;Conclusion;141
9.16.3;References;141
9.17;CHAPTER 28. ADAPTIVE CONTROL OF NON-LINEAR BACTERIAL GROWTH SYSTEMS;142
9.17.1;0. INTRODUCTION;142
9.17.2;1. DESCRIPTION OF THE MODEL;142
9.17.3;3. DEPOLLUTION CONTROL;143
9.17.4;4. METHANE GAS PRODUCTION CONTROL;144
9.17.5;5. PREVENTING A WASH-OUT;144
9.17.6;6. CONCLUSIONS;144
9.17.7;8. REFERENCES;145
9.18;CHAPTER 29. SEQUENTIAL DETECTION OF ABRUPT CHANGES IN ARMA MODELS;148
9.18.1;INTRODUCTION;148
9.18.2;THE EXTENDED KALMAN FILTER;148
9.18.3;DETECTION;149
9.18.4;CONCLUSION;149
10;PART 4: PLENARY SESSION;150
10.1;CHAPTER 30. LQG SELF-TUNERS;150
10.1.1;1. INTRODUCTION;150
10.1.2;2. LQG DESIGN;150
10.1.3;3. PARAMETER ESTIMATION;152
10.1.4;4. SELF-TUNING CONTROL;152
10.1.5;5 . THEORETICAL ISSUES;153
10.1.6;6. ROBUSTNESS;154
10.1.7;7. AN APPLICATION;155
10.1.8;8. REFERENCES;157
10.2;CHAPTER 31. ADAPTIVE CONTROLLERS FOR DISCRETE-TIME SYSTEMS WITH ARBITRARY ZEROS. A SURVEY;160
10.2.1;INTRODUCTION;160
10.2.2;KNOWN PARAMETER CASE;160
10.2.3;ADAPTIVE CASE;162
10.2.4;STABILITY RESULTS;164
10.2.5;CONCLUSIONS;165
10.2.6;REFERENCES;165
10.3;CHAPTER 32. PARAMETRIZATIONS FOR MULTIVARIABLE ADAPTIVE SYSTEMS;168
10.3.1;INTRODUCTION;168
10.3.2;1. NOTATIONS AND PRELIMINARIES;168
10.3.3;2. SOME FACTORIZATIONS OF T(z);169
10.3.4;3. COMPARISON OF MULTIVARIABLE ADAPTIVE CONTROL SCHEMES;171
10.3.5;CONCLUDING REMARKS;174
10.3.6;REFERENCES;175
10.4;CHAPTER 33. LATTICE STRUCTURES FOR FACTORIZATION OF SAMPLE COVARIANCE MATRICES;176
10.4.1;1. INTRODUCTION;176
10.4.2;2. OFF-LINE FACTORIZATION OF THE COVARINACE MATRIX;178
10.4.3;3. ADAPTIVE FACTORIZATION OF THE COVARIANCE MATRIX;178
10.4.4;4. CONCLUSIONS;179
10.4.5;REFERENCES;179
10.4.6;APPENDIX;180
10.5;CHAPTER 34. REAL TIME VIBRATION CONTROL OF ROTATING CIRCULAR PLATES BY TEMPERATURE CONTROL AND SYSTEM IDENTIFICATION;184
10.5.1;INTRODUCTION;184
10.5.2;CRITICAL SPEEDS;184
10.5.3;CONTROL;185
10.5.4;EXPERIMENT;187
10.5.5;CONCLUSIONS;188
10.5.6;NOMENCLATURE;188
10.5.7;ACKNOWLEDGEMENT;191
11;PART 5: STOCHASTIC ADAPTIVE CONTROL;192
11.1;CHAPTER 35. ADAPTIVE CONTROL AND IDENTIFICATION FOR STOCHASTIC SYSTEMS WITH RANDOM PARAMETERS;192
11.1.1;INTRODUCTION;192
11.1.2;THE STOCHASTIC SYSTEM AND THE ADAPTIVE CONTROL ALGORITHM;192
11.1.3;ASYMPTOTICALLY OPTIMAL CONTROL: RANDOM AR PARAMETERS;194
11.1.4;EXTENSION TO THE CASE OF RANDOM MOVING AVERAGE PARAMETERS;196
11.1.5;CONSISTENCY;197
11.1.6;REFERENCES;197
11.2;CHAPTER 36. NEW SYNTHESIS TECHNIQUES FOR FINITE TIME STOCHASTIC ADAPTIVE CONTROLLERS;198
11.2.1;1. INTRODUCTION;198
11.2.2;2. STOCHASTIC CONTROL PROBLEM;199
11.2.3;3. METHOD OF UTILITY COSTS;199
11.2.4;4. A NEW CLASS OF ACTIVE ADAPTIVE CONTROLLERS;200
11.2.5;5. CONCLUSION;203
11.2.6;6. REFERENCES;204
11.3;CHAPTER 37. SUBOPTIMAL CONTROL LAWS OF MARKOV CHAINS: A STOCHASTIC APPROXIMATION APPROACH;206
11.3.1;1. INTHODUCTIQN;206
11.3.2;2. ASSUMPTIONS AND THE ALGORITHM;207
11.3.3;3. MATHEMATICAL BACKGROUND ON WEAK CONVERGENCE THEORY;208
11.3.4;4. SOME PRELlMINARY RESULTS;208
11.3.5;5. TIGHTNESS OF {Xn, n=0};209
11.3.6;6, TIGHTNESS OF {xn(.), n=0};209
11.3.7;7. CONVERGENCE OF THE ALGORITHM;211
11.3.8;8. CONCLUSIONS;211
11.3.9;ACKNOWLEDGEMENTS;211
11.3.10;REFERENCES;211
11.4;CHAPTER 38. AN EFFICIENT NONLINEAR FILTER WITH APPLICATION EXPERIENCES ON MULTIVARIABLE ADAPTIVE CONTROL AND FAULT DETECTION;212
11.4.1;INTRODUCTION;212
11.4.2;THE FILTER ALGORITHM;212
11.4.3;USE IN SIMULTANEOUS STATE AND PARAMETER ESTIMATION;215
11.4.4;APPLICATIONS IN MULTIVARIABLE ADAPTIVE CONTROL;216
11.4.5;APPLICATION IN SENSOR/ACTUATOR FAULT DETECTION;217
11.4.6;CONCLUSIONS;218
11.4.7;REFERENCES;218
11.5;CHAPTER 39. A MV ADAPTIVE CONTROLLER FOR PLANTS WITH TIME-VARYING I/O TRANSPORT DELAY;220
11.5.1;1. INTRODUCTION;220
11.5.2;2. PROBLEM FORMULATION AND THE MV-MUSMAR SELF-TUNER;221
11.5.3;3. THE MV FEEDBACK AS A POSSIBLE CONVERGENCE POINT;222
11.5.4;4. FINAL REMARKS AND CONCLUSIONS;223
11.5.5;REFERENCES;224
11.6;CHAPTER 40. THE PROBLEM OF FORGETTING OLD DATA IN RECURSIVE ESTIMATION;226
11.6.1;INTRODUCTION;226
11.6.2;TRADITIONAL METHODS;226
11.6.3;A NEW METHOD;226
11.6.4;CONCLUSIONS;227
11.6.5;REFERENCES;227
12;PART 6: ADAPTIVE SIGNAL PROCESSING;228
12.1;CHAPTER 41. THE OVERDETERMINED RECURSIVE INSTRUMENTAL VARIABLE METHOD;228
12.1.1;INTRODUCTION;228
12.1.2;PROBLEM FORMULATION;228
12.1.3;DERIVATION OF THE ORIV ALGORITHM;229
12.1.4;SIMULATION RESULTS;230
12.1.5;ACKNOWLEDGEMENT;231
12.1.6;REFERENCES;231
12.2;CHAPTER 42. ADAPTIVE IDENTIFICATION OF STOCHASTIC TRANSMISSION CHANNELS;234
12.2.1;INTRODUCTION;234
12.2.2;STATEMENT OF THE PROBLEM;235
12.2.3;MOTIVATION AND APPLICATIONS;235
12.2.4;IDENTIFICATION OF THE DETERMINISTIC COMPONENT OF THE OPERATOR;236
12.2.5;IDENTIFICATION OF THE STOCHASTIC OPERATOR;237
12.2.6;CONCLUSIONS;239
12.2.7;REFERENCES;239
12.3;CHAPTER 43. CONVERGENCE PROPERTIES FOR A FAMILY OF BOUNDED· FIXED STEP-SIZE ALGORITHMS;242
12.3.1;INTRODUCTION;242
12.3.2;ANALYSIS;242
12.3.3;EXAMPLE;243
12.3.4;CONCLUSION;243
12.3.5;ACKNOWLEDGMENT;243
12.3.6;REFERENCES;243
12.4;CHAPTER 44. A STUDY OF ADPCM USING AN RML PARAMETER ESTIMATOR;244
12.4.1;1. Introduction;244
12.4.2;2. Open Issues and Practical Concerns;244
12.4.3;3. References;245
12.5;CHAPTER 45. PERFORMANCE OF AN ADAPTIVE ARRAY PROCESSOR SUBJECTED TO TIME-VARYING INTERFERENCE;246
12.5.1;1. INTRODUCTION;246
12.5.2;2. STABILITY;248
12.5.3;3. STEADY-STATE PARAMETER-ERROR COVARIANCE;249
12.5.4;4. SUMMARY AND CONCLUSIONS;251
12.5.5;REFERENCES;252
12.6;CHAPTER 46. ADAPTIVE TECHNIQUES FOR TIME DELAY ESTIMATION AND TRACKING;256
12.6.1;INTRODUCTION;256
12.6.2;ADAPTIVE DELAY ESTIMATION USING THE ALL-PASS FILTER;257
12.6.3;ADAPTIVE DELAY ELEMENT;259
12.6.4;EXPERIMENTAL RESULTS;259
12.6.5;CONCLUSIONS;260
12.6.6;REFERENCES;260
12.7;CHAPTER 47. ADAPTIVE ESTIMATOR OF A FILTER AND ITS INVERSE;262
12.7.1;INTRODUCTION;262
12.7.2;CONCLUSIONS;264
12.7.3;REFERENCES;264
13;PART 7: ROBUSTNESS OF ADAPTIVE CONTROL ALGORITHMS 2;266
13.1;CHAPTER 48. EFFECTS OF MODEL STRUCTURE, NONZERO D.C.-VALUE AND MEASUREABLE DISTURBANCE ON ADAPTIVE CONTROL;266
13.1.1;INTRODUCTION;266
13.1.2;DISCRETE-TIME MULTIVARIABLE ADAPTIVE CONTROL ALGORITHMS;267
13.1.3;SIMULATION RESULTS AND DISCUSSION;268
13.1.4;CONCLUSIONS;270
13.1.5;REFERENCES;270
13.2;CHAPTER 49. HOPF BIFURCATION IN AN ADAPTIVE SYSTEM WITH INMODELED DYNAMICS;274
13.2.1;1. Introduction;274
13.2.2;2. Nonlinear Instability;274
13.2.3;3. A Modified Scheme;274
13.2.4;4. Concluding Remarks;275
13.2.5;References;275
13.3;CHAPTER 50. DESIGN OF ADAPTIVE TRACKING SYSTEMS FOR PLANTS OF UNKNOWN ORDER;276
13.3.1;1. INTRODUCTION;276
13.3.2;2. PROBLEM STATEMENT;276
13.3.3;3. A REDUCED ORDER ADAPTIVE OBSERVER;276
13.3.4;4. ADAPTIVE CONTROL;277
13.3.5;4. CONCLUSION;277
13.3.6;REFERENCES;277
13.4;CHAPTER 51. REDUCED ORDER ADAPTIVE POLE PLACEMENT FOR MULTIVARIABLE SYSTEMS;278
13.4.1;1. INTRODUCTION;278
13.4.2;2. THE pxl CASE;278
13.4.3;3. THE pxm CASE;279
13.4.4;4. CONCLUSIONS;280
13.4.5;REFERENCES;280
13.5;CHAPTER 52. SOME PRACTICAL SOLUTIONS FOR THE ROBUSTNESS PROBLEM OF MULTIVARIABLE ADAPTIVE CONTROL;282
13.5.1;I. Introduction;282
13.5.2;II. The controlled system mathematical model;282
13.5.3;III. The control scheme ideas;282
13.5.4;IV. Conclusions;283
13.5.5;V. References;283
14;PART 8: NEW ALGORITHMS;284
14.1;CHAPTER 53. AUTOMATIC TUNING OF SIMPLE REGULATORS FOR PHASE AND AMPLITUDE MARGINS SPECIFICATIONS;284
14.1.1;1. INTRODUCTION;284
14.1.2;2. THE BASIC IDEA;284
14.1.3;3. AMPLITUDE MARGIN AUTO-TUNERS;285
14.1.4;4. PHASE MARGIN AUTO-TUNERS;286
14.1.5;5. EXPERIMENTS;287
14.1.6;6. LIMITATIONS;288
14.1.7;7. CONCLUSIONS;288
14.1.8;8. ACKNOWLEDGEMENTS;289
14.1.9;9. REFERENCES;289
14.2;CHAPTER 54. ROBUSTNESS OF MULTIVARIABLE NON-LINEAR ADAPTIVE FEEDBACK STABILIZATION;290
14.2.1;INTRODUCTION;290
14.2.2;PROBLEM STATEMENT;291
14.2.3;DECENTRALIZED STABILIZATION;291
14.2.4;EVENTUAL STABILITY;292
14.2.5;FIRST AMELIORATION;293
14.2.6;SECOND AMELIORATION;294
14.2.7;CENTRALIZED CONTROL;294
14.2.8;CONCLUSION;295
14.2.9;REFERENCES;295
14.3;CHAPTER 55. ADAPTIVE MODEL ALGORITHMIC CONTROL;296
14.3.1;INTRODUCTION;296
14.3.2;PHASE AND GAIN MARGINS;297
14.3.3;PLANT ROBUSTNESS ANALYSIS;298
14.3.4;CLOSED-LOOP IDENTIFICATION;300
14.3.5;REFERENCES;300
14.4;CHAPTER 56. DESIGN OF DISCRETE-TIME ADAPTIVE SYSTEMS BASED ON NONLINEAR PROGRAMMING;302
14.4.1;INTRODUCTION;302
14.4.2;DESIGN OF ADAPTIVE OBSERVER;302
14.4.3;DESIGN QF ADAPTIVE CONTROLLER;306
14.4.4;CONCLUSION;307
14.4.5;REFERENCE:;307
14.5;CHAPTER 57. A STABLE ADAPTIVE CONTROL FOR LINEAR PLANT WITH UNKNOWN RELATIVE DEGREE;308
14.5.1;INTRODUCTION;308
14.5.2;CONTROL SYSTEM;309
14.5.3;PROPERTY;310
14.5.4;DISCUSSION;311
14.5.5;NUMERICAL EXAMPLE;312
14.5.6;CONCLUSION;312
14.5.7;REFERENCES;312
14.6;CHAPTER 58. DISTRIBUTED CONTROL USING SELF-TUNING REGULATORS;314
14.6.1;1. INTRODUCTION;314
14.6.2;2. DISCUSSION OF DECENTRALIZED SELF-TUNING REGULATORS;315
14.6.3;3. SIMULATION RESULTS;317
14.6.4;4. CONCLUSIONS AND FUTURE RESEARCH;319
14.6.5;REFERENCES;319
15;PART 9: APPLICATIONS OF ADAPTIVE CONTROL;322
15.1;CHAPTER 59. APPLICATION OF MULTIVARIABLE MODEL REFERENCE ADAPTIVE CONTROL TO A BINARY DISTILLATION COLUMN;322
15.1.1;INTRODUCTION;322
15.1.2;THE CONTROLLER;322
15.1.3;THE PLANT;324
15.1.4;EXPERIMENTAL RESULTS;324
15.1.5;CONCLUSION;325
15.1.6;REFERENCES;326
15.1.7;ACKNOWLEDGEMENTS;326
15.2;CHAPTER 60. MODEL REFERENCE ADAPTIVE CONTROL OF AN INDUSTRIAL PHOSPHATE DRYING FURNACE;328
15.2.1;INTRODUCTION;328
15.2.2;PROCESS DESCRIPTION;329
15.2.3;PROCESS MODEL;329
15.2.4;PRACTICAL ASPECTS OF THE CONTROL SYSTEM;331
15.2.5;CONCLUSION;332
15.2.6;REFERENCES;332
15.3;CHAPTER 61. ADAPTIVE CONTROL OF CHEMICALE NGINEERING PROCESSES;336
15.3.1;INTHODUCTION;336
15.3.2;EXPERIMENTAL PROCESS;337
15.3.3;THEORY;337
15.3.4;EXPERIMENTAL SPECIFICATIONS;340
15.3.5;RESULTS AND DISCUSSION;340
15.3.6;CONCLUSION;341
15.3.7;REFERENCES;341
15.4;CHAPTER 62. GLOBAL ADAPTIVE POLE PLACEMENT FOR NON-MINIMUM PHASE PLANTS APPLICATION TO A THERMAL PROCESS;344
15.4.1;Introduction;344
15.4.2;II. Pole Placement of a Known Plant;344
15.4.3;III. Parametric Identification;344
15.4.4;IV. Adaptive Pole Placement;344
15.4.5;V. Application to a Thermal Process;345
15.4.6;References;345
15.5;CHAPTER 63. ADAPTIVE CONTROL OF A SYNCHRONOUS GENERATOR;346
15.5.1;1. INTRODUCTION;347
15.5.2;2. OFF-LINE IDENTIFICATION;347
15.5.3;3. ADAPTIVE CONTROL OF THE SYNCHRONOUS GENERATOR;349
15.5.4;BIBLIOGRAPHY;353
16;PART 10: MULTIVARIABLE ADAPTIVE CONTROL;354
16.1;CHAPTER 64. MULTIVARIABLE WEIGHTED MINIMUM VARIANCE SELF-TUNING CONTROLLERS;354
16.1.1;INTRODUCTION;354
16.1.2;SYSTEM DESCRIPTION;354
16.1.3;WEIGHTED MINIMUM VARIANCE CONTROL LAW;355
16.1.4;PERFORMANCE CRITERION;355
16.1.5;EXPLICIT SELF-TUNING CONTROL;355
16.1.6;IMPLICIT SELF-TUNING CONTROL;357
16.1.7;CONCLUSIONS;358
16.1.8;REFERENCES;358
16.2;CHAPTER 65. AN INDIRECT ADAPTIVE CONTROL SCHEME FOR MIMO SYSTEMS;360
16.2.1;1. INTRODUCTION;360
16.2.2;2. NOTATIONS AND PRELIMINARIES;360
16.2.3;3. LINEAR CONTROL SCHEME;360
16.2.4;4. ADAPTIVE CONTROL SCHEME;362
16.2.5;5. CONCLUDING REMARKS;362
16.2.6;REFERENCES;362
16.3;CHAPTER 66. STOCHASTIC ADAPTIVE CONTROL WITH KNOWN AND UNKNOWN INTERACTOR MATRICES;364
16.3.1;1. INTRODUCTION;364
16.3.2;2. MINIMUM VARIANCE CONTROLLER FOR MULTIVARIABLE SYSTEMS;364
16.3.3;3. ADAPTIVE CONTROL SCHEMES;366
16.3.4;4. A SIMPLE CONTROL LAW WHEN THE INTERACTOR MATRIX IS UNKNOWN;366
16.3.5;5. CONCLUSIONS;367
16.3.6;6. REFERENCES;367
16.4;CHAPTER 67. DISCRETE DIRECT MULTIVARIABLE ADAPTIVE CONTROL;370
16.4.1;1. INTRODUCTION;370
16.4.2;2. FORMULATION OF THE PROBLEM;370
16.4.3;3. THE DISCRETE ADAPTIVE ALGORITHM;371
16.4.4;4. STABILITY ANALYSIS;372
16.4.5;5. EXAMPLES;373
16.4.6;CONCLUSIONS;374
16.4.7;REFERENCES;374
16.5;CHAPTER 68. DISCRETE TIME MULTIVARIABLE ADAPTIVE CONTROL FOR NON-MINIMUM PHASE PLANTS WITH UNKNOWN DEAD TIME;376
16.5.1;INTRODUCTION;376
16.5.2;STATEMENT OF PROBLEM;377
16.5.3;CONTROL OF THE KNOWN PLANT;378
16.5.4;ADAPTIVE CONTROL OF THE UNKNOWN PLANT;378
16.5.5;STABILITY OF CONTROL SYSTEM;379
16.5.6;STRUCTURE OF CONTROL SYSTEM;379
16.5.7;SIMULATION RESULTS;380
16.5.8;CONCLUSION;381
16.5.9;REFERENCES;381
17;PART 11: PLENARY SESSION 3 ROUND TABLE DISCUSSION REPORTS;382
17.1;CHAPTER 69. ROUND TABLE DISCUSSION ON ROBUSTNESS OF ADAPTIVE CONTROL;382
17.2;CHAPTER 70. ROUND TABLE DISCUSSION ON ADAPTIVE SIGNAL PROCESSING;384
17.3;CHAPTER 71. ROUND TABLE DISCUSSION ON APPLICATION OF ADAPTIVE CONTROL;386
17.3.1;Can adaptive control be used in industry?;386
17.3.2;Security issues;386
17.3.3;How relevant is the current theoretical research?;386
17.3.4;Education;386
18;AUTHOR INDEX;388

Leseproben

ADAPTIVE CONTROL OF A CLASS OF LINEAR TIME VARYING SYSTEMS

G.C. Goodwin and Eam Khwang Teoh,     Department of Electrical and Computer Engineering, University of Newcastle, NSW 2308, Australia

Abstract

The key contribution of the paper is to develop a new and explicit characterisation of the concept of persistency of excitation for time invariant systems in the presence of possibly unbounded signals. The implication of this result in the adaptive control of a class of linear time varying systems is also investigated. Simulation results are presented comparing alternative algorithms for the adaptive control of time varying systems.

Keywords

Adaptive control

time varying systems

identifiability

least-squares estimation

1 INTRODUCTION

One of the prime motivations for adaptive control is to provide a mechanism for dealing with time varying systems. However, todate, most of the literature deals with time invariant systems, see for example, Feuer and Morse (1978), Narenda and Valavani (1978), Goodwin, Ramadge and Caines (1980, 1981), Morse (1980), Narenda and Lin (1980), Egardt (1980), Landau (1981), Goodwin and Sin (1981), Elliott and Wolovich (1978), Kreisselmeir (1980, 1982).

Some of the algorithms with proven convergence properties for the time invariant case e.g. gradient type algorithms, are suitable, in principle, for slowly timevarying systems. However, other algorithms, e.g. recursive least squares, are unsuitable for the time varying case since the algorithm gain asymptotically approaches zero. For the latter class of algorithms various ad-hoc modifications have been proposed so that parameter time variations can be accommodated. One approach (Astrom, et. al., 1977, Goodwin and Payne, 1977) is to use recursive least squares with exponential data weighting. Various refinements (Astrom (1981) and Wittenmark and Astrom (1982)) of this approach have also been proposed to avoid burst phenomena e.g. by making the weighting factor a function of the observed prediction error (Fortescue, Kershenbaum and Ydstie, 1981).

The basic consequence of using exponential data weighting is that the gain of the least squares algorithm is prevented from going to zero. A similar end result can be achieved in other ways, for example, by resetting the covariance matrix (Goodwin et. al., 1983); by adding an extra term to the covariance update (Vogel and Edgar, 1982); or, by using a finite or oscillating length data window (Goodwin and Payne, 1977).

Another formulation that has been suggested by several authors (Weislander and Wittenmark, 1979) is to model the parameter time variations by a state-space model and then to use the corresponding Kalman filter for estimation purposes. This again corresponds to adding a term to the covariance update. It has also been suggested that some of the algorithms can be combined (Wittenmark (1979)).

Many of the above algorithms, tailored for the time varying case, have been analyzed in the time invariant situation. This is a reasonable first step since one would have little confidence in an algorithm that was not upwards compatible to the latter case. For example, Cordero and Mayne (1981), have shown that the variable forgetting factor one-step-ahead algorithm of Fortescue et. al. (1981) is globally covergent in the time invariant case provided the weighting factor is set to one when the covariance exceeds some prespecified bound. Similar results have been established by Lozano (1982, 1983) (who uses exponential data weighting where the weighting is made a function of the eigenvalues of the covariance matrix) and by Goodwin, Elliott and Teoh (1983) (who use covariance resetting).

With robustness considerations in mind, Anderson and Johnson (1982) and Johnstone and Anderson (1982b) have established exponential convergence, subject to a persistent excitation condition, of various adaptive control algorithms of the model reference type. These results depend explicitly on the stability properties proved elsewhere (e.g. Goodwin, Ramadge and Caines (1980)) for these algorithms in the time invariant case. The additional property of exponential convergence has implications for time varying systems since it has been shown (Anderson and Johnstone (1983)) that exponential convergence implies tracking error and parameter error boundedness when the plant parameters are actually slowly time varying.

For stochastic systems, Caines and Chen (1982) have presented a counterexample showing no stable control law exists when the parameter variations are an independent process. However, if one restricts the class of allowable parameter variations, then it is possible to design stable controllers for example, Caines and Dorer (1980) and Caines (1981) have established global convergence for a stochastic approximation adaptive control algorithm when the parameter variations are modelled as a (convergent) martingale process having bounded variance. Some very preliminary results have also been described (Hersh and Zarrop (1982) for cases when the parameters undergo jump changes at prespecified instants.

In the current paper we make a distinction between jump and drift parameters. “Jump parameters” refers to the case where the parameters undergo large variations infrequently whereas “drift parameters” refers to the case where the parameters undergo small variations frequently.

In section 2, we will develop a new “persistent excitation” condition for systems having possibly unbounded signals. An important aspect of this result is that it does not rely upon first establishing boundedness of the system variables as has been the case with previous results on persistent excitation (see for example Anderson and Johnson (1982)). The result uses a different proof technique but was inspired by a recent proof of global stability for a direct hybrid pole assignment adaptive control algorithm (Elliott, Cristi and Das (1982)).

In the latter work a two-time-frame estimation scheme is employed such that the parameters are updated at every sample point but the control law parameters are updated only every N samples. A similar idea is explicit in Goodwin, Teoh and McInnis (1982) and implicit in Johnstone and Anderson (1982a). We shall also use two-time-frame estimation here and show that this leads to a relatively simple new result on persistency of excitation with possibly unbounded feedback signals.

We will show in section 3 that the new persistent excitation condition allows one to establish global exponential convergence of standard indirect adaptive pole-assignment algorithms in the time invariant case. In section 4 and 5 we discuss the qualitative interpretation of these results for jump and drift parameters respectively. In section 6, we present some simulation studies and give comparisons of different algorithms for time varying adaptive control.

2 A NEW PERSISTENCY OF EXCITATION CONDITION

We shall consider a single input, single output system described as follows:

(t) = a1(t)y(t-1)-a2(t)y(t-2)….-an(t)y(t-n)+b1(t)u(t-1)+….+bn(t)u(t-n) (2.1)

(2.1)

Note that in the above model the parameters depend upon time. In the time invariant case, the model simplifies to the standard deterministic autoregressive moving average model of the form:

(q-1)y(t)=B(q-1)u(t) (2.2)

(2.2)

where q-1 denotes the unit delay operator, and A(q-1), B(q-1) are polynomials of order n.

The model (2.1) can also be expressed in various equivalent forms. For example we can write

(t,q-1)y(t)=B(t,q-1)u(t) (2.3)

(2.3)

The model (2.1) can also be expressed in regression form as

(t)=?(t-1)T?(t) (2.4)

(2.4)

(t-1)T=[-y(t-1),…,-y(t-n),u(t-1),…,u(t-n)] (2.5)

(2.5)

(t)T=[a1(t),…,an(t),b1(t),…,bn(t)] (2.6)

(2.6)

For the moment, we will restrict attention to the time invariant case and state a key controllability result. We shall subsequently use this controllability result to develop a persistency of excitation condition for use in adaptive control.

We first note that in the time invariant case, the regression vector ?(t) defined in equation (2.5) satisfies the following state space model:

(2.7)

F ?(t-1)+G u(t) (2.8)

(2.8)

If we define x(t) as ?(t-1), then we note that we can use the model (2.8) to construct the following non-minimal 2n dimensional state space model for y(t):

(t+1)=F x(t)+G u(t)...