Design Methods of Control Systems (eBook)

Front Cover 1
Design Methods of Control Systems 4
Copyright Page 5
Table of Contents 10
INTRODUCTION 8
PART I: PLENARY PAPERS 18
CHAPTER 1. DESIGN AND IMPLEMENTATION OF DIGITAL AND ADAPTIVE CONTROLLERS 18
1. Introduction 18
2. Control Design 18
3. Impact of CAGE 19
4. Connections to External World 20
5. Numerics 21
6· Operational Issues 22
7. Real Time Programming 23
8· References 23
CHAPTER 2. EXTREME POINT RESULTS FOR ROBUST STABILITY OF INTERVAL PLANTS: BEYOND FIRST ORDER COMPENSATORS 24
Abstract 24
1. Introduction 24
2. Underlying Convex Direction Problem 25
3. Definition of the AHMC and the Main Result 26
4. Special Cases of the AHMC 26
5. Extreme Point Results for Interval Plants 27
6. Conclusion 28
Appendix A — Proof of Theorem 3.6 29
References 32
CHAPTER 3. H8-OPTIMIZATION 34
1 INTRODUCTION 34
2 SENSITIVITY 34
3 ROBUSTNESS 35
4 A GENERAL PERTURBATION MODEL 36
5 NUMERATOR-DENOMINATOR PERTURBATIONS 36
6 THE MIXED SENSITIVITY PROBLEM 37
7 EXAMPLE 38
8 THE STANDARD .8-OPTIMAL REGULATION PROBLEM 40
9 FREQUENCY DOMAIN SOLUTION OF THE STANDARD PROBLEM 41
10 STATE SPACE SOLUTION OF THE STANDARD PROBLEM 42
11 CONCLUSIONS 43
References 43
PART II: UNEAR CONTROL SYSTEMS DESIGN 46
CHAPTER 4. A CONTROLLER DESIGN METHOD BASED ON MODEL MATCHING IN THE FREQUENCY DOMAIN 46
INTRODUCTION 46
..DÉ APPROXIMANTS AND MARKOV PARAMETERS 46
THE CONTROLLER DESIGN METHOD 47
NUMERICAL RESULTS 48
CONCLUSIONS 48
ACKNOWLEDGMENTS 49
REFERENCES 49
CHAPTER 5. ON THE DESIGN OF SERVOMECHANISMS VIA H2 OPTIMIZATION 50
1. INTRODUCTION 50
2. SOLUTION TO THE SERVOMECHANISM PROBLEM 51
3. A QUADRATIC OPTIMAL CONTROL PROBLEM 52
4. PROBLEM SOLUTION 53
5. EXAMPLES 54
REFERENCES 55
CHAPTER 6. FREQUENCY-SHAPED LQG/LTR DESIGN: APPLICATION TO THE ROBUST STABILIZATION OF AN HELICOPTER1 56
INTRODUCnON 56
FREQUENCY DOMAIN BEHAVIOUR OF THE LQG REGULATOR 56
FREQUENCY-SHAPED LQ DESIGN 57
FREQUENCY-SHAPED LQG/LTR DESIGN 58
APPLICA.ON TO THE ROBUST 
59 
CONCLUSION 60
REFERENCES 61
CHAPTER 7. TOWARDS A COMPLETE FREQUENCY-DOMAIN DESIGN METHODOLOGY 62
ABSTRACT 62
KEYWORDS 62
1. DESIDERATA 62
2. MODEL MATCHING UNDER HARD CONSTRAINTS 63
3. EXAMPLE: EXPLORATION OF THE ATTAINABLE PERFORMANCE 65
4 . CONTROLLER SIMPLIFICATION BY FREQUENCY-WEIGHTED APPROXIMATION 65
5. A UNIFIED VIEW OF THE VARIOUS APPROACHES 66
6 . GENERALIZATION TO THE MULTIVARIABLE CASE 66
7. CONCLUSIONS 67
8. ACKNOWLEDGEMENTS 67
REFERENCES 67
CHAPTER 8. MODAL SYNTHESIS OF TWO-INPUT SYSTEMS 70
INTRODUCTION 70
GENERAL RESULTS IN THE CASE OF TWO-INPUT SYSTENS 70
CONCLUSIONS 74
REFERENCES 75
APPENDIX 75
CHAPTER 9. EIGENSTRUCTURE ASSIGNMENT FOR STATE-CONSTRAINED LINEAR CONTINUOUS TIME SYSTEMS 76
INTRODUCTION 76
PROBLEM PRESENTATION AND PRELIMINARY RESULTS 76
STRUCTURAL CONDITIONS FOR POSITIVE INVARIANCE 77
AN EIGENSTRUCTURE ASSIGNMENT ALGORITHM 80
EXAMPLE 80
CONCLUSION 81
REFERENCES 81
CHAPTER 10. DIRECT SHAPING OF REFERENCE INPUT 
 
82 
INTRODUCTION 82
ALGEBRAIC REPRESENTATION OF SYSTEMS 82
DESIGN EXAMPLES 85
CONCLUSIONS 87
REFERENCES 87
CHAPTER 11. A DESIGN METHOD FOR LOW COMPLEXITY CONTROL LAWS 88
INTRODUCTION 88
LOW COMPLEXITY DESIGN METHODOLOGY 88
APPLICATION EXAMPLES 90
ROBUSTNESS 92
CONCLUSIONS 92
REFERENCES 93
CHAPTER 12. THE GENERALIZED H2 CONTROL PROBLEM 94
INTRODUCTION 94
THE GENERALIZED H2 CONTROL PROBLEM 95
STATE-FEEDBACK / FULL INFORMATION 96
OUTPUT FEEDBACK 98
CONCLUSIONS 99
REFERENCES 99
CHAPTER 13. DUAL MODEL MATCHING 100
1. Introduction 100
2. Characteristic Transfer Function Matrices and Their Properties 100
3. General Description of Control Systems and Fundamental Equations 102
4. Realizable Dual Models 103
5. Design Based on Dual Model Matching 103
6. Example 104
7. The Features of the Design Based on Dual Model Matching 105
8. Conclusion 105
Acknowledgment 105
References 105
CHAPTER 14. A METHOD FOR TRANSFORMING TIME-VARIABLE MODELS INTO A CONSTANT-COEFFICIENT FORM 106
1 Introduction 106
2 The transformation 107
3 Control design 109
4 Conclusion 111
References 111
PART III: CONTROL OF DISCRETE-TIME SYSTEMS 112
CHAPTER 15. POLYHEDRAL SET CONSTRAINED CONTROL FOR DISCRETE-TIME SYSTEMS WITH UNKNOWN ADDITIVE DISTURBANCES 112
INTRODUCTION 112
PROBLEM STATEMENT AND NOTATIONS 112
THE MAXIMAL U-D INVARIANT SET 113
PROJECTION AND INTERSECTION OF POLYHEDRAL SETS. 114
ON-LINE CONTROL COMPUTATION 116
NUMERICAL EXAMPLE 116
CONCLUSIONS 117
REFERENCES 117
CHAPTER 16. A DISCRETE VERSION OF ZAKIAN'S METHOD OF INEQUALITIES 118
INTRODUCTION 118
ZAKIAN'S METHOD OF INEQUALITIES 118
ALGORITHMS OF THE DISCRETE VERSION OF THE METHOD OF INEQUALITIES 118
EXAMPLE 119
CONCLUSIONS 120
REFERENCES 120
CHAPTER 17. MULTIRATE CONTROL ALGORITHMS FOR TIME-VARIABLE SAMPLING PERIODS 122
1. Introduction 122
2. Numerical Integration 123
3. Sampling the Controller Output 125
4. Conclusions 126
References 127
CHAPTER 18. COMPARISON OF DIGITAL PD AND FUZZY CONTROL THEORY ON A HYDRAULIC SERVOSYSTEM 128
INTRODUCTION 128
EXPERIMENTAL SYSTEM 128
FUZZY CONTROL 129
REFERENCES 131
CHAPTER 19. DESIGN OF MULTIVARIABLE CONTROL SYSTEMS FOR LINEAR PERIODIC PROCESSES(*) 132
1. INTRODUCTION 132
2. NOTATIONS AND PROBLEM STATEMENT 132
3. MAIN RESULT 134
4. CONCLUDING REMARKS 136
REFERENCES 136
APPENDIX: T H E CLASSES OF DISTURBANCE FUNCTIONS AND REFERENCE SIGNALS 137
CHAPTER 20. THE TURN OVER DESIGN METHOD FOR 
138 
INTRODUCTION 138
PROBLEM FORMULATION 138
CONTINUOUS TYPE TURN OVER DESIGN METHOD 138
TURN OVER RELATION IN d DIFFERENCE EXPRESSION SYSTEM 139
DESIGN METHOD USING 
 
140 
NUMERICAL EXAMPLE 141
CONCLUSION 143
REFERENCES 143
PART IV: ROBVST CONTROL 144
CHAPTER 21. DESIGN BY SEARCH 144
INTRODUCTION 144
THE DLR STEERING BALL 144
PLANT MODEL AND INITIAL COMPENSATOR 145
DISPLAY 1: STABILITY REGIONS IN THE PLANT PARAMETER SPACE 146
DISPLAY 2: STABILITY REGIONS IN A PLANE OF TWO ADDITIONAL COMPENSATOR PARAMETERS 146
DISPLAY 3: NYQUIST VALUE SETS AND STABILITY MARGINS 147
CONCLUSIONS 149
References 149
CHAPTER 22. COMPUTATION OF THE MINIMUM STABILITY DEGREE OF PARAMETER-DEPENDENT LINEAR SYSTEMS BY A BRANCH AND BOUND ALGORITHM* 150
Introduction 150
The Branch and Bound Algorithm 151
Computation of MSD 152
A Simple Example 154
Conclusions 154
References 154
CHAPTER 23. STRUCTURED STABILITY MARGIN AND THE FINITE ARGUMENT PRINCIPLE 156
References 154
1. Introduction 156
2. The Structured Stability Margin 157
3. Calculation of Stability Margin 158
4. Example 160
5. Conclusions 161
CHAPTER 24. ROBUST DISTURBANCE DECOUPLING PROBLEM FOR PARAMETER DEPENDENT FAMILIES OF LINEAR SYSTEMS 162
INTRODUCTION 162
PRELIMINARIES AND STATEMENT OF THE PROBLEM 163
MAIN RESULT 164
APPENDIX 165
REFERENCES 165
CHAPTER 25. ROBUST D-STABILITY IN FREQUENCY DOMAIN WITH KHARITONOV-LIKE PROPERTIES 166
INTRODUCTION 166
PROBLEM FORMULATON 166
Dt-STABILITY OF A TOLYNOMIAL 166
Df - STABILITY OF A FAMILY OF POLYNOMLALS 169
CONCLUSION 171
REFERENCES 171
CHAPTER 26. INTERVAL IDENTIFICATION AND ROBUST CONTROL DESIGN: A NEW PERSPECTIVE 172
I. INTRODUCTION 172
II. INTERVAL IDENTIFICATION 172
III. Robust Stabilization Problem 174
IV. Interval Pole Assignment 174
V. INTERVAL STABILIZATION 175
VI. CONCLUSION 177
REFERENCES 177
CHAPTER 27. CONTROLLER DESIGN TO ACHIEVE COVARIANCE CONSTRAINTS 178
1. INTRODUCnON 178
2. DEFINITION AND SOLUTIOS 
179 
3. COMPUTATONAL ALGORITHM FOR THE BOCC PROBLEM 180
4. EXAMPLE 181
5. CONCLUSION 182
REFERENCES 182
CHAPTER 28. NORM BASED ROBUST DYNAMIC FEEDBACK CONTROL OF CONSTRAINED SYSTEMS 184
I. Introduction 184
II. Problem Formulation 184
III. Robust Constrained Stability Analysis 185
IV. Linear Robust Constrained Control Synthesis 186
V. Conclusions 189
VI. Acknowledgements 189
References 189
CHAPTER 29. DESIGN OF OPTIMALLY ROBUST CONTROLLERS WITH FEW DEGREES OF FREEDOM 190
1. INTRODUCTION 190
2. PRELIMINARIES AND PROBLEM FORMULATION 191
3. REGULARITY PROPERTIES OF T H E STABILITY MARGIN FOR FAMILIES OF PLANTS WITH INTERVAL AND LINEARLY STRUCURED PERTURBATIONS 192
4. OPTIMALLY ROBUST CONTROLLER WITH ONE OR TWO DEGREES OF FREEDOM 192
5. NUMERICAL EXAMPLE 194
6. CONCLUSIONS 194
ACKNOWLEDGEMENTS 195
REFERENCES 195
CHAPTER 30. ROBUST CONTROL DESIGN FOR LINEAR SYSTEMS WITH UNCERTAIN PARAMETERS 196
l.INTRODUCTION 196
2.PROBLEM FORMULATION 196
3. ROBUSTNESS MEASURE FUNCTION 198
4. ROBUST CONTROLLER DESIGN 199
5. NUMERICAL EXAMPLE 200
6. CONCLUSIONS 201
REFERENCES 201
CHAPTER 31. A ROBUST CONTROL OF FUEL INJECTION SERVO SYSTEM 202
INTRODUCTION 202
IDENTIFICATION 203
OUTLINE OF RMM 203
RMM FOR NON-MINIMUMPHASE PLANT 204
APPLICATION OF RMM TO FUEL INJECTION PUMP 205
ACKNOWLEDGEMENTS 206
EXPERIMENT RESULTS 206
CONCLUSION 206
REFERENCES 206
CHAPTER 32. A HYPERSTABILITY/MULTIOBJECTIVE OPTIMIZATION APPROACH FOR ACTIVE FLEXIBLE STRUCTURES 208
Introduction 208
Hyperstabillty Theory 208
Hyperstability Theory Combined with Multiobjective Optimization 209
Parametrization for an (asymptotic) hyperstable controller 210
Example of a first order SISO controller 210
Multiobjective Optimization 210
Control of flexible structures with colocated position - and rate sensors 210
Example: DLR - Plate Experiment 211
Conclusions 213
Acknowledgment 213
References 213
PART V: .8-OPTIMIZATION 214
CHAPTER 33. ROBUST CONTROL OF A FLEXIBLE WIND TURBINE BASED ON COPRIME FACTORIZATIONS 214
1 Introduction 214
2 Wind turbine model 214
3 Control Design Method 215
4 Control of the turbine 217
5 Conclusions 218
References 218
CHAPTER 34. ROBUST OBSERVER DESIGN FOR DYNAMICAL SYSTEMS UNDER UNKNOWN DISTURBANCES 220
INTRODUCTION AND PROBLEM FORMULATION 220
NOTATION AND PRELIMINARIES 220
PARAMETRIZATION OF OBSERVERS AND ESTIMATION ERROR BEHAVIOUR 221
AN ALGEBRAIC APPROACH TO H8 OPTIMIZATION 222
CONCLUSIONS 225
REFERENCES 225
CHAPTER 35. H8 ESTIMATION FOR CONTINUOUS-TIME LINEAR UNCERTAIN SYSTEMS1 226
1. INTRODUCTION 226
2. PROBLEM FORMULATION 226
3. SOLU.ON VIA ............ APPROACH 227
4. SOLUTION VIA RICCATI EQUATION APPROACH 229
5. CONCLUSION 230
6. REFERENCES 230
CHAPTER 36. QUADRATIC STABILIZABILITY OF LINEAR UNCERTAIN SYSTEMS WITH PRESCRIBED H8 NORM BOUNDS1 232
INTRODUCTION 232
PRELIMINARIES 232
PROBLEM FORMULATION 233
MAIN RESULT 234
EXAMPLES 235
CONCLUSIONS 236
REFERENCES 236
CHAPTER 37. COAL- FIRED POWER PLANT CONTROLLER DESIGN USING H-INFINITY OPTIMIZATION 238
1 Introduction 238
2 Plant and design objectives 238
3 Cost function and weights 239
4 Redesign and model reduction 239
5 Robust performance 240
6 CAD packages 240
7 Conclusion 240
8 Acknowledgements 241
References 241
CHAPTER 38. PARAMETERIZATIONS OF H8 CONTROLLERS FOR NON-STANDARD PLANTS 244
1. INTRODUCTION 244
2. TWO - BLOCKPROBLEM 245
3. NON - STANDARD CASE (I) 245
4. NON-STANDARD CASE (II) 246
5. STATE FEEDBACK CASE 248
6 CONCLUSION 249
REFERENCES 249
CHAPTER 39. H8-OPTIMAL ROBUST ASYMPTOTIC REGULATION WITH NICE STABILITY REGION 250
1. INTRODUCTION 250
2. PROBLEM FORMULATION 250
3. H8 ROBUST STABILIZATION 251
4. BILINEAR TRANSFORMATION 252
5. OPTIMAL ROBUST REGULATION 254
6. CONCLUSIONS 255
REFERENCES 255
CHAPTER 40. DESIGN OF RELIABLE CONTROL SYSTEMS WITH GUARANTEED DISTURBANCE REJECTION PERFORMANCE 256
Introduction 256
An Alternative Actuator-Outage Mode 259
Example 261
Conclusions 261
References 261
CHAPTER 41. FIXED ORDER H2/H8 CONTROL OF UNCERTAIN SYSTEMS 262
INTRODUCTION 262
NORMS AND NOTATIONS 263
NECESSARY CONDITIONS FOR 263
THE FLEXIBLE MECHANISM 265
ROBUST CONTROL SYSTEM DESIGN 266
IMPLEMENTATION RESULTS 266
CONCLUSIONS 266
REFERENCES 266
CHAPTER 42. ROBUST OUTPUT REGULATION USING REDUCED-ORDER CONTROLLERS 268
I Introduction 268
II Preliminaries 268
Ill The Main Results 270
IV Conclusion 272
Reference 273
PART VI: ADAPTIVE CONTROL 274
CHAPTER 43. ON REDUCED ORDER MODEL REFERENCE ADAPTIVE CONTROL 274
INTRODUCnON 274
PROBLEM STATEMENT 275
THE ADAPTIVE CASE 277
CONCLUSIONS 278
REFERENCES 279
CHAPTER 44. DESIGN OF SELF-TUNING CONTROLLERS FOR INDUSTRIAL PLANT 280
INTRODUCTION 280
SELF-TUNING CONTROLLER 280
CASE STUDY 1: ENGINE TEST CELL. 281
CASE STUDY 2: HIGH TEMPERATURE HEATING PLANT 283
CONCLUSIONS 284
ACKNOWLEDGEMENTS 284
REFERENCES 284
CHAPTER 45. B-MRAC: A NEW MODEL REFERENCE ADAPTIVE CONTROLLER BASED ON BINARY CONTROL THEORY 286
INTRODUCTION 286
STATEMENT OF THE PROBLEM 286
THE CONVENTIONAL MRAC 287
THEVS-MRAC 287
Table 2 VS-MRAC 287
BINARY MODEL REFERENCE ADAPTIVE CONTROL 288
SIMULATIONS 289
CONCLUSION 290
REFERENCES 290
APPENDIX 291
CHAPTER 46. DESIGN OF A ROBUST CONTROLLER FOR THE SUBSTRATE CONCENTRATION IN BIOREACTORS 292
INTRODUCTION 293
PROCESS AND MEASUREMENT SYSTEM 293
DESIGN OF THE CONTROLLER 294
APPUCATION OF THE CONTROL SYSTEM 296
CONCLUSIONS 297
REFERENCES 297
CHAPTER 47. STABILIZED LEAST-SQUARES ESTIMATORS FOR TIME-VARIANT PROCESSES 298
INTRODUCTION 298
'CLASSICAL' ALGORITHMS: RLS-EF AND RLS-LF 299
STABILIZED RLS ALGORITHMS 299
STABILITY OF RLS-SF ALGORITHMS 299
ASYMPTOTIC PROPERTIES OF THE COVARIANCE MATRDC FOR NOT PERSISTENTLY EXCITING SIGNALS 300
CONVERGENCE OF RLS-SI ALGORITHM 301
RLS-SI & RLS-LF: A NUMERICAL COMPARISION
CONCLUSIONS 303
REFERENCES 303
CHAPTER 48. ROBUST DESIGN OF MODEL REFERENCE ADAPTIVE CONTROL SYSTEM INCLUDING FIXED COMPENSATOR 304
INTRODUCTION 304
SYSTEM DESCRIPTION 304
CONTROLLERS STRUCTURE 305
ADAPTIVE SCHEME AND STABILITY ANALYSIS 306
DESIGN SCHEME OF FIXED COMPENSATOR 307
DESIGN EXAMPLE 308
CONCLUSIONS 309
REFERENCES 309
CHAPTER 49. ADAPTIVE ROBOT CONTROLLERS: A COMPARATIVE STUDY 310
INTRODUCTION 310
DYNAMICS MODEL OF THE SCARA ROBOT 311
DIRECT ADAPTIVE CONTROLLERS 311
INDIRECT ADAPTIVE CONTROLLERS 312
CONCLUSION 314
ACKNOWLEDGEMENT 315
REFERENCES 315
CHAPTER 50. DESIGN OF COMBINED VARIABLE STRUCTURE SYSTEMS AND REFERENCE EQUATION SYSTEM ALGORITHMS 316
INTRODUCTION 316
BASIC STRUCTURES OF SPEED GRADIENT ALGORITHMS 316
SIGNAL-PARAMETRIC ADAPTIVE CONTROL ALGORITHMS DESIGN 317
CONCLUSION 320
REFERENCES 320
PART VII: VARIABLE STRUCTURE CONTROL 322
CHAPTER 51. DESIGN OF VARIABLE STRUCTURE CONTROL SYSTEMS WITH INTERNAL MODELS 322
INTRODUCTION 322
MAIN RESULTS 322
DESIGN OF HYPERPLANES AND COMPENSATORS 323
EXAMPLE 324
CONCLUSIONS 324
REFERENCES 324
CHAPTER 52. "INTEGRAL LYAPUNOV FUNCTIONS" BASED ON INCOMPLETE STATE FEEDBACK 328
INTRODUCTION 328
STATEMENT OF THE INTERGRAL LYAPUNOV FUNCTION 328
SATISFYING THE LYAPUNOV CONDITIONS 328
EXTENDED STATEMENTS OF THE INTEGRAL LYAPUNOV FUNCTION 330
...LICATIONS: VARIABLE 
330 
APPLICA.ON: "SAFE OBSERVERS" 331
CONCLUSION 332
REFERENCES 332
CHAPTER 53. SLIDING MODE CONTROLLER DESIGN FOR NONLINEAR SYSTEMS: AN EXTENDED LINEARIZATION APPROACH 334
l.INTRODUCTION 334
2. SLIDING MODE CONTROLLERS /IA 
334 
3. SOME ......... EXAMPLES 336
4. CONCLUSIONS 339
5. REFERENCES 339
CHAPTER 54. MULTI-INPUT VARIABLE STRUCTURE CONTROLLERS 340
1. INTRODUCTION 340
2. VSS SWITCHING SURFACES AND SUDING MOTION: 340
3. TWO APPROACHES TO SWITCHING SURFACE DESIGN FOR LINEAR SYSTEMS 342
4. HIERARCHY OF CONTROL 344
5. EXAMPLE 345
6. CONCLUDING REMARKS 345
REFERENCES 345
CHAPTER 55. ROBUST EIGENVALUE ASSIGNMENT TECHNIQUES FOR THE SLIDING MODE 346
INTRODUCTION 346
SLIDING MOTION IN VSC 346
THE REGULATOR SYSTEM 346
CONTROLLER DESIGN FOR EIGENVALUES IN A REGION 347
EXAMPLE 348
ROBUSTNESS 349
CONCLUSION 350
PART VIII: NONLINEAR CONTROL SYSTEMS 352
CHAPTER 56. NONLINEAR CONTROL OF MOLECULAR WEIGHT IN A POLYMERIZATION REACTOR 352
INTRODUCTION 352
THE REACTORMODEL AND THE CONTROL PROBLEM 353
SOLVABILITY IN TERMS OF EXISTENCE OF A COORDINATE CHANGE TO AN EQUIVALENT SOLVABLE SYSTEM 354
ADMISSIBLE REACTOR CONTROL CONFIGURATIONS AND STRUCTURAL ASSESSMENT O F PERFORMANCE 355
SIMULATION TEST 356
CONCLUSIONS 356
REFERENCES 356
APPENDIX: THE REACTOR MODEL 356
CHAPTER 57. A NEW CONVERSE LYAPUNOV RESULT ON EXPONENTIAL STABILITY 358
1 Introduction 358
2 The main result 359
3 Linear time-invariant systems 360
4 Linearization about an equilibrium state 361
5 Conclusions 362
6 Acknowledgments 362
References 362
CHAPTER 58. SYNTHESIS OF PLANAR SLIDING MANIFOLDS FOR NONLINEAR SYSTEMS 364
INTRODUCnON 364
REVIEW OF SOME BASIC FACTS 364
THE P L 
365 
AN EXPLICIT VSS CONTROLLER 366
ROBUSTNESS PROPERTIES 366
EXAMPLE 367
REFERENCES 368
CHAPTER 59. NONLINEAR CONTROL SYSTEM DESIGN BASED ON NEWLY DEVELOPED DYNAMIC PROGRAMMING ALGORITHM 370
INTRODUCTION 370
GENERAL CONTROL PROBLEM 371
CONVENTIONAL DYNAMIC PROGRAMMING 371
ITERATIVE DYNAMIC PROGRAMMING 371
APPLICATION TO NONLINEAR CONTROL SYSTEM DESIGN 372
CONCLUSIONS 375
ACKNOWLEDGMENT 375
REFERENCES 375
CHAPTER 60. POSTPONING CHAOS USING A ROBUST STABILIZER1 
376 
1 Introduction 376
2 The quadratic mapping 376
3 The stabilization principle 377
4 Stabilized dynamics 377
5 Quadratic mapping revisited 378
6 Experiments 379
7 Process parameter estimation 380
8 Higher-dimensional systems 380
9 Conclusions 380
Acknowledgement 380
References 380
CHAPTER 61. DESIGN METHODS OF NONLINEAR DYNAMIC COMPENSATOR BASED UPON CANONICAL FORMS 382
1 Introduction 382
2 System Description and Some Mathematical Notations 382
3 State Feedback Linearization 383
4 Nonlinear Observer 383
5 Nonlinear Dynamic Compensator 384
6 Example 386
7 Conclusions 387
References 387
CHAPTER 62. A COMPENSATING METHOD FOR THE EFFECTS OF THE CHANGE OF OPERATING STATE IN BILINEAR SYSTEMS BY STATE LINEARIZATION TECHNIQUE 388
1. INTRODUCTION 388
2. LINEAR TRANSFORMATION OF NONLINEAR SYSTEM^' 388
3. CONSTRUCTION OF OUTPUT FEEDBACK CONTROL SYSTEM 390
4. CONTROL PERFORMANCES OF A LINEARIZED BILINEAR SYSTEM 390
5. CONCLUSIONS 393
REFERENCES 393
CHAPTER 63. NONLINEAR FEEDBACK SC CONTROL OF A POWER SYSTEM 394
INTRODUCTION 394
MODEL OF SMIB POWER SYSTEM 394
NONLINEAR FEEDBACK OPTIMAL CONTROL 395
THREE-PHASE FAULT SIMULATION FOR MAXIMUM PRINCIPLE-DERIVED CONTROL 395
VARIABLE-STRUCTURE CONTROL 395
VARIABLE-STRUCTURE SIMULATION THREE-PHASE FAULT 396
CONCLUSIONS 397
ACKNOWLEDGEMENT 397
REFERENCES 397
APPENDIX 397
CHAPTER 64. NONLINEAR MODEL-MATCHING DESIGN OF SERVOMECHANISMS 398
INTRODUCTION 398
PROBLEM DEFINITION 398
AN INTERES.NG DESIGN QUESTON 399
DESIGN WITH VOLTERRA OPERATORS 400
PARTIAL LINEARIZATON 400
REALIZATON 400
EXAMPLES 401
CONCLUSION 403
ACKNOWLEDGEMENT 403
REFERENCES 403
CHAPTER 65. TOOLS FOR THE DESIGN OF SINGLE-LOOP CONTROL SYSTEMS WITH ACTUATOR SATURATION APPLIED TO HYDROPOWER CONTROL 404
INTRODUCTION 404
THE HYDROPOWER SYSTEM 404
MODELLING AND IDENTIFICATION 
405 
DESIGN OF THE LINEAR REGULATOR 405
STABILITY ANALYSIS 405
PROPOSAL FOR THE CONTROL SYSTEM. 408
CONCLUSIONS 408
REFERENCES 409
APPENDIX 409
CHAPTER 66. MULTI-LAYER NEURAL NETWORKS FOR THE OPTIMAL CONTROL OF NONLINEAR DYNAMIC SYSTEMS 410
INTRODUCTION 410
STATEMENT OF THE OPTIMAL CONTROL PROBLEM 410
SOLUTION OF THE NONLINEAR PROGRAMMING PROBLEM BY THE GRADIENT METHOD 411
EXAMPLES 412
CONCLUSIONS 414
REFERENCES 414
APPENDIX 415
PART IX: CONTROL OF DISTRIBUTED PARAMETER SYSTEMS 416
CHAPTER 66. ASYMPTOTICALLY POLE LOCATION OF OPTIMAL REGULATOR FOR TIME-DELAY SYSTEMS 416
1. Introduction 416
2. Optimal regulator 417
3. Closed-loop properties and remarks 418
4. Main results 418
5.Conclusion 420
6. Illustrate example 420
Reference 420
CHAPTER 67. ON THE OPTIMAL BOUNDARY CONTROL FOR STOCHASTIC LINEAR ELASTIC SYSTEMS 422
MATHEMATICAL MODEL OF SYSTEM DYNAMICS 422
OPTIMAL BOUNDARY CONTOOL PROBLEMS 423
DERIVATION OF THE OPTIMAL B0UNDARY CONTROL 
423 
CONSTRICTION OF OPTIMAL BOUNDARY CONTROL SYSTEMS 
424 
CONCLUSIONS 424
REFERENCES 424
APPENDICES 425
CHAPTER 68. CONTROL OF HEAT EXCHANGERS BY PLACEMENT OF CLOSED-LOOP POLES 426
INTRODUCTION 426
OUTLINE OF A POLE ASSIGNMENT LAW 426
PARALLEL FLOW HEAT EXCHANCSER 430
REFERENCES 431
CHAPTER 69. NECESSARY AND SUFFICIENT CONDITION OF PARETO OPTIMALITY FOR PROBLEMS WITH MULTI-EQUALITY OPERATOR CONSTRAINTS 432
INTRODUCTIONG 432
DEFINITIONS OF CONES 432
STATEMENT OF A PARETO OPTIMIZATION PROBLEM 433
NECESSARY AND SUFFICIENT CONDITION OF PARETO OPTIMALITY 433
CONCLUSIONS 437
REFERENCES 437
CHAPTER 70. BOUNDARY STABILIZATION OF SEMILINEAR PARABOLIC DISTRIBUTED SYSTEMS 438
1. INTRODUCTION 438
2. CONTROL OBJECT 438
3. MATHEMATICAL FORMULATION OF T H E SYSTEM 438
4. EXISTENCE OF THE SOLUTION UNDER STATIC OUTPUT FEEDBACK 439
5. EXISTENCE AND STABILIZATION OF THE SOLUTION FOR THE SYSTEM WITH A FINITE DIMENSIONAL DYNAMIC COMPENSATOR 441
6. CONCLUTION 442
APPENDIX 1 (DERIVATION OF EQUATION (3.1)) 442
REFERENCES 443
CHAPTER 71. SPLINE-BASED ADAPTIVE CONTROL OF DISTRIBUTED PARAMETER SYSTEMS 444
1. INTRODUCTION 444
2. PRELIMINARIES 445
CONTINUOUS MODELING OF DPS 445
4. CONTROL SYNTHESIS 447
5. ILLUSTRATIVE EXAMPLE 448
6. CONCLUDING REMARKS 449
REFERENCES 449
CHAPTER 72. OBSERVERS FOR INFINITE DIMENSIONAL SYSTEMS WITH UNKNOWN INPUTS 450
INTRODUCTION 450
STATEMENT OF THE PROBLEM 450
CONSTRUCTION OF OBSERVERS 450
CONCLUSION 453
REFERENCES 453
CHAPTER 73. PRACTICAL STABILIZING CONTROL OF UNCERTAIN DIFFUSION SYSTEMS 456
INTRODUCTION 456
THE UNCERTAIN SYSTEM 456
STABILIZATION PROBLEM 457
DIFFUSION SYSTEM 457
VARIABLE STRUCTURE CONTROL 458
PRACTICAL STABILIZING CONTROL 458
VARIABLE STRUCTURE CONTROL 458
COMPUTATIONAL RESULTS 459
CONCLUSIONS 459
REFERENCES 459
APPENDIX 460
PART X: CONTROL OF DISCRETE EVENT SYSTEMS 462
CHAPTER 74. SYNTHESIS OF DEADLOCK-FREE CONTROL STRUCTURES USING PETRI-NETS 462
INTRODUCTION 462
PETRI-NETS 462
SYNTHESIS OF NET CORRECTIONS 464
AN APPLICATION 465
CONCLUDING REMARKS 466
REFERENCES 467
CHAPTER 75. DESIGN OF A DISCRETE EVENT CONTROLLER FOR A MODEL RAILWAY 468
Introduction 468
An Optimal Stopping Problem 468
Solution to the Optimal Stopping Problem 470
Application 470
Conclusion 471
References 472
CHAPTER 76. CONTROL OF ELEMENTARY DISCRETE EVENT SYSTEMS: SYNTHESIS OF CONTROLLER WITH NON-ZERO DECISION TIME 474
1 Introduction 474
2 Time systems 474
3 Controllable behaviours 474
4 Elementary discrete event systems 475
5 Delayed system 475
6 Control problem 476
7 Sufficient conditions 478
8 Conclusion 478
References 479
CHAPTER 77. ON THE DESIGN OF DISCRETE EVENT DYNAMIC SYSTEMS BY MEANS OF THE BOOLEAN DIFFERENTIAL CALCULUS 480
INTRODUCTION 480
PRELIMINARIES 480
A DESIGN ALGORITHM FOR DEDS 481
CONCLUSION 485
REFERENCES 485
CHAPTER 78. AN EFFECTIVE WAY TO UNDO A DISCRETE EVENT SYSTEM OF ITS (DEAD)LOCK 486
NOTATION 486
MODEL AND DEFINITIONS 486
DEADLOCK 487
DEADLOCK FREE CONNECTIONS 487
UNDO THE DEADLOCK 487
AN EXAMPLE 488
CONCLUSION 490
REFERENCES 491
PART XI: HIERARCHICAL AND DECENTRALIZED CONTROL 492
CHAPTER 79. CHARACTERIZATIONS OF DECENTRALIZED FIXED MODES FOR DESCRIPTOR SYSTEMS 492
INTRODUCTION 492
PRELIMINARIES 492
GENERAL CHARACTERIZATIONS OF DECENTRALIZED FIXED MODES FOR DESCRIPTOR SYSTEMS 493
ALGEBRAIC CHARACTERIZATIONS OF DFIM 494
ALGEBRAIC CHARACTERIZATIONS OF DFEM 495
A NUMERICAL EXAMPLE 496
CONCLUSIONS 497
References 497
CHAPTER 80. DECENTRALIZED OPTIMAL CONTROL WITH EXTENSION 498
INTRODUCTION 498
EXTENSION PRINCIPLE 499
CONTRACTABILITY 499
DECENTRALIZED OPTIMAL CONTROL 500
CONCLUSIONS 502
REFERENCES 502
CHAPTER 81. A GENERAL FRAMEWORK FOR CONSTRAINED CONFIGURATION CONTROL LAW DESIGN 504
INTRODUCTION 504
PRELIMINARIES AND NOTATION 504
MAIN RESULTS 505
ILLUSTRATIVE EXAMPLES 507
A NUMERICAL EXAMPLE 508
CONCLUSIONS 509
REFERENCES 509
CHAPTER 82. A PROCEDURE FOR THE DELIMITATION OF TASKS IN CHEMICAL PROCESS CONTROL HIERARCHIES 510
INTRODUCTION 
510 
METHOD 510
EXAMPLES 511
APPLICATION TO PLATFORMER UNIT 513
CONCLUSION 515
REFERENCES 515
CHAPTER 83. DESIGN OF A STABILIZING DECENTRALIZED CONTROL FOR LINEAR INTERCONNECTED SYSTEMS WITH TIME-DELAY 516
INTRODUCTION 516
DECENTRALIZED STABILIZATION 516
NUMERICAL EXAMPLE 518
CONCLUSION 519
REFERENCES 519
PART XII: KNOWLEDGE-BASED AND LEARNING CONTROL 520
CHAPTER 84. DESIGN OF A RULE-BASED CONTROLLER FOR THE INVERTED PENDULUM 520
SURVEY 520
THE ..RATIVE LEARNING PROCESS 521
RESULTS AND CONCLUSION 523
ACKNOWLEDGEMENT 523
REFERENCES 523
CHAPTER 85. IMPROVED ALLOCATION OF WEIGHTS FOR ASSOCIATIVE MEMORY STORAGE IN LEARNING CONTROL SYSTEMS 524
1. Introduction 524
2. The Associative Memory Unit and Training of Weights 524
3. Desirable Properties of the Scheme for the Allocation of Weights 525
4. The Albus Scheme tor Allocating Weights 525
5. An improved Allocation of Weights 525
6. Constructing a Table Qptimum Lattices for General Values of n and p 526
7. Comments on the Tabulated Results 526
References 526
CHAPTER 86. THE CONTROL OF LARGE SCALE SYSTEMS BY USING A KNOWLEDGEBASED CONTROLLER 530
THE PROBLEM STATELIENT 530
THE STRUCTURE OF A KNOWLEDGEBASED CONTROLLER 530
THE OPERATION OF A CONTROL 
531 
APPLICATION: CONTROL OF A LARGESCALE HYDROLOGICAL SYSTEM USING A KNOWLEDGE-BASED CONTROLLER 532
CONCLUDING REMARKS 533
REFERENCES 533
PART XIII: LQG/LTR-DESIGN 536
CHAPTER 87. NECESSARY AND SUFFICIENT CONDITIONS FOR OPTIMAL FIXED-ORDER DYNAMIC COMPENSATION OF LINEAR DISCRETE-TIME SYSTEMS1 536
1. Introduction 536
2. The Optimal Fixed-Order Dynamic Compensation Problem 536
3. Necessary Conditions For Optimal Fixed-Order Dynamic Compensation. 538
4 . Sufficient Conditions For Fixed-Order Optimal Dynamic Compensation. 539
5. Compensatability test and example 540
6 . Conclusions. 540
References 541
CHAPTER 88. LQG MULTIVARIABLE SELF-TUNING CONTROL DESIGN 542
Abstract 542
1. Introduction 542
2. Discrete Multivariable ARMAX System Description 542
3. LQG Control Law 543
4. Multivariable Identification Algorithm 545
5. Self-Tuning Algorithm 546
7. Conclusions 546
References 546
CHAPTER 89. POLYNOMIAL SOLUTION TO THE STANDARD LQ-OPTIMAL CONTROL PROBLEM: SCALAR CASE 548
1 Introduction 548
2 Problem Formulation 549
3 Problem Solution 550
4 Conclusions 552
Acknowledgements 552
References 552
PART XIV: COMPUTER AIDED DESIGN 554
CHAPTER 90. CAD TECHNIQUES FOR A STRUCTURAL APPROACH TO NONINTERACTION AND DISTURBANCE REJECTION 554
INTRODUCTIO N 554
THEORE.CAL FOUNDATONS 554
APPLICATION 1. DISTURBANCE REJECTION 555
APPLICATON 2.INPUT-0UTPUT DECOUPLING 556
APPENDIX A 558
APPENDDC . 558
CONCLUSIONS 558
ACKNOWLEDGEMENTS 559
REFERENCES 559
CHAPTER 91. COMPUTER AIDED PROBLEM FORMULATION OF CONTROL PROBLEMS 560
Abstract 560
Introduction 560
Problems in Control Design Process 560
Notification of Binary Control Problems 561
Additional Parts in Control Concepts 562
Balance Program to Prove Operators Concept 562
Conclusions 563
References 563
PART XV: MODEL MATCHING AND MODEL REDUCTION 564
CHAPTER 92. OUTPUT-FEEDBACK CONTROL OF A HYDRAULIC DRIVE USING BALANCED MODEL REDUCTION DESIGN METHOD 564
INTRODUCTION 564
CONTROLLABILITY, REACHABILITY AND CONSTRUCTIBILITY, OBSERVABILITY 564
MEASURES FOR STRUCTURAL PROPERTIES USING PRINCIPAL COMPONENT ANALYSIS 565
BALANCED REALIZATIONS 566
MODEL REDUCTION 566
OUTPUT FEEDBACK DESIGN 566
DISCRETE TIME SYSTEMS 567
CONTROL OF A HYDRAULIC DRIVE 567
CONCLUSION 568
REFERENCES 568
CHAPTER 93. SUFFICIENCY CRITERIA FOR FREQUENCYDOMAIN APPROXIMATE MODELING OF SISO PLANTS WITH INPUT DEAD-TIME 570
INTRODUCnON 570
FREQUENCY RESPONSE ERRORS 570
CONDITIONS FOR MODELING ERRORS 571
MODELING FRACTIONAL DEAD-TIME 573
CONCLUSIONS 574
REFERENCES 574
CHAPTER 94. MODEL MATCHING OF DESCRIPTOR SYSTEMS BY PROPORTIONAL STATE FEEDBACK 576
Introduction 576
Formulation 576
Properness and Stability 577
Design Procedure 578
Comments 578
References 578
CHAPTER 95. NATURALLY MOTIVATED PROCEDURE FOR THE DESIGN OF A REDUCED-ORDER CONTROLLER 580
INTRODUCTION 580
APPROXIMATON METHOD 580
DESIGN PRiXEDURE 581
DISCUSSION 582
SUMMARY AND CONCLUSION 584
REFERENCES 585
PART XVI: VARIOUS APPUCATIONS 586
CHAPTER 96. A STATE-FEEDBACK CONTROL FOR A 4-DOF MANIPULATOR WITH A TRANSVERSAL FLEXIBLE LINK 586
I. INTRODUCTION 586
II. RIGID LINKS AND ACTUATORS MODEL 587
III. FLEXIBLE LINK DYNAMICS 587
IV. CONTROL OF THE RIGID LINKS 588
V. CONTROL OF THE FLEXIBLE LINK 589
VI. SIMULATION RESULTS AND DISCUSSION 589
VII. CONCLUSIONS 590
ACKNOWLEDGEMENTS 590
REFERENCES 590
CHAPTER 97. CONTROL DESIGN METHODS FOR ACTIVE SOUND REDUCTION SYSTEMS 592
I INTRODUCTION 592
II ADAPTIVE FILTERING 592
Ill GENERALIZED MINIMUM VARIANCE CONTROL 594
IV IDENTIFICATION OF THE ADAPTIVE FILTERING STRATEGY 594
V POLE AND ZERO ASSIGNMENT IN GMV CONTROL 595
VI SIMULATIONS 595
VII CONCLUSIONS 597
VIII ACKNOWLEDGEMENTS 597
IX REFERENCES 597
CHAPTER 98. A PREDICTIVE CONTROL ALGORITHM FOR CONTINUOUS DISTILLATION COLUMNS 598
INTRODUCTION 598
THE PREDIOTVE CONTROL ALGORITHM 599
RESULTS 601
CONCLUSIONS 602
NOMENCLATURE 602
REFERENCES 603
CHAPTER 99. A NEW POWER SYSTEM STABILIZER BASED ON FIELD FLUX CONTROL 604
INTRODUCTION 604
MODEL POWER SYSTEM 604
PROPOSED CONTROL SCHEME 605
EXPERIMENTAL RESULTS 607
CONCLUSIONS 608
REFERENCES 608
APPENDICES 609
APPENDIX I Equations for simulation studies 609
APPENDIX II Coefficients K1 to K8 In Fig. 3 609
APPENDIX III State equations 609
APPENDIX IV Machine parameters 609
NOMENCLATURE 609
AUTHOR INDEX 610
KEYWORD INDEX 612