Robust Control (eBook)

Theory and Applications

Kang-Zhi Liu, Yu Yao (Autoren)

eBook Download: PDF

2016 | 1. Auflage
500 Seiten
Wiley (Verlag)
978-1-118-75441-2 (ISBN)

Infos

Comprehensive and up to date coverage of robust control theory and its application
•   Presented in a well-planned and logical way
•   Written by a respected leading author, with extensive experience in robust control
•   Accompanying website provides solutions manual and other supplementary material

Professor Kang-Zhi Liu, Dept. of Electrical and Electronic Engineering, Chiba University, Japan. Professor Liu achieved his Ph.D. degree in 1991 from Chiba University, Japan.  His areas of expertise include Control Theory, Control and Operation of Power Systems, and System Integration of Smart-Grid, and he has worked in these related areas for 27 years (4 years as a professor, 13 years as an associate professor, 5 years as an assistant professor, and 5 years as a graduate student). He is currently Associate Editor of both the International Journal of Control Theory and Applications, and the International Journal of Systems Science.  He is the author of 6 books (two in Chinese and four in Japanese).

Dr. Yu Yao is a Cheng Kong Scholar Chair Professor at the Harbin Institute of Technology, China. He also serves as Vice President of Harbin University of Engineering, China. His research interests include nonlinear systems, robust control and flight control. He has published over 100 journal papers.

Inhalt

Cover???????????????????????? 1
Title Page?????????????????????????????????? 5
Copyright???????????????????????????????? 6
Dedication?????????????????????????????????? 7
Contents?????????????????????????????? 9
Preface???????????????????????????? 19
List of Abbreviations???????????????????????????????????????????????????????? 21
Notations???????????????????????????????? 23
Chapter 1 Introduction?????????????????????????????????????????????????????????? 25
1.1 Engineering Background of Robust Control?????????????????????????????????????????????????????????????????????????????????????????????????????? 25
1.2 Methodologies of Robust Control???????????????????????????????????????????????????????????????????????????????????? 28
1.2.1 Small-Gain Approach???????????????????????????????????????????????????????????????? 29
1.2.2 Positive Real Method?????????????????????????????????????????????????????????????????? 29
1.2.3 Lyapunov Method???????????????????????????????????????????????????????? 30
1.2.4 Robust Regional Pole Placement?????????????????????????????????????????????????????????????????????????????????????? 30
1.2.5 Gain Scheduling???????????????????????????????????????????????????????? 31
1.3 A Brief History of Robust Control???????????????????????????????????????????????????????????????????????????????????????? 32
Chapter 2 Basics of Linear Algebra and Function Analysis?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 34
2.1 Trace, Determinant, Matrix Inverse, and Block Matrix?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 34
2.2 Elementary Linear Transformation of Matrix and Its Matrix Description???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 36
2.3 Linear Vector Space???????????????????????????????????????????????????????????? 38
2.3.1 Linear Independence???????????????????????????????????????????????????????????????? 39
2.3.2 Dimension and Basis???????????????????????????????????????????????????????????????? 40
2.3.3 Coordinate Transformation???????????????????????????????????????????????????????????????????????????? 42
2.4 Norm and Inner Product of Vector?????????????????????????????????????????????????????????????????????????????????????? 42
2.4.1 Vector Norm???????????????????????????????????????????????? 43
2.4.2 Inner Product of Vector???????????????????????????????????????????????????????????????????????? 44
2.5 Linear Subspace???????????????????????????????????????????????????? 46
2.5.1 Subspace?????????????????????????????????????????? 46
2.6 Matrix and Linear Mapping???????????????????????????????????????????????????????????????????????? 47
2.6.1 Image and Kernel Space?????????????????????????????????????????????????????????????????????? 47
2.6.2 Similarity Transformation of Matrix???????????????????????????????????????????????????????????????????????????????????????????????? 49
2.6.3 Rank of Matrix?????????????????????????????????????????????????????? 50
2.6.4 Linear Algebraic Equation???????????????????????????????????????????????????????????????????????????? 51
2.7 Eigenvalue and Eigenvector?????????????????????????????????????????????????????????????????????????? 52
2.8 Invariant Subspace?????????????????????????????????????????????????????????? 54
2.8.1 Mapping Restricted in Invariant Subspace?????????????????????????????????????????????????????????????????????????????????????????????????????????? 56
2.8.2 Invariant Subspace over Rn?????????????????????????????????????????????????????????????????????????????? 56
2.8.3 Diagonalization of Hermitian/Symmetric Matrix???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 57
2.9 Pseudo-Inverse and Linear Matrix Equation???????????????????????????????????????????????????????????????????????????????????????????????????????? 58
2.10 Quadratic Form and Positive Definite Matrix?????????????????????????????????????????????????????????????????????????????????????????????????????????????? 59
2.10.1 Quadratic Form and Energy Function???????????????????????????????????????????????????????????????????????????????????????????????? 59
2.10.2 Positive Definite and Positive Semidefinite Matrices???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 60
2.11 Norm and Inner Product of Matrix???????????????????????????????????????????????????????????????????????????????????????? 61
2.11.1 Matrix Norm?????????????????????????????????????????????????? 61
2.11.2 Inner Product of Matrices?????????????????????????????????????????????????????????????????????????????? 63
2.12 Singular Value and Singular Value Decomposition?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 64
2.13 Calculus of Vector and Matrix?????????????????????????????????????????????????????????????????????????????????? 67
2.13.1 Scalar Variable?????????????????????????????????????????????????????????? 67
2.13.2 Vector or Matrix Variable?????????????????????????????????????????????????????????????????????????????? 67
2.14 Kronecker Product?????????????????????????????????????????????????????????? 68
2.15 Norm and Inner Product of Function???????????????????????????????????????????????????????????????????????????????????????????? 69
2.15.1 Signal Norm?????????????????????????????????????????????????? 69
2.15.2 Inner Product of Signals???????????????????????????????????????????????????????????????????????????? 71
2.15.3 Norm and Inner Product of Signals in Frequency Domain?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 72
2.15.4 Computation of 2-Norm and Inner Product of Signals???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 73
2.15.5 System Norm?????????????????????????????????????????????????? 74
2.15.6 Inner Product of Systems???????????????????????????????????????????????????????????????????????????? 77
Exercises???????????????????????????????? 79
Notes and References?????????????????????????????????????????????????????? 80
Chapter 3 Basics of Convex Analysis and LMI???????????????????????????????????????????????????????????????????????????????????????????????????? 81
3.1 Convex Set and Convex Function?????????????????????????????????????????????????????????????????????????????????? 81
3.1.1 Affine Set, Convex Set, and Cone?????????????????????????????????????????????????????????????????????????????????????????? 81
3.1.2 Hyperplane, Half-Space, Ellipsoid, and Polytope???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 84
3.1.3 Separating Hyperplane and Dual Problem?????????????????????????????????????????????????????????????????????????????????????????????????????? 88
3.1.4 Affine Function???????????????????????????????????????????????????????? 91
3.1.5 Convex Function???????????????????????????????????????????????????????? 92
3.2 Introduction to LMI???????????????????????????????????????????????????????????? 96
3.2.1 Control Problem and LMI???????????????????????????????????????????????????????????????????????? 96
3.2.2 Typical LMI Problems?????????????????????????????????????????????????????????????????? 97
3.2.3 From BMI to LMI: Variable Elimination???????????????????????????????????????????????????????????????????????????????????????????????????? 98
3.2.4 From BMI to LMI: Variable Change?????????????????????????????????????????????????????????????????????????????????????????? 103
3.3 Interior Point Method*?????????????????????????????????????????????????????????????????? 105
3.3.1 Analytical Center of LMI?????????????????????????????????????????????????????????????????????????? 105
3.3.2 Interior Point Method Based on Central Path???????????????????????????????????????????????????????????????????????????????????????????????????????????????? 106
Exercises???????????????????????????????? 107
Notes and References?????????????????????????????????????????????????????? 108
Chapter 4 Fundamentals of Linear System???????????????????????????????????????????????????????????????????????????????????????????? 109
4.1 Structural Properties of Dynamic System???????????????????????????????????????????????????????????????????????????????????????????????????? 109
4.1.1 Description of Linear System?????????????????????????????????????????????????????????????????????????????????? 109
4.1.2 Dual System???????????????????????????????????????????????? 111
4.1.3 Controllability and Observability???????????????????????????????????????????????????????????????????????????????????????????? 111
4.1.4 State Realization and Similarity Transformation???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 114
4.1.5 Pole?????????????????????????????????? 114
4.1.6 Zero?????????????????????????????????? 115
4.1.7 Relative Degree and Infinity Zero???????????????????????????????????????????????????????????????????????????????????????????? 120
4.1.8 Inverse System?????????????????????????????????????????????????????? 121
4.1.9 System Connections?????????????????????????????????????????????????????????????? 121
4.2 Stability???????????????????????????????????????? 124
4.2.1 Bounded-Input Bounded-Output Stability?????????????????????????????????????????????????????????????????????????????????????????????????????? 124
4.2.2 Internal Stability?????????????????????????????????????????????????????????????? 127
4.2.3 Pole-Zero Cancellation?????????????????????????????????????????????????????????????????????? 130
4.2.4 Stabilizability and Detectability???????????????????????????????????????????????????????????????????????????????????????????? 131
4.3 Lyapunov Equation???????????????????????????????????????????????????????? 132
4.3.1 Controllability Gramian and Observability Gramian???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 135
4.3.2 Balanced Realization?????????????????????????????????????????????????????????????????? 137
4.4 Linear Fractional Transformation?????????????????????????????????????????????????????????????????????????????????????? 138
Exercises???????????????????????????????? 141
Notes and References?????????????????????????????????????????????????????? 142
Chapter 5 System Performance?????????????????????????????????????????????????????????????????????? 143
5.1 Test Signal???????????????????????????????????????????? 144
5.1.1 Reference Input???????????????????????????????????????????????????????? 144
5.1.2 Persistent Disturbance?????????????????????????????????????????????????????????????????????? 145
5.1.3 Characteristic of Test Signal???????????????????????????????????????????????????????????????????????????????????? 145
5.2 Steady-State Response???????????????????????????????????????????????????????????????? 146
5.2.1 Analysis on Closed-Loop Transfer Function???????????????????????????????????????????????????????????????????????????????????????????????????????????? 146
5.2.2 Reference Tracking?????????????????????????????????????????????????????????????? 148
5.2.3 Disturbance Suppression???????????????????????????????????????????????????????????????????????? 151
5.3 Transient Response?????????????????????????????????????????????????????????? 154
5.3.1 Performance Criteria?????????????????????????????????????????????????????????????????? 154
5.3.2 Prototype Second-Order System???????????????????????????????????????????????????????????????????????????????????? 155
5.3.3 Impact of Additional Pole and Zero?????????????????????????????????????????????????????????????????????????????????????????????? 158
5.3.4 Overshoot and Undershoot?????????????????????????????????????????????????????????????????????????? 160
5.3.5 Bandwidth and Fast Response???????????????????????????????????????????????????????????????????????????????? 163
5.4 Comparison of Open-Loop and Closed-Loop Controls?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 164
5.4.1 Reference Tracking?????????????????????????????????????????????????????????????? 164
5.4.2 Impact of Model Uncertainty???????????????????????????????????????????????????????????????????????????????? 166
5.4.3 Disturbance Suppression???????????????????????????????????????????????????????????????????????? 168
Exercises???????????????????????????????? 170
Notes and References?????????????????????????????????????????????????????? 171
Chapter 6 Stabilization of Linear Systems???????????????????????????????????????????????????????????????????????????????????????????????? 172
6.1 State Feedback?????????????????????????????????????????????????? 172
6.1.1 Canonical Forms???????????????????????????????????????????????????????? 174
6.1.2 Pole Placement of Single-Input Systems?????????????????????????????????????????????????????????????????????????????????????????????????????? 178
6.1.3 Pole Placement of Multiple-Input Systems*???????????????????????????????????????????????????????????????????????????????????????????????????????????? 180
6.1.4 Principle of Pole Selection???????????????????????????????????????????????????????????????????????????????? 183
6.2 Observer?????????????????????????????????????? 184
6.2.1 Full-Order Observer???????????????????????????????????????????????????????????????? 185
6.2.2 Minimal Order Observer?????????????????????????????????????????????????????????????????????? 187
6.3 Combined System and Separation Principle?????????????????????????????????????????????????????????????????????????????????????????????????????? 191
6.3.1 Full-Order Observer Case?????????????????????????????????????????????????????????????????????????? 191
6.3.2 Minimal Order Observer Case???????????????????????????????????????????????????????????????????????????????? 192
Exercises???????????????????????????????? 194
Notes and References?????????????????????????????????????????????????????? 196
Chapter 7 Parametrization of Stabilizing Controllers?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 197
7.1 Generalized Feedback Control System???????????????????????????????????????????????????????????????????????????????????????????? 198
7.1.1 Concept???????????????????????????????????????? 198
7.1.2 Application Examples?????????????????????????????????????????????????????????????????? 199
7.2 Parametrization of Controllers?????????????????????????????????????????????????????????????????????????????????? 202
7.2.1 Stable Plant Case???????????????????????????????????????????????????????????? 202
7.2.2 General Case?????????????????????????????????????????????????? 205
7.3 Youla Parametrization???????????????????????????????????????????????????????????????? 208
7.4 Structure of Closed-Loop System???????????????????????????????????????????????????????????????????????????????????? 210
7.4.1 Affine Structure in Controller Parameter?????????????????????????????????????????????????????????????????????????????????????????????????????????? 210
7.4.2 Affine Structure in Free Parameter?????????????????????????????????????????????????????????????????????????????????????????????? 211
7.5 2-Degree-of-Freedom System?????????????????????????????????????????????????????????????????????????? 212
7.5.1 Structure of 2-Degree-of-Freedom Systems?????????????????????????????????????????????????????????????????????????????????????????????????????????? 212
7.5.2 Implementation of 2-Degree-of-Freedom Control???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 215
Exercises???????????????????????????????? 217
Notes and References?????????????????????????????????????????????????????? 220
Chapter 8 Relation between Time Domain and Frequency Domain Properties?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 221
8.1 Parseval's Theorem?????????????????????????????????????????????????????????? 221
8.1.1 Fourier Transform and Inverse Fourier Transform???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 221
8.1.2 Convolution???????????????????????????????????????????????? 222
8.1.3 Parseval's Theorem?????????????????????????????????????????????????????????????? 223
8.1.4 Proof of Parseval's Theorem???????????????????????????????????????????????????????????????????????????????? 224
8.2 KYP Lemma???????????????????????????????????????? 224
8.2.1 Application in Bounded Real Lemma???????????????????????????????????????????????????????????????????????????????????????????? 225
8.2.2 Application in Positive Real Lemma?????????????????????????????????????????????????????????????????????????????????????????????? 228
8.2.3 Proof of KYP Lemma*???????????????????????????????????????????????????????????????? 233
Exercises???????????????????????????????? 238
Notes and References?????????????????????????????????????????????????????? 238
Chapter 9 Algebraic Riccati Equation?????????????????????????????????????????????????????????????????????????????????????? 239
9.1 Algorithm for Riccati Equation?????????????????????????????????????????????????????????????????????????????????? 239
9.2 Stabilizing Solution?????????????????????????????????????????????????????????????? 242
9.3 Inner Function?????????????????????????????????????????????????? 247
Exercises???????????????????????????????? 248
Notes and References?????????????????????????????????????????????????????? 248
Chapter 10 Performance Limitation of Feedback Control???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 249
10.1 Preliminaries?????????????????????????????????????????????????? 250
10.1.1 Poisson Integral Formula???????????????????????????????????????????????????????????????????????????? 250
10.1.2 All-Pass and Minimum-Phase Transfer Functions?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 251
10.2 Limitation on Achievable Closed-loop Transfer Function???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 252
10.2.1 Interpolation Condition?????????????????????????????????????????????????????????????????????????? 252
10.2.2 Analysis of Sensitivity Function???????????????????????????????????????????????????????????????????????????????????????????? 253
10.3 Integral Relation?????????????????????????????????????????????????????????? 255
10.3.1 Bode Integral Relation on Sensitivity?????????????????????????????????????????????????????????????????????????????????????????????????????? 255
10.3.2 Bode Phase Formula???????????????????????????????????????????????????????????????? 258
10.4 Limitation of Reference Tracking???????????????????????????????????????????????????????????????????????????????????????? 261
10.4.1 1-Degree-of-Freedom System???????????????????????????????????????????????????????????????????????????????? 261
10.4.2 2-Degree-of-Freedom System???????????????????????????????????????????????????????????????????????????????? 267
Exercises???????????????????????????????? 268
Notes and References?????????????????????????????????????????????????????? 268
Chapter 11 Model Uncertainty?????????????????????????????????????????????????????????????????????? 269
11.1 Model Uncertainty: Examples?????????????????????????????????????????????????????????????????????????????? 269
11.1.1 Principle of Robust Control?????????????????????????????????????????????????????????????????????????????????? 271
11.1.2 Category of Model Uncertainty?????????????????????????????????????????????????????????????????????????????????????? 271
11.2 Plant Set with Dynamic Uncertainty???????????????????????????????????????????????????????????????????????????????????????????? 272
11.2.1 Concrete Descriptions?????????????????????????????????????????????????????????????????????? 272
11.2.2 Modeling of Uncertainty Bound?????????????????????????????????????????????????????????????????????????????????????? 275
11.3 Parametric System?????????????????????????????????????????????????????????? 277
11.3.1 Polytopic Set of Parameter Vectors???????????????????????????????????????????????????????????????????????????????????????????????? 279
11.3.2 Matrix Polytope and Polytopic System???????????????????????????????????????????????????????????????????????????????????????????????????? 281
11.3.3 Norm-Bounded Parametric System???????????????????????????????????????????????????????????????????????????????????????? 282
11.3.4 Separation of Parameter Uncertainties?????????????????????????????????????????????????????????????????????????????????????????????????????? 286
11.4 Plant Set with Phase Information of Uncertainty?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 288
11.5 LPV Model and Nonlinear Systems?????????????????????????????????????????????????????????????????????????????????????? 290
11.5.1 LPV Model?????????????????????????????????????????????? 290
11.5.2 From Nonlinear System to LPV Model???????????????????????????????????????????????????????????????????????????????????????????????? 291
11.6 Robust Stability and Robust Performance?????????????????????????????????????????????????????????????????????????????????????????????????????? 293
Exercises???????????????????????????????? 294
Notes and References?????????????????????????????????????????????????????? 295
Chapter 12 Robustness Analysis 1: Small-Gain Principle?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 296
12.1 Small-Gain Theorem???????????????????????????????????????????????????????????? 296
12.2 Robust Stability Criteria?????????????????????????????????????????????????????????????????????????? 300
12.3 Equivalence between H? Performance and Robust Stability 301
12.4 Analysis of Robust Performance???????????????????????????????????????????????????????????????????????????????????? 303
12.4.1 Sufficient Condition for Robust Performance?????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 304
12.4.2 Introduction of Scaling?????????????????????????????????????????????????????????????????????????? 305
12.5 Stability Radius of Norm-Bounded Parametric Systems?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 306
Exercises???????????????????????????????? 307
Notes and References?????????????????????????????????????????????????????? 311
Chapter 13 Robustness Analysis 2: Lyapunov Method???????????????????????????????????????????????????????????????????????????????????????????????????????????????? 312
13.1 Overview of Lyapunov Stability Theory?????????????????????????????????????????????????????????????????????????????????????????????????? 312
13.1.1 Asymptotic Stability Condition???????????????????????????????????????????????????????????????????????????????????????? 313
13.1.2 Condition for State Convergence Rate???????????????????????????????????????????????????????????????????????????????????????????????????? 314
13.2 Quadratic Stability?????????????????????????????????????????????????????????????? 314
13.2.1 Condition for Quadratic Stability?????????????????????????????????????????????????????????????????????????????????????????????? 315
13.2.2 Quadratic Stability Conditions for Polytopic Systems???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 316
13.2.3 Quadratic Stability Condition for Norm-Bounded Parametric Systems?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 318
13.3 Lur'e System???????????????????????????????????????????????? 320
13.3.1 Circle Criterion???????????????????????????????????????????????????????????? 324
13.3.2 Popov Criterion?????????????????????????????????????????????????????????? 328
13.4 Passive Systems?????????????????????????????????????????????????????? 331
Exercises???????????????????????????????? 334
Notes and References?????????????????????????????????????????????????????? 335
Chapter 14 Robustness Analysis 3: IQC Approach?????????????????????????????????????????????????????????????????????????????????????????????????????????? 336
14.1 Concept of IQC???????????????????????????????????????????????????? 336
14.2 IQC Theorem?????????????????????????????????????????????? 338
14.3 Applications of IQC?????????????????????????????????????????????????????????????? 340
14.4 Proof of IQC Theorem*?????????????????????????????????????????????????????????????????? 343
Notes and References?????????????????????????????????????????????????????? 345
Chapter 15 H2 Control???????????????????????????????????????????????????????? 346
15.1 H2 Norm of Transfer Function???????????????????????????????????????????????????????????????????????????????? 346
15.1.1 Relation with Input and Output???????????????????????????????????????????????????????????????????????????????????????? 347
15.1.2 Relation between Weighting Function and Dynamics of Disturbance/Noise?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 348
15.1.3 Computing Methods?????????????????????????????????????????????????????????????? 349
15.1.4 Condition for ||G||2 < ?
15.2 H2 Control Problem???????????????????????????????????????????????????????????? 353
15.3 Solution to Nonsingular H2 Control Problem???????????????????????????????????????????????????????????????????????????????????????????????????????????? 355
15.4 Proof of Nonsingular Solution?????????????????????????????????????????????????????????????????????????????????? 356
15.4.1 Preliminaries?????????????????????????????????????????????????????? 356
15.4.2 Proof of Theorems 15.1 and 15.2?????????????????????????????????????????????????????????????????????????????????????????? 358
15.5 Singular H2 Control?????????????????????????????????????????????????????????????? 359
15.6 Case Study: H2 Control of an RTP System?????????????????????????????????????????????????????????????????????????????????????????????????????? 361
15.6.1 Model of RTP???????????????????????????????????????????????????? 361
15.6.2 Optimal Configuration of Lamps???????????????????????????????????????????????????????????????????????????????????????? 363
15.6.3 Location of Sensors?????????????????????????????????????????????????????????????????? 364
15.6.4 H2 Control Design?????????????????????????????????????????????????????????????? 364
15.6.5 Simulation Results???????????????????????????????????????????????????????????????? 366
Exercises???????????????????????????????? 367
Notes and References?????????????????????????????????????????????????????? 369
Chapter 16 H? Control 370
16.1 Control Problem and H? Norm 370
16.1.1 Input-Output Relation of Transfer Matrix's H? Norm 370
16.1.2 Disturbance Control and Weighting Function???????????????????????????????????????????????????????????????????????????????????????????????????????????????? 371
16.2 H? Control Problem 372
16.3 LMI Solution 1: Variable Elimination???????????????????????????????????????????????????????????????????????????????????????????????? 373
16.3.1 Proof of Theorem 16.1?????????????????????????????????????????????????????????????????????? 374
16.3.2 Computation of Controller?????????????????????????????????????????????????????????????????????????????? 375
16.4 LMI Solution 2: Variable Change?????????????????????????????????????????????????????????????????????????????????????? 375
16.5 Design of Generalized Plant and Weighting Function???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 376
16.5.1 Principle for Selection of Generalized Plant???????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 376
16.5.2 Selection of Weighting Function?????????????????????????????????????????????????????????????????????????????????????????? 377
16.6 Case Study???????????????????????????????????????????? 378
16.7 Scaled H? Control 379
Exercises???????????????????????????????? 382
Notes and References?????????????????????????????????????????????????????? 383
Chapter 17 ? Synthesis 384
17.1 Introduction to ? 384
17.1.1 Robust Problems with Multiple Uncertainties?????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 384
17.1.2 Robust Performance Problem???????????????????????????????????????????????????????????????????????????????? 387
17.2 Definition of ? and Its Implication 388
17.3 Properties of ? 389
17.3.1 Special Cases?????????????????????????????????????????????????????? 389
17.3.2 Bounds of ??(M) 390
17.4 Condition for Robust H? Performance 392
17.5 D-K Iteration Design???????????????????????????????????????????????????????????????? 393
17.5.1 Convexity of the Minimization of the Largest Singular Value?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 394
17.5.2 Procedure of D-K Iteration Design?????????????????????????????????????????????????????????????????????????????????????????????? 394
17.6 Case Study???????????????????????????????????????????? 395
Exercises???????????????????????????????? 397
Notes and References?????????????????????????????????????????????????????? 398
Chapter 18 Robust Control of Parametric Systems???????????????????????????????????????????????????????????????????????????????????????????????????????????? 399
18.1 Quadratic Stabilization of Polytopic Systems???????????????????????????????????????????????????????????????????????????????????????????????????????????????? 399
18.1.1 State Feedback???????????????????????????????????????????????????????? 399
18.1.2 Output Feedback?????????????????????????????????????????????????????????? 400
18.2 Quadratic Stabilization of Norm-Bounded Parametric Systems???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 403
18.3 Robust H? Control Design of Polytopic Systems 403
18.4 Robust H? Control Design of Norm-Bounded Parametric Systems 406
Exercises???????????????????????????????? 406
Chapter 19 Regional Pole Placement?????????????????????????????????????????????????????????????????????????????????? 408
19.1 Convex Region and Its Characterization???????????????????????????????????????????????????????????????????????????????????????????????????? 408
19.1.1 Relationship between Control Performance and Pole Location???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 408
19.1.2 LMI Region and Its Characterization?????????????????????????????????????????????????????????????????????????????????????????????????? 409
19.2 Condition for Regional Pole Placement?????????????????????????????????????????????????????????????????????????????????????????????????? 411
19.3 Composite LMI Region???????????????????????????????????????????????????????????????? 416
19.4 Feedback Controller Design???????????????????????????????????????????????????????????????????????????? 418
19.4.1 Design Method?????????????????????????????????????????????????????? 418
19.4.2 Design Example: Mass-Spring-Damper System?????????????????????????????????????????????????????????????????????????????????????????????????????????????? 420
19.5 Analysis of Robust Pole Placement?????????????????????????????????????????????????????????????????????????????????????????? 420
19.5.1 Polytopic System???????????????????????????????????????????????????????????? 420
19.5.2 Norm-Bounded Parametric System???????????????????????????????????????????????????????????????????????????????????????? 422
19.6 Robust Design of Regional Pole Placement???????????????????????????????????????????????????????????????????????????????????????????????????????? 426
19.6.1 On Polytopic Systems???????????????????????????????????????????????????????????????????? 426
19.6.2 Design for Norm-Bounded Parametric System?????????????????????????????????????????????????????????????????????????????????????????????????????????????? 427
19.6.3 Robust Design Example: Mass-Spring-Damper System???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 429
Exercises???????????????????????????????? 430
Notes and References?????????????????????????????????????????????????????? 430
Chapter 20 Gain-Scheduled Control???????????????????????????????????????????????????????????????????????????????? 431
20.1 General Structure?????????????????????????????????????????????????????????? 431
20.2 LFT-Type Parametric Model?????????????????????????????????????????????????????????????????????????? 432
20.2.1 Gain-Scheduled H? Control Design with Scaling 434
20.2.2 Computation of Controller?????????????????????????????????????????????????????????????????????????????? 437
20.3 Case Study: Stabilization of a Unicycle Robot?????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 438
20.3.1 Structure and Model?????????????????????????????????????????????????????????????????? 438
20.3.2 Control Design???????????????????????????????????????????????????????? 442
20.3.3 Experiment Results???????????????????????????????????????????????????????????????? 444
20.4 Affine LPV Model???????????????????????????????????????????????????????? 446
20.4.1 Easy-to-Design Structure of Gain-Scheduled Controller?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 447
20.4.2 Robust Multiobjective Control of Affine Systems?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 449
20.5 Case Study: Transient Stabilization of a Power System?????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 452
20.5.1 LPV Model?????????????????????????????????????????????? 453
20.5.2 Multiobjective Design?????????????????????????????????????????????????????????????????????? 454
20.5.3 Simulation Results???????????????????????????????????????????????????????????????? 454
20.5.4 Robustness???????????????????????????????????????????????? 456
20.5.5 Comparison with PSS?????????????????????????????????????????????????????????????????? 456
Exercises???????????????????????????????? 458
Notes and References?????????????????????????????????????????????????????? 459
Chapter 21 Positive Real Method???????????????????????????????????????????????????????????????????????????? 460
21.1 Structure of Uncertain Closed-Loop System?????????????????????????????????????????????????????????????????????????????????????????????????????????? 460
21.2 Robust Stabilization Based on Strongly Positive Realness???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 462
21.2.1 Variable Change?????????????????????????????????????????????????????????? 463
21.2.2 Variable Elimination???????????????????????????????????????????????????????????????????? 464
21.3 Robust Stabilization Based on Strictly Positive Realness???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 465
21.4 Robust Performance Design for Systems with Positive Real Uncertainty???????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????????? 466
21.5 Case Study???????????????????????????????????????????? 469
Exercises???????????????????????????????? 472
Notes and References?????????????????????????????????????????????????????? 473
References?????????????????????????????????? 474
Index???????????????????????? 479
EULA 485

Produkt-Details

• Erscheint lt. Verlag: 15.9.2016
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Informatik ► Theorie / Studium
• Themenwelt: Naturwissenschaften
• Themenwelt: Technik ► Elektrotechnik / Energietechnik
• ISBN-10: 1-118-75441-7 / 1118754417
• ISBN-13: 978-1-118-75441-2 / 9781118754412