Robust control design: an optimal control approach

378 Pages·2007·2.335 MB·English

by  Feng Lin

Robust Control Design
RSP SERIES IN CONTROL THEORY
AND APPLICATIONS
SeriesEditor: ProfessorWitoldPedrycz
DepartmentofElectricalandComputerEngineering,UniversityofAlberta
FuzzyControlandFuzzySystems,Second,ExtendedEdition
WitoldPedrycz
Robust Control Design
An Optimal Control Approach
Feng Lin
Wayne State University,
USA and Tongji University, China
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Lin,Feng.
Robustcontroldesign:anoptimalcontrolapproach/FengLin.
p. cm.
Includesindex.
ISBN978-0-470-03191-9(cloth)
1. Automaticcontrol. I. Title.
TJ213.L4552007
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2007020129
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Contents
Preface xi
Notation xiii
1 Introduction 1
1.1 Systems and Control 1
1.2 Modern Control Theory 5
1.3 Stability 6
1.4 Optimal Control 8
1.5 Optimal Control Approach 9
1.6 Kharitonov Approach 10
1.7 H and H Control 11
(cid:2) 2
1.8 Applications 12
1.9 Use of this Book 13
2 Fundamentals of Control Theory 15
2.1 State Space Model 16
2.2 Responses of Linear Systems 17
2.3 Similarity Transformation 25
2.4 Controllability and Observability 33
2.5 Pole Placement by State Feedback 44
2.6 Pole Placement Using Observer 52
2.7 Notes and References 63
2.8 Problems 63
3 Stability Theory 69
3.1 Stability and Lyapunov Theorem 69
3.2 Linear Systems 73
viii CONTENTS
3.3 Routh–Hurwitz Criterion 75
3.4 Nyquist Criterion 85
3.5 Stabilizability and Detectability 93
3.6 Notes and References 98
3.7 Problems 98
4 Optimal Control and Optimal Observers 101
4.1 Optimal Control Problem 101
4.2 Principle of Optimality 105
4.3 Hamilton–Jacobi–Bellman Equation 110
4.4 Linear Quadratic Regulator Problem 112
4.5 Kalman Filter 120
4.6 Notes and References 127
4.7 Problems 127
5 Robust Control of Linear Systems 133
5.1 Introduction 134
5.2 Matched Uncertainty 137
5.3 Unmatched Uncertainty 145
5.4 Uncertainty in the Input Matrix 154
5.5 Notes and References 169
5.6 Problems 170
6 Robust Control of Nonlinear Systems 173
6.1 Introduction 174
6.2 Matched Uncertainty 176
6.3 Unmatched Uncertainty 180
6.4 Uncertainty in the Input Matrix 188
6.5 Notes and References 210
6.6 Problems 210
7 Kharitonov Approach 213
7.1 Introduction 213
7.2 Preliminary Theorems 214
7.3 Kharitonov Theorem 227
7.4 Control Design Using Kharitonov Theorem 231
7.5 Notes and References 236
7.6 Problems 236
8 H and H Control 239
(cid:2) 2
8.1 Introduction 239
8.2 Function Space 240
8.3 Computation of H and H Norms 244
2 (cid:2)
8.4 Robust Control Problem as H and H Control
2 (cid:2)
Problem 252
CONTENTS ix
8.5 H /H Control Synthesis 256
2 (cid:2)
8.6 Notes and References 273
8.7 Problems 273
9 Robust Active Damping 277
9.1 Introduction 277
9.2 Problem Formulation 279
9.3 Robust Active Damping Design 282
9.4 Active Vehicle Suspension System 287
9.5 Discussion 290
9.6 Notes and References 295
10 Robust Control of Manipulators 297
10.1 Robot Dynamics 297
10.2 Problem Formulation 302
10.3 Robust Control Design 304
10.4 Simulations 306
10.5 Notes and References 316
11 Aircraft Hovering Control 317
11.1 Modelling and Problem Formulation 317
11.2 Control Design for Jet-borne Hovering 322
11.3 Simulation 330
11.4 Notes and References 336
Appendix A: Mathematical Modelling of Physical Systems 339
References and Bibliography 351
Index 363