Essentials of Robust Control

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This chapter gives a brief description of the problems considered in this book and the key results presented in each chapter. This chapter gives a brief description of the problems considered in this book and the key results presented in each chapter.
P reface Robustness of control systems to disturbances and uncertainties has always been the central issue in feedback control. Feedback would not be needed for most control systems if there were no disturbances and uncertainties. Developing multivariable robust control methods has been the focal point in the last two decades in the control community. The state-of-the-art Hoo robust control theory is the result of this effort This book introduces some essentials of robust and Hoo control theory. It grew from another book by this author, John C. doyle, and Keith glover, entitled Robust and Optimal control, which has been extensively class-tested in many universities around the world. Unlike that book, which is intended primarily as a comprehensive reference of robust and Hoo control theorv this book is intended to be a text for a graduate course in multivariable control. It is also intended to be a reference for practicing control engineers who are interested in applying the state-of-the-art robust control techniques in their applications. With this objective in mind. I have streamlined the presentation addcd morc than 50 illustrative examples, included many rclated MATLAB commands and more than 150 exercise problems, and added some recent developments in the area of robust control such as gap metric, v-gap metric, model validation, and mixed A problem. In addition, many proofs are completely rewritten and some advanced topics are either deleted completely or do not get an in-depth treatment The prerequisite for reading this book is some basic know ledge of classical control theory and state-space theory. The text contains more material than could be covered in detail in a one-semester or a one-quarter course. Chapter I gives a chapter-by-chapter suInlllary of the Illain results presented in the book, which could be used as a guide for the selection of topics for a specific course. Chapters 2 and 3 can be used as a refresher for somc lincar algebra facts and somc standard lincar systcm thcory. A coursc focusing on loo control should cover at least most parts of Chapters 4-6, 8, 9, 11-13, and Sections 14. 1 and 14.2. An advanced Hoo control course should also include the rest of Chapter 14, Chapter 16, and possibly Chapters 10, 7, and 15. A course focusing on robustness and model uncertainty should cover at least Chapters 4, 5, and 8 10. Chapters 17 and 1& can be added to any advanced robust and Hoo control course if time permits I have tried hard to eliminate obvious mistakes. It is, however, impossible for me to make the book perfect. Readers are encouraged to send corrections, comments, and MATLAB is a registered trademark of The Math Works, Inc PREFACE suggestions to me, preferably by electronic mail, at kemin@ee.lsu.edu I am also planning to put any corrections, modifications, and extensions on the Internet so that they can be obtained either from the following anonymous ftp ftp gate.ee.Isu. edu cd pub/kemin/books/essentials/ or from the author's home page http://kilo.ee.lsuedu/kenin/books/essentials/ This book would not be possible without the work donc jointly for the previous book with Professor John C. Doyle and Professor Keith Glover. I thank them for their influence on mv research and on this book Their serious a ttitudes toward scientific research have been reference models for me. I am especially grateful to John for having me as a research fellow in Caltech, where I had two very enjoyable years and had opportunities to catch a glimpse of his"BIG PICTURE of contro I want to thank my editor from Prentice Hall, Tom Robbins, who originally proposed the idea for this book and has been a constant source of support for me while writing it Without his support and encouragement, this pro ject would have been a difficult one It has been my great pleasure to work with him I would like to express my sincere gratitude to Professor Bruce A. Francis for giving me many helpful comments and suggestions on this book. Professor Francis has also kindly provided many exercises in the book. I am also grateful to Professor Kang-Zhi Liu rofessor Zheng-Hua Luo, who have made many useful comments and suggestions I want to thank Professor Glen Vinnicombe for his generous help in the preparation of Chapters 16 and 17. Special thanks go to Professor Jianqing Mao for providing me the opportunity to present much of this material in a series of lectures at Beijing University of Aeronautics and Astronautics in the summer of 1996 In additioN, I would like to thaik all those who have helped in Manly ways in Making his book possible, especiall y Professor pramod P. Khargonekar, Professor Andre tits Professor Andrew Packard, Professor Jie Chen, Professor Jakob Stoustrup, Professor Hans Henrik Niemann, Professor Malcolm Smith, Professor Tryphon Georgiou, Profes sor Tongwen Chen, Professor Hitay Ozbay, Professor Gary Balas, Professor Carolyn Beck. Professor Dennis s. bernstein. Professor mohamed Darouach. Dr. Bobby boden heimer, Professor Guoxiang Gu, Dr. Weimin Lu, Dr. John Morris, Dr. Matt Newlin Professor Li Qiu, Professor Hector P. Rotsteill, Professor Andrew Teel, Professor Ja gannathan Ramanujam, Dr Linda g. Bushnell, Xiang Chen, Greg Salomon, Pablo A Parrilo, and many othcr people I would also like to thank the following agencies for supporting my research: National Science Foundation, Army Research Office(ARO), Air Force of Scientific Research, and the board of regents in the State of louisiana Finally, I would like to thank my wife, Jing, and my son, Eric, for their generous support, understanding, and patience during the writing of this book Kemin zhou PREFACE Here is how 7o is pronounced in Chinese 愛趣無窮 It means "The joy of love is endless Contents Preface Notation and Symbols List of AcronlyIlls 1 Introduction 1.1 What is this book abe 1.2 Highlights of This Book 1.3 Notes and references 1.4 Problems 10 2 Linear Algebra 11 2.1 Linear Subspaces 11 2.2 Eigenvalues and Eigenvectors 12 2. 3 Matrix Inversion formulas 13 2. 4 Invariant Subspaces 15 2.5 Vector Norms and Matrix Norms 16 2.6 Singular Value Decomposition 19 2. 7 Semidefinite Matrices 23 2. 8 Notes and references 翻b鲁 24 2.9 Problems 3 Linear Systems 27 3.1 Descriptions of Linear Dynamical Systems 27 3.2 Controllability and Observability 28 3.3 Obscrvcrs and obscrvcr-Bascd Controllers 31 3.4 OperatiOns on SysteIIs 34 3.5 State-Space Realizations for Transfer Matrices 35 3.6 Multivariable System Poles and Zeros 38 3.7 Notes and references 41 3.8 Problems 42 XIl CONTENTS 42andH。 Spaces 45 4.1 Hilbert Spaces 45 4.2 H2 and Hoo spaces 47 4.3 Computing L2 and H2 Norms 53 4.4 Computing Loo and Hoo Norms 55 4.5 Notes anld References 61 4.6 Problems 5 Internal Stability 65 5.1 Feedback Structure 65 5.2 Well-Posedness of Feedback Loop 66 5.3 Internal Stability 5. 4 Coprime factorization over RH 71 5.5 Notes and references 77 5.6 Proble 77 6 Performance Specifications and limitations 81 6.1 Feedback pl 81 6.2 Weighted H2 and Hoo Performance 85 6.3 Sele of Weighting functions 89 6.4 Bodes Gain and phase relation 94 6.5 Bodes Sensitivity Integra.I 98 6.6 Analyticity Constraints 100 6.7 Notes and References 6.8 Problems ......102 7 Balanced model reduction 105 7. 1 Lyapunov Equations 106 7. 2 Balanced realizations 107 7.3 Model reduction by Balanced Truncation ...117 7. 4 Frequency-Weighted Balanced Model reduction 124 7.5 Notes and rcfcrcnccs 126 7.6 Proble 127 8 Uncertainty and Robustness 12g 8.1 Model Uncertainty 129 8.2 Small gain theorem 137 8.3 Stability under Unstructured Uncertainties 141 8. 4 Robust performance 147 8.5 Skewed specifications 150 8.6 Classical Control for MIMO Systcms 154 8. 7 Notes and References 157 8.8 Proble 158 CONTENTS 9 Linear fractional Transformation 165 9.1 Linear Fractional Transformations 165 9.2 Basic Principle 173 9.3 Redheffer Star Products 178 9.4 Notes and References ...180 9.5 Problems 181 10μ and p Synthesis 183 10.1 General Framework for System robustness 184 10.2 Structured Singular value 187 10.3 Structured Robust Stability anld Performance 200 10.4 Overview of p Synthesis 213 10.5 Notes and references .216 10.6 Problems 17 l1 Controller parameterization 221 11.1 Existencc of Stabilizing Controllers 222 1.2 ParallleterizatiOn of All Stabilizing Controllers 224 11.3 Coprime Factorization Approach 228 11.4 Notes and References 231 11.5 Problems ,,..231 12 Algebraic Riccati Equations 233 12. 1 Stabilizing Solution and Riccati Operator .234 12.2 Inner Functions 12.3 Notes and references 246 12.4 Proble 246 13 H2 Optimal Control 253 13.1 Introduction to Regulator Problem 3 13.2 Standard lQr problem 番番 255 13.3 Extended LQR Problen 258 13.4 Guaranteed Stability Margins of LQR 259 13.5 Standard H2 Problem 61 13.6 Stability Margins of H2 Controllers 265 13.7 Notes and references ,267 13.8 Problems 267 14H Control 269 14.1 Problem formulation 269 14. 2 A Simplified Ho Control Problem .270 14.3 Optimality and limiting beh 14.4 Minimum Entropy Controller 286 14.5 An Optimal Controller 286 CONTENTS 14. 6 General t solutions 288 14.7 Relaxing Assumpti 291 14.8 H2 and Hoo Integral Control 294 14.9 Ho filtering 297 14.10Notes and references 299 14.11 Problems 300 15 Controller reduction 305 15. 1 H Controller reductions 306 15.2 Notes and refe 5) 15.3 Problcms 313 16 too Loop shaping 315 16. 1 Robust Stabilization of Coprime factors 315 16.2 Loop-Shaping Design 325 6.3 Justification for Hoo Loop Shaping 328 16.4 Further Guidelines for Loop Shaping 334 16.5 Notes and refe 341 16.6 Proble 342 7 Gap Metric and v-Gap Metric 349 17.1 Gap metric 350 17.2 v-Gap metric 357 17.3 Geometric Interpretation of v-Gap Metric 370 17.4 Extended Loop-Shaping Design 373 17.5 Controller Order Reduction 375 17.6 Notes and References 375 17.7 Problems 375 18 Miscellaneous Topics 377 18.1 Model validation 377 18.2 Mixed u Analysis and Synthesis .381 18.3 Notes and References .389 18.4 Problems Bibliography 391 Index 407

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narrowmiss 很好,这本书是故障诊断的基础
2015-06-10
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