Robust Control System Design : Advanced State Space Techniques

This book presents a synthesized design principle versus the existing separation principle of modern control theory of over six decades since the start. Guided by this new principle, a generalized state feedback control can be designed based on the parameters of observer and for a great majority of plant systems, and the robust property of this control can be fully realized. The robust property of the existing state feedback control which is designed separate from the parameters of its realizing observer, cannot be realized for a great majority of plant systems. By freely design and adjust the observer order, the corresponding generalized state feedback control can unify completely the existing state feedback control and static output feedback control, and can adjust effectively the tradeoff between performance and robustness. This generalized state feedback control can assign eigen-structure, and can improve performance and robustness far more effectively than the control designed using classical control theory. Equally significant, the results of this book are very simple that can be comprehended and grasped very easily. These results are introduced and illustrated from the basic level, and use only the basic mathematical tools. Ample examples and exercise problems that can be solved by hand computation, are provided. This third edition made substantial improvement on this aspect. Modern control theoreticians only formulated the feedback control design problem in various ways, the point however is to really solve this problem. This book presents a synthesized design principle versus the existing separation principle of modern control theory of over six decades since the start. Guided by this new principle, a generalized state feedback control can be designed based on the parameters of observer and for a great majority of plant systems. Cover 1 Half Title 2 Title Page 4 Copyright Page 5 Table of Content 6 Preface 10 Preface (Second Edition) 14 Author 18 1. System Mathematical Models 20 1.1 Two Kinds of Mathematical Models 20 1.2 Eigenstructure Decomposition of the State Space Model 27 1.3 System Order, Controllability, and Observability 30 1.4 System Poles and Zeros 37 Exercises 39 2. Single-System Performance and Sensitivity 44 2.1 System Performance 44 2.2 System Sensitivity and Robustness 53 2.2.1 The Sensitivity of Eigenvalues (Robust Performance) 56 2.2.2 The Sensitivity of System Stability (Robust Stability) 60 2.3 Conclusion 65 Exercises 65 3. Feedback System Sensitivity 68 3.1 Sensitivity and Loop Transfer Function of the Feedback Systems 68 3.1.1 Sensitivity to System Model Uncertainty 70 3.1.2 Sensitivity to Control Input Disturbance 72 3.2 Sensitivity of Feedback Systems of the Modern Control Theory 75 3.2.1 State Feedback Control Systems 75 3.2.2 Static Output Feedback Control Systems 79 3.2.3 Observer Feedback System – Loop Transfer Recovery 81 3.3 Summary 89 4. A New Feedback Control Design Principle/Approach 92 4.1 Basic Observer Design Concept – Generating State Feedback Signal Directly Without Generating Explicit System States 93 4.2 Performance of the Observer Feedback System – Separation Property 96 4.3 Eight Drawbacks and Irrationalities of the Modern Control Design and Separation Principle 98 4.3.1 Drawback 1 of Separation Principle: Invalid Basic Assumption 98 4.3.2 Drawback 2 of Separation Principle: Ignor Key Parameters 99 4.3.3 Drawback 3 of Separation Principle: Wrong Design Priority 99 4.3.4 Drawback 4 of Separation Principle: Unnecessary Design Requirement 100 4.3.5 Drawback 5 of Separation Principle: Abandon Existing Control Structure 100 4.3.6 Drawback 6 of Separation Principle: Failed Robust Realization 101 4.3.7 Drawback 7 of Separation Principle: Two Extreme Controls 103 4.3.8 Drawback 8 of Separation Principle: Two Extreme Control Structures 103 4.4 A New Design Principle That Guarantees the General and Full Realization of Robustness of the Generalized State Feedback Control 104 Exercises 111 5. Solution of Matrix Equation TA−FT = LC 116 5.1 Computation of System’s Observable Hessenberg Form 116 5.1.1 Single-Output Systems 116 5.1.2 Multiple-Output Systems 118 5.2 Computation of the Solution of Matrix Equation TA−FT = LC 124 5.2.1 Eigen-Structure Case A 125 5.2.2 Eigen-Structure Case B 128 Exercises 134 6. Observer Design for Robust Realization 136 6.1 Solution of Matrix Equation TB = 0 137 6.2 Analysis and Examples of This Design Solution 139 6.3 Complete Unification of Two Existing Basic Modern Control System Structures 152 6.4 Observer Order Adjustment to Tradeoff between Performance and Robustness 154 Exercises 157 7. Observer Design for Other Special Purposes 162 7.1 Minimal-Order Linear Functional Observer Design 163 7.1.1 Simplest Possible Design Formulation – Most Significant Theoretical Development 163 7.1.2 Really Systematic Design Algorithm and Guaranteed Observer Order Upper Bound 165 7.1.3 The Lowest Possible Observer Order Upper Bound – The Best Possible Theoretical Result – The Whole Design Problem Is Essentially Solved 174 7.2 Fault Detection, Isolation, and Control Design 176 7.2.1 Fault Models and Design Formulation of Fault Detection and Isolation 176 7.2.2 Design Algorithm and Examples of Fault Detection and Isolation 179 7.2.3 Adaptive Fault Control and Accommodation (Tsui, 1997) 182 7.2.4 The Treatment of Model Uncertainty and Measurement Noise (Tsui, 1994b) 186 Exercises 190 8. Control Design for Eigenvalue Assignment 196 8.1 Eigenvalue (Pole) Selection 196 8.2 Eigenvalue Assignment by State Feedback Control 198 8.3 Eigenvalue Assignment by Generalized State Feedback Control 200 8.4 Modifications of Generalized State Feedback Control for Eigenstructure Assignment (Tsui, 2004b,c, 2005) 212 8.5 Summary of Eigenstructure Assignment Designs 216 Exercises 218 9. Control Design for Eigenvector Assignment 222 9.1 Numerical Iterative Methods (Kautsky et al., 1985) 223 9.2 Analytical Decoupling Method 228 9.3 Summary of Eigenstructure Assignment of Chapters 8 and 9 238 Exercises 239 10. Control Design for LQ Optimal Control 242 10.1 Direct State Feedback Control Design 244 10.2 Design of Generalized State Feedback Control 246 10.3 Comparison and Conclusion of Feedback Control Designs 250 Exercises 253 Appendix A: Linear Algebra & Numerical Linear Algebra 256 Appendix B: Design Projects and Problems 282 References 290 Index 300 Feedback,System;,Matrix,Equation;,Robust,Realization;,Observer,Design;,Eigenvalue,Assignment;,Eigenvector,Assignment;,LQ,Optimal,Control Feedback System,Matrix Equation,Robust Realization,Observer Design,Eigenvalue Assignment,Eigenvector Assignment,LQ Optimal Control