3rd Edition

# Robust Control System Design Advanced State Space Techniques

ISBN 9781032195193
320 Pages 41 B/W Illustrations
Published June 1, 2022 by CRC Press

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ISBN 9781003259572
320 Pages 41 B/W Illustrations
Published June 1, 2022 by CRC Press

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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.

1. System Mathematical Models and Basic Properties
1.1 Two kinds of mathematical models
1.2 Eigenstructure decomposition of a state space model
1.3 System order, controllability, and observability
1.4 System poles and zeros
Exercises
2. Single-System Performance and Sensitivity
2.1 System Performance
2.2 System sensitivity and robustness
Conclusion
Exercises
3. Feedback System Sensitivity
3.1 Sensitivity and loop transfer function of feedback systems
3.2 Sensitivity of feedback systems of modern control theory
Summary
4. A New Feedback Control Design Principle and Approach
4.1 Basic design concept of observers---direct generation of state feedback control signal without explicit system states
4.2 Performance of observer feedback system---separation property
4.3 Eight drawbacks of the current state space control design and separation principle
4.4 A new design principle that guarantees the realization of robustness of generalized state feedback control, and its dynamic output compensator structure
Exercises
5. Computation of the Solution of Matrix Equation TA – FT = LC
5.1 Computation of system’s observable Hessenberg form
5.2 Computation of the solution of matrix equation TA – FT = LC
Exercises
6. Observer Design 1: For Robustness Realization
6.1 Solution of matrix equation TB = 0
6.2 Analysis and examples of this design solution
6.3 Complete unification of two existing basic control structures
Exercises
7. Observer Design 2: For Other Special Purposes
7.1 Minimal order linear functional observer design
7.2 Fault detection, isolation and control design
Exercises
8. Feedback Control Design for Eigenvalue (Pole) Assignment
8.1 Selection of the feedback system poles
8.2 Pole placement by state feedback control
8.3 Pole placement by generalized state feedback control
8.4 Adjustment of generalized state feedback control design
8.5 Summary of eigen-structure assignment designs
Exercises
9. Feedback Control Design for Eigenvector Assignment
9.1 Numerical iterative methods
9.2 Analytical decoupling method
Exercises
10. Feedback Control Design for Quadratic Optimal Control
10.1 Design of state feedback control
10.2 Design of generalized state feedback control
10.3 Comparison and conclusion of feedback control designs
Exercises
Appendix A: Relevant Linear Algebra and Numerical Linear Algebra
Appendix B: Real Design Projects and Problems
References
Index

### Biography

Chia-Chi Tsui was born in 1953, Shanghai, China. He worked at a state farm in northeast China between 1969 and 1975. He received Bachelor of Computer Science degree from Concordia University, Montreal, Canada in 1979. He received his Masters and Ph. D. degrees from Electrical Engineering Department, State University of New York at Stony Brook in 1980 and 1983, respectively. He has held teaching positions at Northeastern University, City University of New York Staten Island College, and DeVry University New York. His research interest is linear feedback control system design, including robust control design.

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