Introduction to Feedback Control

Prof. Li Qiu received the B.Eng degree from Hunan University, Changsha, Hunan, China, in 1981. He received the M.A.Sc. and Ph.D. degrees from the University of Toronto, Toronto, Ont., Canada, in 1987 and 1990, respectively. He joined Hong Kong University of Science and Technology, Hong Kong SAR, China, in 1993, where he is now a professor of Electronic and Computer Engineering. Prof. Qiu's research interests include system, control, information theory, and mathematics for information technology. He served as an associate editor of the IEEE Transactions on Automatic Control and an associate editor of Automatica. He is now a Distinguished Lecturer of IEEE Control Systems Society and the general chair of the 7th Asian Control Conference, which is to be held in Hong Kong in 2009. He is a fellow of IEEE.   Prof. Kemin Zhou was born in Wuhu, China, in 1962. He received B.S. degree from Beijing University of Aeronautics and Astronautics in 1982, M.S.E.E. and Ph.D. degrees from University of Minnesota in 1986 and 1988, respectively. Since 1990, he has been with Louisiana State University where he is currently Mark and Carolyn C. Guidry Distinguished Professor in Electrical and Computer Engineering. He is the leading author of two books in the field: Robust and Optimal Control (Prentice Hall, 1995), which has been used worldwide as graduate textbook and research references and has been translated into Japanese (1997) and Chinese (2002), and Essentials of Robust Control (Prentice Hall, 1997). He is/was an Associate Editor of Automatica, IEEE Transactions on Automatic Control, SIAM Journal on Control and Optimization, Systems and Control Letters, Journal of System Sciences and Complexity, andJournal of Control Theory and Applications. He was named the Oskar R. Menton Endowed Professor in 1998 and Voorhies Distinguished Professor in 2004, recognized for outstanding accomplishments and contributions to LSU by the House of Representatives of the Louisiana Legislature in 2004, and received outstanding young investigator award from Natural Science Foundation of China in 2004. He was also selected in 2004 as the prestigious Chang Jiang Jiang Zuo Professor. He has also been honored as one of LSU 2008 Rainmakers. He was elected IEEE Fellow in 2003.

1 Overview 1

1.1 Introduction

1.2 Basic Concepts

1.3 Basic Structures of Feedback Systems

1.4 About This Book

1.5 Problems

1.6 Notes and References

 

2 Modeling and Simulation 15

2.1 Modeling Based on First Principles

2.1.1 Electrical systems

2.1.2 Mechanical systems

2.1.3 Electromechanical systems

2.2 State Space Model and Linearization

2.3 Transfer Functions and Impulse Responses

2.4 Simplifying Block Diagrams

2.5 Transfer FunctionModeling

2.6 MATLAB Manipulation of LTI Systems

2.7 Simulation and Implementation of Systems

2.7.1 Hardware simulation and implementation

2.7.2 Software simulation and implementation

2.8 MISO and SIMO Systems

2.9 Modeling of Closed-Loop Systems

2.10 Case Studies

2.10.1 Ball and beam system

2.10.2 Inverted pendulum system

2.11 Problems

2.12 Notes and References

 

3 Stability and Stabilization

3.1 Concept of Stability

3.2 Routh Criterion

3.3 Other Stability Criteria

3.4 Robust Stability

3.5 Stability of Closed-Loop Systems

3.6 Pole PlacementDesign

3.7 All Stabilizing Controllers*

3.8 All Stabilizing 2DOF Controllers*

3.9 Case Studies

3.9.1 Ball and beamsystem

3.9.2 Inverted pendulum system

3.10 Problems

3.11 Notes and References

 

4 Time Domain Analysis

4.1 Responses to Typical Input Signals

4.2 Step Response Analysis

4.3 Dominant Poles and Zeros

4.4 Steady-State Response and System Type

4.5 InternalModel Principle

4.6 Undershoot

4.7 Overshoot

4.8 Time-Domain Signal and System Norms

4.9 Computation of the Time Domain 2-Norm

4.10 Problems

4.11 Notes and References

 

5 Root Locus Method

5.1 Root Locus Techniques

5.2 Derivations of Root Locus Rules*

5.3 Effects of Adding Poles and Zeros

5.4 Phase-Lag Controller

5.5 PI Controller

5.6 Phase-Lead Controller

5.7 PD Controller

5.8 Lead-Lag or PID Controller

5.9 2DOF Controllers

5.10 General Guidelines in Root Locus Design

5.11 Complementary Root Locus

5.12 Strong Stabilization

5.13 Case Study — Ball and Beam System

5.14 Problems

5.15 Notes and References

 

6 Frequency Domain Analysis

6.1 Frequency Response

6.2 Bode Diagrams

6.3 Nyquist Stability Criterion

6.4 Gain Margin and Phase Margin

6.5 Closed-loop Frequency Response

6.6 Nichols Chart

6.7 Riemann Plot

6.8 Problems

6.9 Notes and References

 

7 Classical Design in Frequency Domain

7.1 Phase-Lag Controller

7.2 PI Controller

7.3 Phase-Lead Controller

7.4 PD Controller

7.5 Lead-Lag or PID Controller

7.6 Ziegler and Nichols Tuning Rules

7.7 Derivative Control

7.8 Alternative PID Implementation

7.9 Integral Control and Antiwindup

7.10 Design by Loopshaping

7.11 Bode’s Gain and Phase Relation

7.12 Bode’s Sensitivity Integral

7.13 Problems

7.14 Notes and References

 

8 Performance and Robustness

8.1 Frequency Domain 2-Norm of Signals and Systems

8.2 Frequency Domain 8-Normof Systems

8.3 Model Uncertainties and Robust Stability

8.4 Chordal and Spherical Distances

8.5 Distance between Systems

8.6 Uncertainty and Robustness

8.7 Problems

8.8 Notes and References

 

9 Optimal and Robust Control

9.1 Controller with Optimal Transient

9.2 Controller with Weighted Optimal Transient

9.3 Minimum Energy Stabilization

9.4 Derivation of the Optimal Controller*

9.5 Optimal Robust Stabilization

9.6 Stabilization with Guaranteed Robustness

9.7 Problems

9.8 Notes and References

 

Bibliography

A Laplace Transform

A.1 Definition

A.2 Properties

A.3 Inverse Laplace Transform

A.4 Problems

A.5 Notes and References

 

B Matrices and Polynomials

B.1 Matrices

B.2 Polynomials

B.3 Problems

B.4 Notes and References