Introduction to Feedback Control

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