Table of Contents
1 Introduction 1
1.1 Feedback Control Systems 1
1.2 Mathematical Models 5
2 Modeling, Uncertainty, and Feedback 9
2.1 Finite Dimensional LTI System Models 9
2.2 Infinite Dimensional LTI System Models 11
2.2.1 A Flexible Beam 11
2.2.2 Systems with Time Delays 12
2.2.3 Mathematical Model of a Thin Airfoil 14
2.3 Linearization of Nonlinear Models 16
2.3.1 Linearization Around an Operating Point 16
2.3.2 Feedback Linearization 17
2.4 Modeling Uncertainty 20
2.4.1 Dynamic Uncertainty Description 20
2.4.2 Parametric Uncertainty Transformed to Dynamic Uncertainty 22
2.4.3 Uncertainty from System Identification 26
2.5 Why Feedback Control? 27
2.5.1 Disturbance Attenuation 29
2.5.2 Tracking 29
2.5.3 Sensitivity to Plant Uncertainty 30
2.6 Exercise Problems 31
3 Performance Objectives 35
3.1 Step Response: Transient Analysis 35
3.2 Steady State Analysis 40
3.3 Exercise Problems 42
4 BIBO Stability 43
4.1 Norms for Signals and Systems 43
4.2 BIBO Stability 45
4.3 Feedback System Stability 49
4.4 Routh-Hurwitz Stability Test 53
4.5 Stability Robustness: Parametric Uncertainty 55
4.5.1 Uncertain Parameters in the Plant 55
4.5.2 Kharitanov's Test for Robust Stability 57
4.5.3 Extensions of Kharitanov's Theorem 59
4.6 Exercise Problems 61
5 Root Locus 63
5.1 Root Locus Rules 66
5.1.1 Root Locus Construction 67
5.1.2 Design Examples 70
5.2 Complementary Root Locus 79
5.3 Exercise Problems 81
6 Frequency Domain Analysis Techniques 85
6.1 Cauchy's Theorem 86
6.2 Nyquist Stability Test 87
6.3 Stability Margins 91
6.4 Stability Margins from Bode Plots 96
6.5 Exercise Problems 99
7 Systems with Time Delays 101
7.1 Stability of Delay Systems 103
7.2 Padé Approximation of Delays 105
7.3 Roots of a Quasi-Polynomial 110
7.4 Delay Margin 113
7.5 Exercise Problems 119
8 Lead, Lag, and PID Controllers 121
8.1 Lead Controller Design 125
8.2 Lag Controller Design 131
8.3 Lead-Lag Controller Design 133
8.4 PID Controller Design 135
8.5 Exercise Problems 137
9 Principles of Loopshaping 139
9.1 Tracking and Noise Reduction Problems 139
9.2 Bode's Gain-Phase Relationship 144
9.3 Design Example 146
9.4 Exercise Problems 152
10 Robust Stability and Performance 155
10.1 Modeling Issues Revisited 155
10.1.1 Unmodeled Dynamics 156
10.1.2 Parametric Uncertainty 158
10.2 Stability Robustness 160
10.2.1 A Test for Robust Stability 160
10.2.2 Special Case: Stable Plants 165
10.3 Robust Performance 166
10.4 Controller Design for Stable Plants 170
10.4.1 Parameterization of all Stabilizing Controllers 170
10.4.2 Design Guidelines for Q(s) 171
10.5 Design of H∞ Controllers 178
10.5.1 Problem Statement 178
10.5.2 Spectral Factorization 180
10.5.3 Optimal H∞ Controller 181
10.5.4 Suboptimal H∞ Controllers 186
10.6 Exercise Problems 189
11 Basic State Space Methods 191
11.1 State Space Representations 191
11.2 State Feedback 193
11.2.1 Pole Placement 194
11.2.2 Linear Quadratic Regulators 196
11.3 State Observers 199
11.4 Feedback Controllers 200
11.4.1 Observer Plus State Feedback 200
11.4.2 H2 Optimal Controller 202
11.4.3 Parameterization of all Stabilizing Controllers 204
11.5 Exercise Problems 205
Bibliography 209
Index 215
