Introduction to Feedback Control Theory

Introduction to

Feedback Control Theory

1 Introduction
1.1 Feedback Control Systems
1.2 Mathematical Models
2 Modeling, Uncertainty, and Feedback
2.1 Finite Dimensional LTI System Models
2.2 Infinite Dimensional LTI System Models
2.2.1 A Flexible Beam
2.2.2 Systems with Time Delays
2.2.3 Mathematical Model of a Thin Airfoil
2.3 Linearization of Nonlinear Models
2.3.1 Linearization Around an Operating Point
2.3.2 Feedback Linearization
2.4 Modeling Uncertainty
2.4.1 Dynamic Uncertainty Description
2.4.2 Parametric Uncertainty Transformed to Dynamic Uncertainty
2.4.3 Uncertainty from System Identification
2.5 Why Feedback Control?
2.5.1 Disturbance Attenuation
2.5.2 Tracking
2.5.3 Sensitivity to Plant Uncertainty
2.6 Exercise Problems
3 Performance Objectives
3.1 Step Response: Transient Analysis
3.2 Steady State Analysis
3.3 Exercise Problems
4 BIBO Stability
4.1 Norms for Signals and Systems
4.2 BIBO Stability
4.3 Feedback System Stability
4.4 Routh-Hurwitz Stability Test
4.5 Stability Robustness: Parametric Uncertainty
4.5.1 Uncertain Parameters in the Plant
4.5.2 Kharitanov's Test for Robust Stability
4.5.3 Extensions of Kharitanov's Theorem
4.6 Exercise Problems
5 Root Locus
5.1 Root Locus Rules
5.1.1 Root Locus Construction
5.1.2 Design Examples
5.2 Complementary Root Locus
5.3 Exercise Problems
6 Frequency Domain Analysis Techniques
6.1 Cauchy's Theorem
6.2 Nyquist Stability Test
6.3 Stability Margins
6.4 Stability Margins from Bode Plots
6.5 Exercise Problems
7 Systems with Time Delays
7.1 Stability of Delay Systems
7.2 Pade Approximation of Delays
7.3 Roots of a Quasi-Polynomial
7.4 Delay Margin
7.5 Exercise Problems
8 Lead, Lag, and PID Controllers
8.1 Lead Controller Design
8.2 Lag Controller Design
8.3 Lead--Lag Controller Design
8.4 PID Controller Design
8.5 Exercise Problems
9 Principles of Loopshaping
9.1 Tracking and Noise Reduction Problems
9.2 Bode's Gain-Phase Relationship
9.3 Design Example
9.4 Exercise Problems
10 Robust Stability and Performance
10.1 Modeling Issues Revisited
10.1.1 Unmodeled Dynamics
10.1.2 Parametric Uncertainty
10.2 Stability Robustness
10.2.1 A Test for Robust Stability
10.2.2 Special Case: Stable Plants
10.3 Robust Performance
10.4 Controller Design for Stable Plants
10.4.1 Parameterization of all Stabilizing Controllers
10.4.2 Design Guidelines for Q(s)
Minimum phase plants
Non-minimum phase plants
Smith predictor
10.5 Design of H-infinity Controllers
10.5.1 Problem Statement
10.5.2 Spectral Factorization
10.5.3 Optimal H-infinity Controller
10.5.4 Suboptimal H-infinity Controllers
10.6 Exercise Problems
11 Basic State Space Methods
11.1 State Space Representations
11.2 State Feedback
11.2.1 Pole Placement
11.2.2 Linear Quadratic Regulators
11.3 State Observers
11.4 Feedback Controllers
11.4.1 Observer Plus State Feedback
11.4.2 H_2 Optimal Controller
11.4.3 Parameterization of all Stabilizing Controllers
11.5 Exercise Problems
Bibliography
Index

Introduction to

Feedback Control Theory

TABLE OF CONTENTS