# Contents. PART I METHODS AND CONCEPTS 2. Transfer Function Approach Frequency Domain Representations... 42

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1 Contents Preface xiii 1. Introduction Continuous and Discrete Control Systems Open-Loop and Closed-Loop Control Systems State Space and Transfer Functions Mathematical Modeling of Real Physical Systems Models of Some Control Systems Linearization of Nonlinear Systems MATLAB Computer Analysis and Design Book Organization References Problems PART I METHODS AND CONCEPTS 2. Transfer Function Approach Frequency Domain Representations System Transfer Functions Block Diagrams Modeling and Block Diagrams of a DC Motor Block Diagram Algebra Signal Flow Graphs and Mason s Rule Sampled Data Control Systems Open-Loop Transfer Functions Closed-Loop Transfer Functions Transfer Functions of Digital Control Systems Transfer Function MATLAB Laboratory Experiment References Problems State Space Approach State Space Models The State Space Model and Differential Equations State Space Variables from Transfer Functions Time Response from the State Equation Time Domain Solution Solution Using the Laplace Transform State Space Model and Transfer Function

2 3.3 Discrete-Time Models Difference Equations and State Space Form Discrete Transfer Function and State Space Model Discretization of Continuous-Time Systems Solution of the Discrete-Time State Equation Solution of the Discrete State Equation by the -transform Response Between Sampling Instants Euler s Approximation The System Characteristic Equation and Eigenvalues Multiple Eigenvalues Modal Decomposition State Space MATLAB Laboratory Experiments Experiment 1 The Inverted Pendulum Experiment 2 Response of Continuous Systems Experiment 3 Response of Discrete Systems References Problems Linear System Stability Stability Concept and Main Definitions System Eigenvalues and Stability Stability of Distinct Eigenvalues Stability of Multiple Eigenvalues Case Studies Jordan Canonical Form Multiple Eigenvalues on the Imaginary Axis Case Study: Flexible Space Structure Lyapunov Stability of Linear Systems The Routh Hurwitz Criterion The Routh Table Algebraic Stability Tests for Discrete Systems Jury s Test Bilinear Transformation and the Routh Hurwitz Method Frequency Domain Stability Study MATLAB Laboratory Experiment References Problems

3 5. Controllability and Observability Observability of Discrete Systems Observability of Continuous Systems Controllability of Discrete Systems Controllability of Continuous Systems Additional Controllability/Observability Topics Observer (Estimator) Design Full-Order Observer Design Reduced-Order Observer (Estimator) MATLAB Case Study: F-8 Aircraft MATLAB Laboratory Experiment References Problems PART II ANALYSIS AND DESIGN 6. Transient and Steady State Responses Response of Second-Order Systems Transient Response Parameters Transient Response of High-Order Systems Steady State Errors Response of High-Order Systems by MATLAB Control System Performance Specifications MATLAB Laboratory Experiment References Problems Root Locus Technique Introduction Construction of the Root Locus Motivation for Time Domain Controller Design Discrete-Time Root Locus MATLAB Case Studies Case Study: F-8 Aircraft Case Study: A Synchronous Machine MATLAB Laboratory Experiments Hydro Power Plant Experiment Discrete-Time Root Locus Experiment References Problems

5 9.5 MATLAB Case Study Comments on Discrete-Time Controller Design MATLAB Laboratory Experiment References Problems Control System Theory Overview Time-Varying Systems Stochastic Linear Control Systems Optimal Linear Control Systems Optimal Deterministic Regulator Problem Optimal Kalman Filter Optimal Stochastic Regulator Problem Linear Time-Delay Systems System Identification and Adaptive Control System Identification Adaptive Control Nonlinear Control Systems Comments References Appendix A. Laplace Transform A.1 Definition of the Laplace Transform and its Main Property A.2 Tables of Properties and Common Pairs B. -Transform B.1 Definition of the -Transform and its Main Property B.2 Relation between the Z and Laplace Transforms B.3 Tables of Properties and Common Pairs C. Some Results from Linear Algebra D. MATLAB Manual MATLAB Tutorial Linear Systems and Control Index

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