Chapter 1 Introduction to Control Systems
1.1 Historical Review of Automatic Control Theory
1.2 Modern Control Theory versus Conventional Control Theory
1.2.1 Modern control theory
1.2.2 Modern control theory versus conventional control theory
1.2.3 Definitions
1.3 Design of Control Systems
1.4 Future Evolution of Control Systems
1.5 Outline of this Book
Chapter 2 Modeling In State Space
2.1 State Variable and State Space Expression
2.1.1 Some basic concept and definitions
2.1.2 State space expression
2.1.3 Relationship between transfer functions (or transfer matrix) and state - space equations
2.2 State Space Representation of Linear Dynamic System
2.2.1 State space representation of differential equation
2.2.2 From transfer function to state space representation
2.3 From Block Diagram to State Space Representation
2.4 Linear Transform of State Space Expression
2.4.1 Nonsingular linear transform (or similarity transformation)
2.4.2 Eigenvalues and eigenvectors of an n×n matrix A
2.4.3 State - space representation in canonical forms
2.5 State Space Representations of Discrete Systems
2.5.1 State - space representation of nth - order systems of linear difference equations in which the forcing function does not
involve difference terms
2.5.2 State space representation of nth - order systems of linear difference equations in which the forcing function involves
difference terms
2.6 Transformation of System Models with MATLAB
2.6.1 Transformation from transfer function to state space formulation
2.6.2 Transformation from state space to transfer function
Exercises
Chapter 3 Dynamic Analysis of Control System in State Space
3.1 Solving the Time - invariant Homogeneous State Equation
3.1.1 General solution of the scalar differential equation
3.1.2 General solution of the vector - matrix differential equation
3.1.3 State - transition matrix
3.2 Properties of State - transition Matrice
3.3 Calculation of Matrix Exponential Function
3.3.1 Direct calculation approach
3.3.2 Laplace transform approach
3.3.3 Linear transform approach
3.3.4 Cayley - Hamilton Theorem
3.4 Solution of Nonhomogeneous State Equations
3.4.1 Direct method (or integral method)
3.4.2 Laplace Transform Approach
3.5 Solution of Discrete Nonhomogeneous State Equations
3.5.1 Discretization of linear time - invariant dynamic equation
3.5.2 Approximation
3.5.3 Recursive algorithms of the discrete state equation
3.5.4 Z transform approach to the solution of the discrete state equation
3.6 Computation of Control System Response with MATLAB
3.6.1 Response to initial condition
3.6.2 Obtaining the response to an initial condition by use of the command initial
Exercises
Chapter 4 Controllability and Observability
4.1 Controllability of Linear Time - invariant Continuous System
4.1.1 Definition of controllability
4.1.2 Complete controllability criteria of continuous - time systems
4.1.3 Complete output controllability of continuous - time systems
4.2 Observability of Linear Time - invariant Continuous System
4.2.1 Definition of observability
4.2.2 Complete observability criteria of continuous - time systems
4.3 Controllable Canonical Form and Observable Canonical Form
4.3.1 Controllable canonical form of the single input system
4.3.2 Observable canonical form of the single output system
4.4 Principle of Duality
4.4.1 Dual system
4.4.2 Principle of duality
4.5 Controllability and Observability of Discrete Time - Invariant System
4.5.1 Controllability of discrete system
4.5.2 Observability of discrete system
4.5.3 Controllability and Observability of Discretized Systems
4.6 Structure Decomposition of Linear Time - invariant Continuous S
