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 System 4.6.1 Structure decomposition according to controllability 4.6.2 Structure decomposition according to observability 4.6.3 Structure decomposition according to both controllability and observability 4.7 Computation of Controllability and Observability Matrix with MATLAB Exercises Chapter 5 Lyapunov Stability Analysis 5.1 Stability of Lyapunov Significance 5.1.1 Equilibrium state 5.1.2 Stability in the sense of Lyapunov 5.1.3 Asymptotic stability in a whole 5.1.4 Unstability 5.2 Definiteness of Scalar Function and Sylvester Theorem 5.2.1 Positive definite and semidefinite functions 5.2.2 Negative definite and semidefinite functions 5.2.3 Indefinite functions 5.2.4 Quadratic function 5.2.5 Sylvester theorem 5.3 Main Theorems of Lyapunov's Second Method 5.3.1 Lyapunov stability for time - varying system 5.3.2 Lyapunov stability for time - invariant system 5.3.3 Lyapunov stability for time - varying or time - invariant system 5.3.4 Instability for time - varying or time - invariant system 5.4 Stability Criteria for Linear Time - Invariant Systems 5.4.1 Basic theorem 5.4.2 Lyapunov function of linear time - invariant continuous systems 5.4.3 Lyapunov function of linear time - invariant discrete systems Exercises
Chapter 6 Design of Control Systems in State Space 6.1 State Feedback and Output Feedback 6.1.1 State feedback 6.1.2 Output feedback 6.1.3 Controllability and observability of state feedback system 6.2 Pole Placement 6.2.1 Design by state feedback 6.2.2 Necessary and sufficient condition for arbitrary pole placement 6.2.3 Determination of state feedback matrix K 6.2.4 Choosing the locations of desired closed - loop poles 6.2.5 Comments on selecting state feedback gain matrix K 6.3 Stabilization Problem of Systems 6.4 Solving Pole Placement Problems with MATLAB 6.5 State Observers 6.5.1 Full - order state observer 6.5.2 Necessary and sufficient condition for full - order state observer 6.5.3 Determination of full - order state observer gain matrix Kc 6.5.4 Comments on selecting state observer gain matrix Kc 6.5.5 Integrated full - state feedback and observer 6.5.6 Separation property 6.5.7 Reference inputs for integrated full - state feedback and observer 6.5.8 Reduced - dimension state observer 6.6 Design of State Observers with MATLAB 6.7 Optimal Control Design 6.7.1 Optimal control design using error - squared performance indices 6.7.2 Optimal control design using riccati equation 6.8 Solving Quadratic Optimal Control Problems with MATLAB 6.9 Internal Model Design 6.9.1 Internal model design for tracking of a step input 6.9.2 Internal model design for tracking of a ramp input Exercises References
[