现代控制理论基础

Section Ⅰ State Space Analysis and Synthesis of LinearSystems
　1　State Space Description of Dynamic Systems
　　1.1 Introduction
　　1.2 State and state space
　　1.3 State space description of dynamic systems
　　1.4 Canonical form of SISO state space representation
　　1.4.1 Controllable canonical form
　　1.4.2 Observable canonical form
　　1.4.3 Diagonal form and Jordan canonical form
　　1.5 Some examples of developing state space descriptions
　　1.6 Equivalent state equations
　　?1.6.1 Similarity transformation
　　　1.6.2 An application of similarity transformation--Diagonal formand Jordan form
　　1.7 Relationship between I/O description andstate-spacedescription
　　　1.7.1 Transfer function from state-space description
　　　1.7.2 State-space representations from transferfunctionsRealizations
　　Problems
　2　Solution of State Equations of Linear Systems
　　2.1 Introduction
　　2.2 Solution of linear homogeneous state equation
　　2.3 Properties and calculations of the matrix exponentialfunction
　　2.3.1 Properties of □
　　2.3.2 Calculation of □
　　2.4 Solution of state equations
　　2.5 State transition matrix of linear time-invariantsystemsProblems
　3　Controllability and Observability
　　3.1 Introduction
　　3.2 Controllability
　　　3.2.1 Definition of complete state controllability
　　　3.2.2 Controllability criterion for time-invariant systems witharbitrary eigenvalues
　　　3.2.3 Controllability criterion for time-invariant systems withdistinct □genvalues
　　　3.2.4 Controllability criterions for time-invariant systemswithmulti-eigenvalues
　　3.3 Observability
　　　3.3.1 Definition of complete state observability
　　　3.3.2 Observability criterion for time-invariant systems witharbitrary eigenvalues
　　　3.3.3 Observability criterion for time-invariant systems withdistinct eigenvalues
　　　3.3.4 Observability criterion for time-invariant systems withmulti-eigenvalues
　　3.4 Principle of duality
　　3.5 Obtaining the controllable and observable canonicalforms forSISO systems
　　　3.5.1 Controllable canonical form of SISO systems
　　　3.5.2 Observable canonical form of SISO systems
　　3.6 Canonical decomposition
　　　3.6.1 Decomposition according to controllability
　　　3.6.2 Decomposition according to observability
　　　3.6.3 Canonical structure of system
　　Extensions and Proofs
　　Problems
　4　Desigh of State Feedback Control Systems
　　4.1 Introduction
　　4.2 State feedback
　　　4.2.1 State feedback scheme
　　　4 2 2 The effect of state feedback on system properties
　　4.3 Pole assignment using state feedback
　　　4.3.1 Description of pole assignment problem
　　　4.3.2 Necessary and sufficient condition for arbitrary poleassignment
　　　4.3 3 Pole assignment via control canonical form of stateequations
　　　4.3.4 Pole assignment via Ackermann's formula
　　　4.3.5 Direct calculation of gains by comparing characteristicequations
　　4.4 Design of state observers
　　4.5 Feedback from estimated states
　　Problems
Section Ⅱ Linear Discrete-time Systems
　5 Discrete-time Systems and Computer Control Systems
　　5.1 Introduction
　　5.2 Sample-data control and computer control systems
　　5.3 Related theories
　　5.4 Sampling process and sample theorem
　　5.5 The z transform
　　5.6 The computation of z transform and the z transform ofelementary functions
　　5.7 Important properties of the z transform
　　5.8 The inverse z transform
　　5.9 Difference equation
　　5.10 The z transform method for solving differenceequations
　　5.11 The model of a discrete-time control system and the pulsetransfer function
　　5.12 The difference equation and pulse transfer function
　　Problems
　6　Analysis and Design of Discrete-Time Control Systems
　　6.1 Introduction
　　6.2 Mapping between the s plane and the z plane
　　6.3 Stability analysis of closed-loop systems in the zplane
　　6.4 Steady-state response analysis
　　6.5 The dynamic analysis for the control system in the zplane
　　6.6 The design of the discrete-time compensator
　　　6.6.1 Dead-beat control with intersampling ripples
　　　6.6.2 Dead-beat control without intersampling ripples
　　　6.6.3 Shortcomings of the Dead-beat control
　　6.7 Realization of digital controller
　　Problems
Section Ⅲ Nonlinear Systems
　7　Introduction to Nonlinear Control Systems
　　7.1 Introduction
　　7.2 Common nonlinear elements
　　7.3 Properties of nonlinear systems
　　7.3.1 Classification of nonlinearities
　　7.3.2 Some common nonlinear system behaviors
　　7.4 Approaches to the analysis of nonlinear control systems
　8　Describing Function Analysis
　　8.1 Introduction
　　8.2 Describing function fundamentals
　　　8.2.1 Basic assumptions
　　　8.2.2 Basic definitions
　　　8.2.3 Computing describing functions
　　8.3 Describing functions of common nonlinearities
　　8.4 Describing function analysis of nonlinear system
　　　8.4.1 Prediction and stability of self oscillations
　　　8.4.2 Plot of curves of G(□) and -□
　　　8.4.3 Reliability of the describing function method
　　8.5 Conclusion
　　Problems
　9　Phase Plane Analysis
　　9.1 Introduction
　　9.2 Basic ideas of phase plane analysis
　　9.3 Characteristics of phase plane trajectories
　　9.4 Constructing phase portraits
　　9.4.1 The method of isoclines
　　9.4.2 Analytical method
　　9.5 Phase plane analysis of nonlinear systems
　　9.5.1 Linearization of nonlinear system
　　9.5.2 Phase trajectories for linear systems
　　9.6 Conclusions
　　Problems
　10 Lyapunov Stability Theory
　　10.1 Introduction
　　10.2 Equilibrium states and concepts of stability
　　10.2.1 Equilibrium state
　　10.2.2 Concepts of lyapunov stability
　　10.3 Lyapunov's linearization method
　　10.4 Lyapunov's direct method
　　　10.4.1 Basic idea
　　　10.4.2 Some concepts of singular scalar functions
　　　10.4.3 Lyapunov's stability theorems
　　10.5 Construction of Lyapunov function
　　　10.5.1 Lyapunov equation
　　　10.5.2 The variable gradient method (Schultz-Gilbsonmethod)
　　　10.5.3 Aiserman method
　　10.6 Conclusions
Problems
References