Variable Structure Control For Uncertain Nonlinear Systems

The real plant behavior can be usually described as an uncertain nonlinear system. The control problem of uncertain nonlinear systems has attracted a lot of attention and was studied extensively. Variable structure control (VSC) shows a strong vigor on controlling an uncertain nonlinear system for its excellent robustness and complete adaptability to matching uncertainties and external perturbations. However, it is the chattering problem that prevents the VSC from being applied in engineering, some schemes devoted to avoid the chattering have been presented in the literature, but up to now, the chattering problem has yet not solved completely. In addition, owing to the complexity of nonlinear systems, VSC cannot deal with the mismatching uncertainties in a nonlinear system, which restricts greatly the applicable area of VSC. In order to give some hints on the solution of these problems, based on the status of VSC, we have studied systematically in this dissertation the methods of VSC and its related theories. Our study addresses the following topics: Firstly, the theory of feedback linearization is introduced. Feedback linearization is a versatile control technique for nonlinear systems, which converts a nonlinear system model into a convenient and equivalent model for the control design. In the process of design for nonlinear system, feedback linearization is often used to transform the original system model. The basic theory and method of feedback linearization, including input-output linearazation, zero dynamic subsystem, and input-state linearazation etc, are introduced. The steps of input-output linearazation and input-state linearazation are described in detail. For a class of matching uncertain nonlinear systems,the design approach of a variable structure controller is proposed and the global stability of the closed-loop system is guaranteed. One common approach called boundary layer approach is adopted in VSC for chattering reduction, but this approach always causes a large steady-state error. Based on analyzing the reasons of chattering reduction and steady-state error producing in VSC with boundary layer approach, a new approach of VSC -programming control based VSC with boundary layer is proposed firstly in this paper. By means of this proposed approach, we have decreased the steady-state error and realized perfect tradeoff between the tracking performance and chattering reduction. For a class of mismatching uncertain nonlinear systems,the design approach of a variable structure controller based on adaptive backstepping scheme is presented. Considering the absolute robustness of VSC to the matching uncertainties whose form is not fixed and adaptive backstepping scheme can deal with parametric mismatching uncertainties, a design approach that combines adaptive backstepping and VSC is studied. In the approach, the means to deal with uncertainties comes from VSC and the design steps come from the backstepping scheme. The control problem of nonlinear systems with nonparametric mismatching uncertainties is solved successfully by the proposed design method. The control method is verified by designing a controller for an SISO affine nonlinear system, simulation results demonstrate the efficiency of the method. For a class of model-unknown nonlinear systems, the adaptive fuzzy variable structure control method is studied. Firstly, the basic theory of fuzzy logic system is introduced, on the basis of that, a basic adaptive fuzzy variable structure controller, which combines variable structure control and adaptive fuzzy logic system, is designed. The fuzzy logic systems are used to approximate the unknown system functions in designing the VSC of nonlinear system. Based on Lyapunov method, the parameter adaptive laws are proposed and the stability of the closed-loop system is guaranteed. To guarantee the system stability under the approximate error existing, we proposed an improved fuzzy VSC with an appended supervisory controller and parameter projection. The stability and convergence of the control system are proved in this paper. In the end, computer simulation results are illustrated. The conclusion and perspective are given in the end of the paper.