Problems On Study And Applications Of Sliding Mode Control For Some Kinds Of Control Systems

The sliding mode control that was brought in 1950's is a modern control theory design method based on phase plane technique. It has come into being relative integrity system during the 50 years. In the sliding mode control, the system behavior on sliding mode becomes totally insensitive to a particular class of uncertainty which satisfies so called matched condition. Its invariance property is stronger than robustness and is called as ideal robustness also, which clearly makes the methodology an appropriate candidate for robust control. In addition, sling mode control has been receiving extensive attention of lots of researchers for its distinct merits and salient feature.1980's, sliding mode control theory has been deeply studied and developed. Now it already becomes an important research branch of control theory. With the development of the research areas of control theory, such as time-delay system control, stochastic system control, nonlinear system control, discrete system control etc, however, the new requirements are put forward in the control robust stability, control speediness and control precision. At the same time the new requirements are put forward in sliding mode control as well.Based on the research results and new practical requirements of the sliding mode control theory, to the terminal sliding mode, dynamic sliding mode and output sliding mode problems are studied in this dissertation. And some related results are obtained based on sliding mode control theory. The main contents are as follows:The design of terminal sliding mode controller is studied. A terminal sliding mode decomposed control method is presented for the stability of a class of nonlinear systems. First, decompose the whole system into two second-order systems and design their separate sliding surface of each subsystems. Then embed the control target of one subsystems to another subsystems. Utilize a control action to make both subsystems converge to the equilibrium poits in finite time. With simple control, the proposed method has signification for high-order systems.The design problem for a dynamic output feedback controller for a class of uncertain linear systems is investigated. The proposed controller consists of nonlinear and linear parts. Attention is focused on the design of the linear part with full dynamics which completely handles mismatched uncertainties and, on the other hand, the nonlinear part is simplified as possible. By using the Lyapunov theory and linear matrix inequality method, the sufficient condition of existence of dynamic output feedback variable structure control law is derived and transformed as the feasibility problem described by linear matrix inequality, which can be solved by Matlab LMI toolbox to obtain the variable structure control for a class of system. A Matlab simulation example is given to illustrate that the analysis method and the result are valid and feasible.The problem of output feedback discrete-time sliding mode control of linear systems with mismatched uncertainties is investigated. The output feedback control doesn't need full observability. A criterion for the existence of the sliding surface is derived based on the linear matrix inequality (LMI) technique combined with the Lyapunov method. The design of sliding mode control is presented according to the reachability condition. The proposed control is more practical than state feedback. Finally, an illustrative example is presented to show the feasibility and effectiveness of the proposed method.The problem of output feedback variable control of discrete uncertain system with time-delay is studied in this paper. The output feedback control doesn't need full observability. The system mentioned above is simplified by nonsingular transform. the sliding surface is designed by using linear matrix inequality (LMI) technique when there exists the unmatched uncertainties. The sufficient condition for the existence of stable sliding surface is derived in terms of LMIS. For a class slowly varying system, the proposed controller regards the influence of parameter uncertainties as an equivalent disturbance and generates an on-line estimation to cancel the uncertainties by the mechanism of time delay. The controller is designed by using discrete approach law. The simulation results are offered to illustrate the effectiveness of the proposed approach.The application of sliding mode control theory is investigated. A terminal sliding mode controller of a class of second-order chaotic systems is studied. The finite time synchronization of chaotic systems is realized by designing a continuous terminal sliding mode controller with an improved sliding surface introduced to get rid of the singularity phenomenon resulting from improper choice of parameter. Based on T-S fuzzy model the problem of controlling Chua chaotic system can be solved by combined fuzzy control with mature linear system variable structure control. The fuzzy controller is simple and need no much rules. An adaptive hierarchical sliding-mode control (AHSMC) strategy for a class of second-order underactuated systems is presented. The AHSMC law is derived in Lyapunov sense when the uncertainties are bounded by an unknown constant.The conclusions are drawn for the whole dissertation, and the further research directions are put forward in the end of the paper.