Sliding Mode Variable Structure Control For Several Kinds Of Control Systems With Uncertainties

There exist uncertainties, time delay and nonlinearity in many real dynamic systems. Hence, control of nonlinear system, system with uncertainties and time-delays has been an active field of research in control theory and applications which many scholars are interested in.The variable structure control (VSC) theory has been made great progress since it was proposed in 1950s. It is considered as an effective method for the control of nonlinear systems and systems with uncertainties in the past several decades. The VSC systems have various attractive features such as following: The design of controller is relative simple. The system can be decomposed into two low dimensional subsystems and has robustness of stability. The sliding mode is invariant to parameter perturbations and internal and external disturbance.However, its major drawback in practical applications is the chattering problem which is caused by discontinuous switching. It’s undesirable in some dynamic systems. So, eliminating the sliding-mode chattering has been an active researching field in variable structure control theory and applications.Fuzzy logic control (FLC) is a rule-based type of control that uses fuzzy set concepts and fuzzy logic. It can deal with complex and ill-defined systems for which the application of conventional control techniques is not straightforward or feasible. Furthermore, the combination of FLC and VSC can effectively eliminate the sliding mode chattering in some dynamic systems.Firstly, the relative studies on the VSC and FLC up to now are given in details. The derivation, developments, primary principles and characteristics are introduced. Based on present research, stability of a class of nonlinear system via a smooth saturation method combined variable structure control, chattering-free sliding mode control for linear uncertain systems with multiple time-delays, fuzzy sliding mode control for a kind of uncertain linear system and discrete sliding-mode control of uncertain systems with time delays are researched. Some new research conclusions are obtained. The main contents are given as follows.1. The quadratic parabola (which it is called smooth saturation function) is adopted to approximate to traditional discontinuous sign function used in VSC. A smooth saturation function method is given, and used in the design of variable structure controller for a class of nonlinear system. Owing to its continuity and smoothness, the chattering can be reduced greatly. The trajectory of the nonlinear control system which is globally uniformly ultimately bounded is obtained. Under certain conditions, the asymptotically stability at the origin is given for the nonlinear system. The validity and feasibility are illustrated by an example for the results of the paper.2. The sliding mode control for linear uncertain systems with multiple time-delays is considered. A new chattering-free sliding mode control law is designed with saturation function instead of sign function for time-delay systems. The control algorithm divides the control process into two phases. When the system trajectory is outside of the given the boundary layer, the chattering-free control law is used to drive the trajectory converged to the boundary layer. When the trajectory is inside the boundary layer, by choosing the appropriate width of the boundary layer, the asymptotically stable of the system can be guaranteed. This control algorithm eliminates the sliding mode chattering caused by the discontinuity of traditional SMC law for the uncertain time-delay system. The validity and feasibility are explanted by a numerical example for the proposed method in the paper.3. The fuzzy sliding mode control method is given for a kind of uncertain linear system by using the theory of sliding mode control and Lyapunov approach. Choosing switching function s , s and s& are the inputs of the fuzzy controller. The output of the fuzzy controller is u. The reaching condition ss& <0 and asymptotic stability of the uncertain linear system are proved by the method. In addition, the chattering phenomena of the sliding mode can be effectively alleviated and performance of control is improved. The validity and feasibility of the method in handling uncertainty and disturbance is illustrated by simulation example.4. Robust problem is researched for the discrete sliding-mode control (D-SMC) design for a class of uncertain linear systems with time-varying delays. By using a descriptor model transformation and Moons inequality for bounding cross terms, a delay-dependent sufficient condition for the existence of stable sliding surface is given by means of linear matrix inequalities (LMI). Based on this existence condition, the synthesized sliding mode controller can guarantee the sliding mode reaching condition of the specified discrete-time sliding surface for all admissible uncertainties and time-varying multiple state delays. An illustrative example verifies the effectiveness and feasibility of the proposed method.5. The fuzzy sliding mode control method is given for a kind of uncertain system with multiple time delays by using the theory of sliding mode control and Lyapunov approach. Choosing switching function s , s and s& are the inputs of the fuzzy controller. The output of the fuzzy controller is u. The reaching condition ss& <0 of the uncertain system is guranteed by the method. In addition, the chattering phenomena of the sliding mode can be effectively alleviated and performance of control is improved. The validity and feasibility of the method in handling uncertainty and disturbance is illustrated by an example.6.Finally, the main work in this paper is summarized and some problems are proposed on the research work in the future.