Variable Structure Control For Discrete-time Systems And Its Simulations

The Variable Structure Control (VSC) is a way for robust control for both linear and nonlinear systems. For the self-adapting of the quasi-sliding mode, which is the most important merit of the VSC systems, people have paid a lot of attention to the VSC. A rounded theory system has been formed in the continuous systems at present. Due to the sampling interval, the methods of VSC for discrete-time systems are greatly different from those for continuous systems. Therefore, the main works of this paper is to study the methods of VSC for discrete-time systems. Two new discrete-time approximation laws are presented. The proposed approximation laws can guarantee the stability of the system at the origin and restrain chattering along switching surface effectively. And furthermore the system input u ( k ) is restricted notably and switch range of the control u ( k ) ? u ( k-1) is decreased remarkably. The dynamic performance of discrete-time sliding control systems is improved. The main contents consist of several parts as follows:The first section is a summary of the basic definitions, principles and methods about VSC, and introduces the present research situation about VSC for discrete-time systems.In the second part, the basic definitions, principles and methods about VSC for discrete-time systems are introduced. Chattering brought by the conventional discrete reaching law is analyzed and the stationary chattering range is given. The problem of the system input u ( k ) and switch range of the control u ( k ) ? u ( k-1) are also considered.In the third section, two new discrete-time approximation laws are presented. Simulations are given and compared with some methods before. In the end, simulation results show the validity of the proposed methods.