Study On Variable Structure Control For Discrete-time System And Its Simulations

Chattering is a main obstacle to the application of variable structure control (VSC). Due to the sampling interval, the methods of VSC for discrete-time systems are greatly different from those for continuous systems. Moreover, Time-delay makes studying VSC more difficult about discrete-time systems. Therefore, the main works of this dissertation is to study the methods of VSC for discrete-time systems. Two improved methods reducing chattering are proposed. And these two methods are also developed to VSC for time-delay discrete systems. The main contents consist of several parts as follows.1. The broad research situation about VSC for discrete-time systems and VSC for time-delay systems is summarized.2. The basic definitions, principles and methods about VSC for discrete-time systems are introduced. Chattering is analyzed brought by the conventional discrete reaching law and the stationary chattering range is given.3. Based on attenuating control, the attenuating exponential control and corresponding discrete reaching law are proposed in this dissertation. Hence the first improved method about VSC for discrete-time systems is put forward. Subsequently the time-varying attenuating power reaching law is also proposed in this dissertation. And the second improved method about VSC for discrete-time systems is brought forward. Finally, using these two methods reducing chattering, simulations are given and compared with the presented methods before. Simulation results show the proposed methods of this dissertation are effective.4. Firstly, the basic definitions, principles and methods about VSC for time-delay discrete systems are introduced. Secondly, the stability of ideal quasi-sliding mode about VSC for time-delay discrete systems is analyzed using matrix inequality method, and the conditions ensuring it asymptotically stable is given. Thirdly, the accessibility, approachability, invariability and robustness of quasi-sliding mode are discussed. Fourthly, two improved methods reducing chattering about VSC for time-delay discrete systems are proposed. Finally, using these two methods reducing chattering, VSC for systems with time-delay in control input is studied. With time-delay transformation, this control problem is changed to VSC problem for discrete systems without time-delay in control input and so the VSC strategy is given.