Study On Variable Structure Control For Discrete-time Systems

One of the most distinguished features of the variable structure control (VSC) is the invariance of its sliding mode, i.e. it shoots to move with systems irrelevant, so it catch great attention from the control field. Significant progress has been made in continuous systems. Due to the sampling interval, the methods of VSC for discrete-time systems are greatly different from those for continuous systems. Chattering is a main obstacle to the application of variable structure control (VSC) to 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 improving system performance effectively. The main contents consist of several parts as follows.1. The broad research situation about VSC for discrete-time systems is introduced.2. The basic definitions, principles and methods about VSC for discrete-time systems are summarized. Chattering is analyzed brought by the conventional discrete reaching law and the stationary chattering range is given.3. The variable structure control of discrete time systems using discrete reaching law is researched in this paper. An improved discrete reaching law is given. As the time-varying chattering region of quasi-sliding mode decreasingly approaches to zero, the proposed method can eliminate system chattering and improve system performance effectively. 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. The design of variable structure control for discrete time systems is discussed. The attenuating exponential reaching law group based on attenuating control and the time-varying attenuating power reaching law group are proposed . The theory analysis demonstrates that the proposed methods can make the system chattering decreasingly attenuate at exponential rate. So the stationary chattering is eliminated which ensures the asymptotic stability of the closed loop systems, and that it has perfect performance. Simulation results show the given method is effective.