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Problems on Theory of Variable Structure Sliding Mode Control for Discrete-time Systems

Author: LuoLiuMin
Tutor: ZhengYan
School: Northeastern University
Course: Control Theory and Control Engineering
Keywords: Discrete-time systems Sliding mode variable structure control Approximation law Chattering Predictive sliding mode control Global sliding mode control
CLC: TP13
Type: Master's thesis
Year: 2009
Downloads: 89
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Abstract


Variable structure sliding mode control is well known for its robustness to system parameter variations and external disturbances. But what all most researchers study on are continuous-time systems. In the past few years, with the development of the micro processors, In practical systems the control implementation by digital computer requires a certain sampling interval. Finite sampling frequency may cause not only chattering along the switching surface but also instability with large gain. In addition the ideal robustness in continuous time variable structure sliding mode control systems does not exit in discrete time sliding mode control systems as well. Therefore discrete-time variable structure sliding mode control theory is worthy of being investigated from both theory and application point of view.In this dissertation, the variable structure sliding mode problem of discrete time system is analyzed all round. The main contributions are as follows.(1) The first section introduces the present research situation about the variable structure sliding mode control for discrete-time systems.(2) The related definitions of the variable structure sliding mode problem of discrete time system are proposed. After analyzing the arrival condition, the existence condition and stabilization of sliding mode in the variable structure problem of discrete time system.(3) The design of approximation law for the discrete-time variable structure sliding mode control systems is studied. Two types of novel the exponentially approaching rule of the discrete time system to resolve the problem existed in the both exponentially approaching rule and variable rate reaching law. The stability of origin can be ensured, the chattering in discrete time sliding mode control systems can be avoided effectively and the system control input being restricted is also considered. 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 and feasible.(4) To settle the problem of the uncertainty and the disturbance, the predictive sliding mode control strategy is proposed. Variable structure global sliding mode control based on prediction uses receding horizon optimization and feedback correction to optimize the reaching process of sliding mode for the purpose of chattering elimination and enhancing robustness. Since the algorithm to make the beginning of the initial state falls on the surface of sliding mode, reducing the time to reach the sliding surface, The results of a numerical example proofs the closed-loop system is robust stable even though the upper bounds of uncertainties and external disturbances are unknown.At last, the conclusions are drawn, and the further research directions are presented.

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