Sliding Mode Control For Discrete-time Systems With Uncertainties

Siding mode control has received considerable amount of research interests in the recent thirty years as an effective robust control strategy for uncertain systems, and has made great research achievements especially in the continuous-time systems. Simultaneously, with the wide use of the computer control, the problem of sliding mode control for discrete-time systems has been received more attention increasingly. However, due to the limits of the sampling interval in the discrete-time systems, there exist essential differences between the continuous systems and the discrete-time systems in the nature of the sliding mode, the existence condition and the reachability condition. Meanwhile, there commonly exist various uncertainties in actual control systems. All of these can affect the performance of the control systems, even cause systems instability. Therefore, the research of the sliding mode control for discrete-time systems with uncertainties has quite theoretical and practical significant.Based on the analysis of the discrete-time sliding mode control deeply, this paper respectively studies the sliding mode control problems for the discrete-time systems under the following circumstances:systems with the external disturbance, systems with possible actuator degradation and systems with nonlinearity, and have made some significant research results.The main contents of the paper include:(1) Aiming at a class of uncertain discrete-time systems, an optimal integral-like sliding mode surface is designed to ensure the robustness for sliding dynamics. By combing with the discrete reaching law, the reachability condition is proved and the bandwidth of the quasi-sliding mode is also derived. Finally, the effectiveness of the proposed method is verified by example simulations.(2) Aiming at the problem of sliding mode reliable control for uncertain state-delayed discrete-time systems, in which the controlled system maybe subject to partial degradation. A model of actuator fault is firstly given. An integral-like sliding surface and a sliding mode controller are then designed. A sufficient condition is derived to ensure that the sliding mode dynamics is asymptotically stable. And a new sliding mode controller is designed to ensure the reachability of the sliding mode dynamics despite the effects of actuator degradation. The simulations further show the effectiveness of the proposed method.(3) Aiming at the uncertain state-delayed discrete-time systems with dead-zone and input saturation, the sliding mode control method is designed. There exist uncertainties in both state matrix and input matrix. An integral-like sliding surface is designed. A sufficient condition is then derived by the methods of the Lyapunov and Linear Matrix Inequality such that the sliding mode dynamics is asymptotically stable. And a new sliding mode controller is designed to ensure the reachability of the sliding mode dynamics despite the effects of dead-zone and saturation. The simulations are provided to illustrate the effectiveness of the method.