Study On Delay-Dependent Variable Structure Control And Applications For Uncertain System With Time-varying Delay

Variable structure control was proposed in 1950s. It received a great attention, and became one of the most important control methods in automation area because of its non-sensitivity to interference and uncertainty. It is suitable for linear and nonlinear systems, continuous and discrete systems, time-delay systems and uncertain systems. Time-delay and uncertainty widely exist in reality, which may result in the poor performance or even instability of the system. So the design of a robust controller has a theoretical and practical significance in full consideration of the effects caused by delay and uncertainty on the system control. According to the research situation, the variable structure control of delay uncertain systems was discussed asymptotically in this paper. The control law was applied to the truck-trailer automatic reverse control system, which achieved promising control effect. The main work and research results are as follows:1. For delay continuous-time uncertain linear system with time-varying delay, proper state transformation was introduced to divide the system into two subsystems. By ensuring the asymptotically stability of the first subsystem, the expected value of the second state variable was obtained, and then the sliding mode was built by the difference of the second state variable and its expected value. The delay-dependent stable condition was translated into the solving of linear matrix inequality (LMI). On the basis of reaching conditions, sliding-mode variable structure control law was obtained. Simultaneously, delay dependent sliding mode variable structure control was expanded into discrete-time case, sliding mode variable structure control for time-varying delay discrete uncertain system was designed. Numerical simulation results verify that the control algorithm is correct and effective for both continuous and discrete-time cases.2. In order to deal with nonlinear systems with time-varying delays, T-S fuzzy model-based delay-dependent sliding mode variable structure controllers for continuous-time and discrete-time systems were proposed respectively. Numerical simulation results verify the correctness and effectiveness of the proposed control algorithms.3. Based on truck-trailer automatic reverse model, delay dependent sliding-mode variable structure control was used to realize the automatic reverse movement of truck-trailer from initial position to the expected position. Simulation results show that this control algorithm for the system is effective.