The Survey Of Sliding Mode Variable Structure Control For Classes Of Uncertain Distributed Parameter Systems With Time-Delay

Time delays and uncertainties can cause system instability and dynamic performance degradation, they widely exist in various types of real systems, therefore designing of strong robustness controller for uncertain time-delay systems has important theoretical significance and practical value. Because of the ideal sliding mode dynamics of sliding mode control (SMC) systems has fully robustness to matched parameter uncertainties and external disturbances, the system dynamic performance on sliding mode dynamics can be pre-designed, SMC is an effective robust control approach for systems have uncertainties, time-delays, time-varying and multiple interferences. Due to these good properties, many researchers have paid attention to this method.In this thesis, the problem of sliding mode variable structure control (SMVSC) for uncertain distributed parameter systems with time-delay is studied, the SMVSC methods for classes of different uncertain distributed parameter systems with time-delay are given.The main contents consist of several parts as follows.1. The historical development and research situation about SMC for distributed parameter systems with time-delay is summarized.2. The problem of memoryless sliding mode control is studied for a class of distributed parameter systems with continuous distributed delays. Firstly, by constructing auxiliary function and using matrix norm inequalities techniques, a sufficient condition of delay-dependent exponential asymptotic stability for the sliding mode dynamics is derived. Secondly, by constructing auxiliary function and using matrix norm inequalities techniques, a memoryless sliding mode controller is designed; Furthermore, the approximate time estimate from any initial state to sliding surface is obtained. Simulation results demonstrate the effectiveness of the proposed method.3. The problem of sliding mode control is studied for a class of interval distributed parameter systems with time-delay. Firstly, this system is represented in the uncertain distributed parameter systems with time-delay, and a sufficient condition for robust asymptotic stability is obtained for the sliding mode dynamics by constructing Lyapunov functional, employing linear matrix inequality (LMI). Secondly, a sliding mode controller is designed, and, the approximate time estimate from any initial state to sliding surface is obtained. Finally, a numerical example is given, and the feasibility and effectiveness of this method is explained.4. The problem of sliding mode control is discussed for a class of uncertain distributed parameter systems with Markovian jumping parameters and time-varying delay. Firstly, a concept of the subordinated reachability for the sliding surface is introduced to approach approximately the specified sliding surface. By using the direct analysis method, the represent sliding mode controller relating to transition rates of modes can cope with the effect of Markovian switching and guarantee the sliding surface subordinated reachable. Furthermore, a sufficient condition is given such that the sliding mode dynamics is mean-square asymptotic stability. The designed sliding surface corresponding to every mode is established. Finally, a numerical example is given, and the feasibility and effectiveness of this method is explained.