Sliding Mode Control Of Uncertain T-S Fuzzy Model

As well-know, the presents of input constraint, time-delay and uncertainties is existed commonly in actual control systems. All of these factors affect the performance of the control systems, even cause system instability, and fuzzy modeling base on T-S fuzzy model provides a new research ideas for analysis and synthesis of nonlinear control systems, in addition, the sliding mode control become a good robust control method because of the dynamics on the specified sliding surface is not sensitive to system's parameter perturbation and external disturbances. Therefore, the research of the sliding mode control about the uncertain T-S fuzzy systems has quite theoretical and practical significant.In this thesis, based on analysis the T-S fuzzy model method and sliding mode control deeply, we consider the sliding mode control problem for uncertain T-S fuzzy system with input delay and input constraint, and obtain some innovative results. The main contents conclude:(1) Aiming at the problem of the sliding mode control for the uncertain T-S fuzzy system subject to input constraint, an integral-switching-surface depending on fuzzy parameters is chosen, and the sliding mode controller is designed such that the state trajectories can be driven onto the specified sliding surface in finite time. Moreover, the sufficient condition for the asymptotical stability of the sliding mode dynamics is derived. Finally, the effectiveness of the proposed method is verified by an example simulation.(2) Aiming at the problem of sliding mode control for uncertain T-S fuzzy systems with input and state delays, in which the uncertain is unmatched, an integral-switching-surface depending on the state and input delay is designed, and the reachability of the specified sliding surface is proven by Lyapunov stability theory. Furthermore, the sufficient condition for the asymptotical stability of the sliding mode dynamics is derived. Finally, the numerical simulation results show that close-loop control system can attain better robust stability.(3) The above method is applied in the manipulator system. Firstly, the two-link robot manipulator is modeled as a T-S fuzzy model, and then, a sliding mode control law base on T-S fuzzy model is designed, and the reachability of the sliding mode surface is analyzed. Moreover, the asymptotic stability of the sliding mode dynamics is proven, which is further verified by a numerical simulation example.