Study On Control Synthesis And Fault Detection Of T-S Fuzzy Systems Based On Integral Lyapunov Function

The validity and importance of fuzzy control theory have been proved by the theory of automatic control system and the successful application in industrial production.On the one hand,due to the factors of the complex control system such as the nonlinear process,random disturbance,it is difficult to establish accurate mathematical models.But the inherent nonlinear characteristics of the fuzzy control system can effectively overcome these difficulties and realize the effective control of complex systems.On the other hand,with the increasing complexity and efficiency of the control system,higher requirements have been put forward for the safety and reliability of the equipment and control system.Although the model-based fault detection technology in the linear system theory has achieved a lot of results,the research of the fault detection technology in the nonlinear control system theory is still an important task for the fuzzy control theory.In particular,the rapid development of computer technology and control system theory has also provided a powerful tool for the study of fuzzy control theory.Therefore,the research on the control synthesis and fault detection of T-S(Takagi-Sugeno)fuzzy system has attracted the interest of scholars and experts,and has become a hot issue in the field of automation control.In this thesis,based on the integral Lyapunov function,we deeply discuss the problem of control synthesis and fault detection of T-S fuzzy systems from aspects of theoretical methods,technical implementation and application simulation.The main contributions are as follows:(1)Based on the integral Lyapunov function,the design of T-S fuzzy system controller is studied.The integral Lyapunov function is combined with the parallel distributed compensation(PDC)strategy,and the time derivative of the membership function is avoided in the stability analysis conditions of the T-S fuzzy systems.The two stability analysis conditions and controller design methods of T-S fuzzy systems are presented.(2)The design of fault detection observer based on T-S fuzzy time-delay system is studied.By introducing the relaxation variable,the stability analysis conditions and H_index sensitivity conditions of T-S fuzzy time-delay system are obtained.Furthermore,the method of the fault detection observer design of T-S fuzzy time-delay system is presented.Finally,the effectiveness of the method is proved by numerical simulation.(3)The H_∞control problem of T-S fuzzy control system is studied.Firstly,the analysis conditions of the H_∞performance for closed-loop system are given by using the integral Lyapunov function.However,the integral Lyapunov function method can cause bilinear matrix inequalities(BMIs)to be solved in the stabilization control design of the closed-loop system.In order to solve this problem and reduce the conservativeness of the design,the H_∞performance index of the optimal solution of linear matrix inequality(LMIs)is obtained by introducing several relaxation variables.(4)The fault detection problem of T-S fuzzy system with local nonlinear model is studied.Combined with the local nonlinear model scheme,the T-S fuzzy system with fewer fuzzy rules is presented to reduce the computational burden.The proposed fuzzy fault detection observer design method cannot only ensure the stability of the residual system,but also improve the H_performance index.