Research On Fault Tolerant Control And Fault Detection For Nonlinear Systems Based On Polynomial Fuzzy Model

In recent years,the methods based on polynomial fuzzy models have received extensive attention due to their ability to model nonlinear systems.At present,the stability analysis and controller synthesis based on polynomial fuzzy systems are gradually improved,but there are still some limitations in the controller design for continuous polynomial fuzzy time delays systems.In addition,with the development of control theory,large nonlinear control systems,such as aero-engines and nuclear engineering,have provided convenience for our life,but it will lead to fatal accidents once they encounter fault.Therefore,it is important and significant to investigate the fault-tolerant control and fault detection based on polynomial fuzzy model.This paper studies the fault tolerant control and fault detection problems based on polynomial fuzzy nonlinear systems.The main contributions are given as follows:Firstly,the problem of fault-tolerant controller design based on general polynomial fuzzy time delay system is considered.A polynomial fault-tolerant controller is designed to make the closed-loop polynomial fuzzy time delay system stable under normal and fault conditions.In order to solve the non-convex condition caused by the nonlinear term and the time delay term,a novel square sum optimization method is proposed to transform the non-convex condition into an optimizable index.By means of the optimization of the sum of squares,the indexs can reach the desired zero optimal value simultaneously.In addition,in order to reduce the conservativeness of the controller design conditions,the upper and lower bound information of the membership function and the relaxation matrix are introduced into the stability analysis.At the same time,the flexibility of the design is enhanced by using the unmatched premise membership function between the polynomial fuzzy model and the polynomial fault-tolerant controller.The effectiveness of the proposed method is verified via a numerical simulation example.Secondly,the event-triggered fault detection problem based on continuous-time polynomial fuzzy model is considered.An event-triggered fault detection filter is designed to detect the occurrence of a fault in real time.The stability analysis is achieved based on the Lyapunov stability theorem and satisfying the optimized H? performance index ?.In addition,in order to save the limited network resources,a polynomial event triggering mechanism is designed,which increases the design flexibility compared with the traditional quadratic event triggering mechanism.The event-triggered fault detection is first time applied to the continuous-time polynomial fuzzy system,and the numerical example and the inverted pendulum system are simulated at the same time,which verif the effectiveness of the method.Thirdly,the problem of fault detection for continuous polynomial fuzzy systems with sensor nonlinearity is considered.The polynomial fuzzy fault detection filter design is implemented with the sensor output subject to polynomial nonlinearity.The upper and lower bounds of the membership function and the relaxation matrix are introduced into the stability analysis,so that a less conservative stability condition is obtained.In addition,the stability analysis is achieved based on the Lyapunov stability theorem and satisfying a given H?performance index ?.At the same time,a proper threshold function is selected to detect the occurrence of the fault in real time when a fault occurs.In this regard,the problem of fault detection for a continuous-time polynomial fuzzy model with sensor nonlinearities is solved.Finally,some conclusions are presented at the end of this thesis and the direction of the future work is discussed.