Sliding Mode Control Of Interval Type-Ⅱ Fuzzy Singular System With Time Delay

Physical systems in engineering practice are essentially non-linear,so it is of realistic significance to study the design of non-linear system controllers.It is well known that the Takagi-Sugeno(T-S)fuzzy model can fuzzify a complex nonlinear system and transform it into a set of linear state equations,which is helpful for the application of perfect linear system theory to the controller design of complex nonlinear systems.At present,the interval type-ⅡT-S fuzzy model is superior to the traditional T-S fuzzy model in terms of uncertainty description,and it is more suitable for nonlinear systems in engineering practice.In order to adapt to unknown but bounded nonlinear disturbances,adaptive control is combined with sliding mode variable structure control to ensure that the state of interval type-Ⅱ T-S fuzzy singular closed-loop system can arrive the sliding mode surface stably.Therefore,this paper applies sliding mode controller to interval type-Ⅱ T-S fuzzy model to solve complex nonlinear system controller design problems.The following describes the specific study of this paper:(1)An adaptive sliding mode controller is designed for the interval type-Ⅱ T-S fuzzy singular system with time-varying time delay and nonlinear disturbance.Firstly,the integral sliding mode surface which is dependent on derivative matrix E,membership function and state delay term is constructed.Then,we select the delay-dependent Lyapunov-Krasovskii functional,and use the free weight matrix technique combined with the integral inequality method to derive the sufficient condition that the sliding mode system is admissible.An adaptive sliding mode controller with unknown disturbance parameters is constructed by using the upper and lower bounds of membership function.The effectiveness of this sliding mode variable structure controller is verified by the simulation of inverted pendulum system.(2)For interval type-Ⅱ T-S fuzzy singular systems with nonlinear interference,uncertain system parameters and time-varying time delays in the system state,the design problem of its guaranteed cost sliding mode controller is studied.On the basis of the research in Chapter 2,the integral sliding surface is improved.By using the method of linear matrix inequality,the sufficient condition that the system H2/H∝ guaranteed cost performance index can be realized and solved by LMI toolbox is obtained,and the solution method is given.The adaptive sliding mode controller with H2/H∞ guaranteed cost performance can be obtained by designing the control rate that can adapt to unknown parameters.(3)The design problem of sliding mode controller based on output observer for interval type-Ⅱ T-S fuzzy singular systems with time delay is studied when the states are not measurable.In order to evaluate the unpredictable state of the system,a new fuzzy output observer is designed.Based on the error system and considering the time-varying time delay of the system,the Lyapunov-Krasovskii stability theory combined with the LMI technology is used to design a fuzzy integral sliding mode surface related to the membership function.For compensate the unknown but bounded nonlinear disturbance,the adaptive control and sliding mode variable structure control are combined to ensure that the closed-loop system state can quickly reach the sliding surface and move stably.