Fuzzy Control For The Nonlinear Delayed Distributed Parameter Systems

Many practical engineering systems can be modeled as distributed parameter systems(DPSs),which can be described by partial differential equations(PDEs),such as the non-isothermal piston flow reactors described by first-order hyperbolic PDE,the temperature distributions on the surface of reentry vehicles represented by parabolic PDE.Due to the infinite-dimensional characteristic,the stability analysis and controller design of DPSs become more difficult.In addition,the nonlinear phenomena and time-delay exist widely in the actual DPSs,and the influence of these factors should be considered in the stability analysis and controller design.The fuzzy control method based on Takagi-Sugeno(T-S)model has been widely used for nonlinear systems,which can combine the advantages of fuzzy logic theory and linear system theory.Therefore,the fuzzy control problem of nonlinear delayed DPS that described by parabolic PDE and hyperbolic PDE is studied by using T-S fuzzy modeling and control technology and Lyapunov direct method.The main research contents and innovations are given as follows:1.Note that the system state in actual processes is not available and the actuators and sensors are placed in different spatial positions,a dynamic fuzzy non-collocated boundary output feedback control method of nonlinear parabolic DPS with random time-varying delay satisfying Bernoulli distribution is proposed.Sufficient conditions to ensure the mean square exponential stability are established for nonlinear delayed DPS.Finally,the effectiveness of the presented method is verified by two examples.2.Note that the uncertainty,time delay,and disturbance in actual systems,a robust non-fragile H_∞fuzzy control method for uncertain nonlinear delayed hyperbolic DPS is proposed,which provides a theoretical basis for the stability analysis and controller design of hyperbolic DPS under complex conditions.Sufficient conditions based on linear matrix inequalities(LMIs)are established to ensure the exponential stability and H_∞performance of uncertain nonlinear delayed DPS.The gain matrices of robust non-fragile H_∞fuzzy controller is obtained by solving LMIs.Finally,the effectiveness of the proposed results is verified by applying the theoretical results to a class of Lotka-Volterra DPSs and non-isothermal piston flow reactor in chemical industry.3.Note that the existence of time-varying delay in actual systems,a fuzzy boundary control method for nonlinear delayed second-order hyperbolic DPS is proposed.Compared with distributed control,boundary control method requires few actuators and sensors and greatly reduces the control cost.Sufficient conditions based on LMIs are established to ensure the exponential stability of nonlinear delayed second-order hyperbolic DPS,and the gains of fuzzy boundary controller is obtained by solving the LMIs.Finally,an example is given to verify the effectiveness of the presented method.