Research On Nonlinear System Predictive Control Based On T-S Fuzzy State Equation Model

Model predictive control is widely used with its superior performance and ability to take account of the constraints.However,there are still many difficulties in the research of predictive control for nonlinear systems: Firstly,it is difficult to establish an accurate mathematical model,and the form of the model is complex;Secondly,it needs to solve the nonlinear optimization problem online,the calculation is very large and it needs a lot of time to finish it.The T-S fuzzy model can not only approximate the smooth nonlinear function on any compact convex set with arbitrary precision,but also can decompose the nonlinear system into several linear systems and reduce the difficulty of system control.In this paper,a nonlinear system modeling method based on T-S fuzzy model is studied.By using the clustering algorithm to divide the workspace consists of input and output data of the original nonlinear system,the nonlinear system can be expressed as a combination of local linear systems,which is smoothly connected by membership functions.On this basis,this paper researches the predictive control problem of nonlinear system based on T-S fuzzy model.By designing different predictive controller separately for different linear subsystem in T-S fuzzy model,the controller of nonlinear system is the fuzzy weighted integration of local ones.The main contents of this paper are concluded as followings:(1)This paper researches the method and procedure of modeling nonlinear system by using T-S fuzzy models.The FCM clustering algorithm is used to divide the workspace consists of input and output data of the original nonlinear system,the results are used to determine the range of work for each linear subsystem and identify the premise parameters of T-S fuzzy model;The consequent parameters of T-S fuzzy model are identified by the least squares method.(2)Due to the shortcoming of FCM clustering algorithm,which is sensitive to the initial selection of the center,the artificial bee colony algorithm is introduced into it.First,the artificial bee colony algorithm is improved to increase its convergence rate,and the validity of the algorithm is tested by benchmark functions.Then,a k-means algorithm based on improved artificial bee colony algorithm is proposed to make the clustering results more accurate and stable.(3)The structure of premise part and consequence part in T-S fuzzy model is improved to increase the flexibility of the model and reduce the difficulty of modeling.The simulation results of several typical SISO and MIMO nonlinear systems also prove the effectiveness of the improved model.(4)The predictive control of constrained linear systems based on state space model is studied,and a method of obtaining the approximate function of control low under constraint condition is proposed.The simulation results on the SISO linear system prove the feasibility of the algorithm.(5)The problem of nonlinear system predictive control based on T-S fuzzy model is studied.The controller is designed separately for each linear subsystem by parallel distributed compensation method,and the problem of predictive control of nonlinear system is translated into the traditional linear predictive control problem,which reduces the difficulty of nonlinear system predictive control.