Design And Analysis Of Predictive Function Controllers For Several Types Of Nonlinear Systems

As the most promising control theory,nonlinear system control theory has become the theme of modern control theory.In the strict sense,the ideal linear system does not exist in actual production.When the degree of non-linearity of the system is weak,the linear approximation method that using Taylor expansion in a small range near the equilibrium point is usually adopted.However,when the degree of non-linearity of the system is strong,the ordinary single linear approximation method will produce large error,which not only makes the controller's control effect poor,but also causes model mismatch problems.With the advantages of multi-step prediction,rolling optimization and feedback correction,model predictive control has made much progress in dealing with nonlinear system constraints,system parameter uncertainty,actuator saturation.As one of the classic MPC algorithms,predictive functional control has small calculation,strong robustness and good control effect,which attracts widespread attention from scholars.In this paper,a predictive functional control algorithm is designed for several different types of nonlinear systems to make the closed-loop system stable.The main job of this paper can be summed up as the following three parts:Firstly,the predictive functional control problem for a class of nonlinear systems with state and input constraints is studied.First of all,according to the “piece-wise embedding”principle,multiple LPV models are applied to approximate the nonlinear system.Then,a predictive functional controller based on a linear combination of known basis functions is designed for each LPV model.At the same time,a switching law of controllers is designed to ensure that the system can smoothly enter the next LPV model.Under the constraint of switching law,the system switches reasonably between various LPV models,which can ensure the closed-loop system is stable eventually.Finally,two simulation examples are given to verify the effectiveness of the proposed algorithm.Secondly,the predictive functional control problem for a class of nonlinear systems with time delay is studied.First of all,multiple LPV models are used to approximate the nonlinear system.Then,the corresponding LPV model can be selected according to the region of the parameter,and predictive functional controller is designed for each LPV model.At the same time,a switching law is designed.Under the constraint of switching law,the system switches reasonably between various LPV models,which can ensure the closed-loop system is stable eventually.Finally,two simulation examples are given to verify the effectiveness of the proposed algorithm.Thirdly,the predictive functional control problem for a class of nonlinear unsymmetrical systems is studied.As a special kind of nonlinear systems,the characteristic of the unsymmetrical system is: the dynamic response of the system is completely different when the control input increases and decreases.According to the characteristic of unsymmetrical systems,a positive-negative model is established to approximate the unsymmetrical system.Predictive functional controller based on a linear combination of known basis functions is designed for the positive-negative model.Then,a switching law is designed,so that the controller can switch between positive controller and negative controller reasonably,which can ensure the closed-loop system is stable eventually.Finally,three simulation examples are given to verify the effectiveness of the proposed algorithm.