Research On Optimization For Fractional Predictive Control System

Fractional model is usually used to describe the genetic properties of various materials and reaction process.For many practical systems,compared with integer order model,fractional model is more suitable for the actual data and can greatly improve the modeling accuracy.However,many traditional control methods are proposed based on the integer order model.To improve the control performances,more accurate fractional models are necessary to describe the actual process and to design the controller.Predictive control is an advanced optimization control method based on the model.How to solve the optimization problem is the key to realize the predictive control.Fractional order model provides excellent congenital conditions for predictive control.How to solve the optimization problem in fractional predictive control is worthy of further study.Predictive control has been widely applied in integer order system,but its application for fractional order system needs further study.On the basis of previous research,this paper focuses on solving the optimization problem in the predictive control for fractional order model.A new method is proposed for fractional linear system identification and predictive control and predictive control of fractional order nonlinear systems.This thesis includes the following main innovations:1.For fractional-order linear systems,the improved NLJ algorithm is proposed to realize the parameter identification of the fractional linear system.The algorithm is the fusion of New Luus-Jaakola(NLJ)algorithm and Random adaptive search with identification and diversification(RasID)method.The algorithm obtains the optimal value by quadratic iteration,which greatly improves the efficiency of identification.Then,predictive control scheme is designed based on the obtained fractional model.The numerical calculation method of the fractional differential equation is used,and the generalized predictive control algorithm is extended to the fractional field.Finally,the optimal control law is obtained by matrix inversion.The control effect of the controller is verified by simulation experiments.2.For complex fractional-order nonlinear systems,a model predictive controller based on fractional gradient descent is proposed.Firstly,Neural network model is established for fractional order system.Then,Fractional calculus theories are used to construct fractional gradient descent method and to calculate control laws in non-linear predictive control.Compared with common neural networks,extreme learning machine(ELM)has the advantages of faster training speed and fewer adjustable parameters.The proposed ELM is used to establish a nonlinear system model instead.The designed fractional nonlinear model predictive controller is applied to a fractional nonlinear system.Simulation results show that the proposed method can obtain fast tracking response and strong stability.A fractional nonlinear predictive control algorithm based on the Legendre polynomial is proposed.The algorithm uses the Legendre polynomial to fit the characteristics of any arbitrary nonlinear function.Based on the properties of fractional calculus,the algorithm approximates the state variable and the control variable in the whole optimization time domain,and then solves the nonlinear programming problem.Simulation results verify the effectiveness of the scheme.