Research On Fractional Order Model Predictive Control Algorithm

Theoretical study on fractional calculus is not new,but its research on the control is still worth studying.The conventional study is for integer order model and integer order controller.However,the industrial processes are essentially the fractional systems and the integer order models cannot be used to describe these types of dynamic processes better than fractional order model.Meanwhile,it is difficult for the controllers based on integer order models for the fractional actual processes to obtain good performance of the system.Along with the increasing demands for the control accuracy,cost,security etc.,more accurate models describing the actual process and better controller to achieve good performance are urgently needed to be put forward.On the basis of previous research results,two main aspects have been done in this thesis.On one hand,the fractional order predictive functional control method is designed for the fractional order linear systems.The Oustaloup approximation is employed to derive the approximate model of the fractional order system.Meanwhile,to extend the integer order predictive functional control algorithm to the fractional order predictive functional control,the Grünwald-Letnikov definition and the fractional calculus operator are used in its cost function.And then the optimal control of fractional order controlled system is obtained.The simulation results reveal that the fractional order controller yields improved control performance.On the other hand,the extended non-minimal state space fractional model predictive control method is proposed for the fractional order model of a heating furnace.The fractional calculus definition of Grünwald-Letnikov is to define the input-output model of the fractional system.Then,based on the extended non-minimal state space model and the selected cost function with the fractional calculus operator,the new fractional predictive controller is designed.The simulation results indicate that improved performance of fractional order controller is obtained and which promote the applications of model predictive control method in fractional order systems.