A new design of fractional-order dynamic matrix control with proportional–integral–derivative-type structure

Abstract

Most dynamic systems in practice are of fractional order and often the models using fractional-order equations can grasp their intrinsic properties with more accuracy compared with conventional differential equations. In this paper, a fractional-order modeling-based proportional–integral–derivative-type dynamic matrix control is developed and tested on a typical industrial heating furnace system with fractional-order dynamics. The Oustaloup approximation method is first adopted to obtain the model approximation of the processes, which paves the way for the application of integer order dynamic matrix control to the fractional-order systems. Meanwhile, a set of proportional–integral–derivative-type operators are introduced in the cost function to further optimize the dynamic matrix control in terms of tracking and disturbance-rejection performance. The resulting controller bears both the merits of the dynamic matrix control and the proportional–integral–derivative, and thus improved control performance is obtained. In addition, an industrial heating furnace process system is given to test the performance of the proposed method in comparison with traditional integer order model-based dynamic matrix control, and results show that the proposed method gives improved system performance.