Retrofitting fractional-order dynamics to an existing feedback control system: from classical proportional-integral (PI) control to fractional-order proportional-derivative (FOPD) control

Abstract

This paper presents a method of retrofitting an external controller into an existing feedback control system governed by a classical proportional-integral (PI) controller to improve the overall dynamics of the entire control system by benefitting from the advantages of fractional-order dynamics in the form of a fractional-order proportional-derivative (FOPD) controller. The retrofitting activity requires having access to the input and output signals of the existing control system ideally configured as a unity-feedback system. The difference between the input and output signals is then used as the input to an external controller having a fractional-order element. The design of the external controller is derived from the original values of the PI controller in the existing control system and the parameters of the desired FOPD controller to be used. A numerical example is presented in this paper to demonstrate how straightforward the process is. Discussion on some issues related to its hardware design and implementation is also presented in this paper.