Comparison of Fractional PI Controller with Classical PI using Pareto Optimal Fronts

Abstract

AbstractA comparison between the fractional order PI (FOPI) controller and integer-order PI (IOPI) controller, and also between FOPI and IOPI with lead circuit, is conducted in this paper. The performance comparisons are conducted for a servo system. The FOPI controller is a controller with fractional-order integral, where the order parameter can be used to adjust the closed loop response of the servo system. The controllers are compared using the Pareto Optimal Front (POF) of each controller. The FOPI is approximated using Oustaloup’s approximation method. The approximated FOPI cannot achieve the positive values of the ideal FOPI in the phase-magnitude Bode plot. The POFs show that the FOPI is not always better than IOPI. The IOPI with lead circuit achieves performance which is similar to FOPI. Thus that the IOPI controller with lead circuit can be used to obtain a performance that closely matches the performance of the FOPI controller. The implemented FOPI controller did not track the setpoint. The IOPI controller, and also with a lead circuit, tracked the setpoint.KeywordsFractional PIInteger PIPareto optimal frontOustalou’s approximation method