Tuning of fractional PI controllers for fractional order system models with and without time delays

In this paper, a servo control strategy for tuning of fractional order PI (FO-PI) controllers is proposed for fractional order system models with and without time delays. The proposed strategy is based on a reference model, whose open-loop transfer function is given by Bode´s ideal transfer function, which provides an infinite gain margin and constant phase margin. To come up with satisfactory tuning parameters of the controller, an iterative optimization method is suggested, based on minimization of a quadratic cost function. This cost function is defined as weighted sum of squares of control input moves and sum of the integral squared error (ISE) between the time response of the reference model and the fractional system with the FO-PI controller. The resulting closed-loop system is shown to exhibit features of robustness to process gain variations and the step responses exhibit iso-damping property. Simulation results are presented and analyzed here to illustrate the effectiveness of the proposed algorithm.