Tuning of Fractional Order PID Controllers based on the Frequency Response Approximation Method

Fractional Order PID (FOPID) controllers have been heavily studied in recent years, but most of the methods developed for its optimal design rely on the idea of including several robustness and performance specifications in the objective function. Thus they suffer from the same problem, namely the difficulty in finding the optimal controller parameters due to the impossibility of meeting all the specifications, and the high sensitivity to the initial parameter values. In this work, a new optimization based tuning method for FOPID controllers is proposed. The method presents fast convergence and consists of specifying a desired closed-loop transfer function and finding the FOPID controller which gives the closed-loop behavior closest to the specified. The parameterization of the controller is shown, and the optimization procedure used is detailed. Then the proposed method is applied to design a FOPID to control an underdamped third order system with time delay, obtaining good robustness and performance. (C) 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.