Robust FOPI and FOPID Controller Design for FFOPDT Plants in Embedded Control Applications using Frequency-domain Analysis

In this paper, we address the problem of fractional-order PID (FOPID) controller design for a fractional first-order plus dead time (FFOPDT) plant, the characteristics of which are studied. All the equations involved in the computation of control system robustness criteria in the frequency domain are derived, and an algorithm based on the Newton-Raphson method is proposed to obtain the solutions thereof. The performance criteria are considered as the basis for optimizing the parameters of the FOPID controller. The initial gains of the controller are obtained using well established conventional PID tuning rules. For optimization a simple parameter sweep method is used, as well as the Nelder-Mead simplex search method. An illustrative example of the controller design procedure is provided. The results are partially carried over to a FOPID controller prototype. The results of this work can be applied to embedded control and are useful in solving automatic controller tuning problems.