Fractional-order PI Controller Design for Integrating Processes Based on Gain and Phase Margin Specifications

Abstract

Fractional-order PID controllers have been introduced as a general form of conventional PID controllers and gained considerable attention latterly due to the flexibility of two extra parameters (fractional integral order λ and fractional derivative order µ) provided. Designing fractional controllers in the time domain has still difficulties. Moreover, it has been observed that the techniques based on gain and phase margins existing in the literature for integer-order systems are not completely applicable to the fractional-order systems. In this study, stability regions based on specified gain and phase margins for a fractional-order PI controller to control integrating processes with time delay have been obtained and visualized in the plane. Fractional integral order λ is assumed to vary in a range between 0.1 and 1.7. Depending on the values of the order λ, and phase and gain margins, different stability regions have been obtained. To obtain stability regions, two stability boundaries have been used; RRB (Real Root Boundary) and CRB (Complex Root Boundary). Obtained stability regions can be used to design all stabilizing fractional-order PI controllers.