A ROBUST TUNING METHOD FOR FRACTIONAL ORDER PI CONTROLLERS

Abstract

The application of fractional controller attracts more attention in the recent years. In this paper, a new tuning method for PIα controller design is proposed for a class of unknown, stable, and minimum phase plants. We are able to design a PIα controller to ensure that the phase Bode plot is flat, i.e., the phase derivative w.r.t. the frequency is zero, at a given gain crossover frequency so that the closed-loop system is robust to gain variations and the step responses exhibit an iso-damping property. Several relay feedback tests can be used to identify the plant gain and phase at the given frequency in an iterative way. The identified plant gain and phase at the desired tangent frequency are used to estimate the derivatives of amplitude and phase of the plant with respect to frequency at the same frequency point by Bode's integral relationship. Then, these derivatives are used to design a PIα controller for slope adjustment of the Nyquist plot to achieve the robustness of the system to gain variations. No plant model is assumed during the PIα controller design. Only several relay tests are needed.