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Auto-tuning of FOPI and FO[PI] controllers with iso-damping property

A systematical design method for robust integer order proportional-integral-derivative(IOPID) controller with an iso-damping property was suggested in [3]. In this paper, two auto-tuning methods of Fractional Order Proportional Integral(FOPI) and Fractional Order [Proportional Integral] (FO[PI]) controllers with iso-damping property for a class of unknown, stable and minimum phase plants are designed and summarized. The FOPI and FO[PI] controllers designed by the two methods ensure that the phase Bode plot is flat, i.e., the phase derivative w.r.t. the frequency is zero at a given frequency called the “tangential frequency”, so that the closed-loop system is robust to gain variations and the unit step responses exhibit iso-damping property. During the process of the FOPI and FO[PI] controllers design and simulation, no plant models are assumed. Several relay feedback tests are used to identify the plant gain and phase at the tangential frequency in an iterative way. Simulation results are presented to validate the proposed auto-tuning methods for robust FOPI and FO[PI] controllers with iso-damping property.