On tuning fractional order [proportional–derivative] controllers for a class of fractional order systems

This paper deals with a method recently proposed for tuning fractional order [proportional–derivative] (FO-[PD]) controllers. Using this tuning method, the tuned FO-[PD] controller can ensure the desired phase margin, the desired gain crossover frequency, and the flatness of the phase Bode plot at such a frequency. In the present paper, the achievable region of this tuning method in the gain crossover frequency–phase margin plane is obtained analytically. Also, the continuity of this region and uniqueness of the tuned parameters are investigated. Moreover, the achievable region of the aforementioned tuning method in the presence of time delay in the feedback loop is found.