Fractional-order optimization of piλ dμ controllers for time-delay systems

This article discusses the fractional-order optimization design and the phase and gain margins tuning of PI^λ D^μ controllers for fractional-order time-delay systems. A graphical stability criterion for fractional-order time-delay systems is first applied to determine the stabilizing regions in integral-gain and derivative-gain space. Then, the stabilizing region is maximized with respect to fractional-order parameters λ and μ, to expect more various behaviors of the closed-loop systems. Furthermore, in the bigger stabilizing region, the phase margin and gain margin specifications are considered. Finally, an algorithm for achieving the given phase and gain margins is proposed. Illustrating examples are followed in each step to show the design procedures.