A graphical tuning of PIλDµ controllers for fractional-order systems with time-delay

This article provides a graphical tuning method of PI^λD^μ controllers for fractional-order processes with time-delay. First, the stabilizing regions are drawn in 2-dimensional and 3-dimensional spaces, based on a graphical stability criterion applicable to fractional-order time-delay systems, for different λ and μ values to find the maximal stabilizing region in which the most various behaviors of the closed-loop systems are expected. Then, in this maximized region, the performances of stability margins and relative stability degree are considered, respectively. Finally, illustrative examples are given to show the design procedure and the flexible characteristic of the proposed graphical tuning approach.