A graphical tuning of PI λ controllers for fractional-delay systems

Abstract

This article provides a graphical parameter tuning method of PIλ controllers for fractional-order time-delay systems. First, the complete stabilizing region of PIλ controller in proportional-integral plane, for a fixed λ, is determined in terms of a graphical stability criterion applicable to fractional-delay systems. Then, the stabilizing region is maximized analytically with respect to parameter λ to expect the most various behaviors of the closed-loop systems. Finally, by defining appropriate functions relative to the requirements of gain and phase margins, the curves in the maximized stabilizing region satisfying the pre-specified gain and phase margins are drawn, which releases a flexible parameter tuning procedure. Numerical examples are given to illustrate the design steps.