Analytic approach to design PID controller for stabilizing fractional systems with time delay

The paper considers the problem of PID controller design for stabilizing fractional systems with time delay. An analytic approach developed for rational systems with time delay is extended for fractional systems with time delay. It consists in determining the stability regions in the PID controller parameters planes and choosing the optimal controller by analyzing the stability of the closed-loop corrected system using a graphical criterion, like the dual-locus diagram. The performances of the proposed approach are illustrated using two numerical examples.