Abstract
This paper presents a new design procedure to tune the fractional order PID controller that stabilizes a first order plant with time delay. The procedure is based on a suitable version of the Hermite-Biehler Theorem and the Pontryagin Theorem. A Theorem and a Lemma are developed to compute the global stability region of the PID controller in the (k(p),k(i),k(d)) space. Hence, this Theorem and Lemma allow us to develop an algorithm for solving the PID stabilization problem of the closed loop plant. The proposed approach has been verified by numerical simulation that confirms the effectiveness of the procedure.