A New Tuning Method for Stabilization Time Delay Systems Using PIλDμ Controllers

This paper presents a new design procedure to tune the fractional order PI^λD^μ 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 PI^λD^μ controller in the (k_p,k_i,k_d) space. Hence, this Theorem and Lemma allow us to develop an algorithm for solving the PI^λD^μ stabilization problem of the closed loop plant. The proposed approach has been verified by numerical simulation that confirms the effectiveness of the procedure.