A New Tuning Method for Stabilization Time Delay Systems Using <i>P</i><i>I</i>^<i>λ</i><i>D</i>^<i>μ</i> Controllers

Abstract

Abstract This paper presents a new design procedure to tune the fractional order P I λ D 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 P I λ D 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 P I λ D μ stabilization problem of the closed loop plant. The proposed approach has been verified by numerical simulation that confirms the effectiveness of the procedure.