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A New Tuning Method for Stabilization Time Delay Systems Using P I λ D μ Controllers
Author(s) -
Hafsi Sami,
Laabidi Kaouther,
Farkh Rihem
Publication year - 2015
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.931
Subject(s) - lemma (botany) , mathematics , control theory (sociology) , controller (irrigation) , stability (learning theory) , order (exchange) , pontryagin's minimum principle , pure mathematics , discrete mathematics , optimal control , mathematical optimization , computer science , control (management) , ecology , poaceae , finance , artificial intelligence , machine learning , agronomy , economics , biology
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.