Open AccessOptimal fractional‐order controller design using direct synthesis method
Author(s) -
Yumuk Erhan,
Güzelkaya Müjde,
Eksin İbrahim
Publication year - 2020
Publication title -
iet control theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.059
H-Index - 108
eISSN - 1751-8652
pISSN - 1751-8644
DOI - 10.1049/iet-cta.2020.0596
Subject(s) - transfer function , closed loop pole , control theory (sociology) , closed loop transfer function , fractional calculus , integer (computer science) , mathematics , controller (irrigation) , fractional order system , function (biology) , loop (graph theory) , stability (learning theory) , order (exchange) , mathematical optimization , computer science , full state feedback , engineering , agronomy , control (management) , artificial intelligence , evolutionary biology , machine learning , programming language , finance , economics , combinatorics , electrical engineering , biology
In this study, an optimal fractional‐order controller is proposed for a type of fractional‐order model utilising the direct synthesis method. In that respect, the fractional counterpart of the second‐order integer transfer function is selected as a closed‐loop reference transfer function. The stability region of the fractional‐order closed‐loop reference transfer function is given via a theorem and related lemmas. Considering that a unity feedback loop is used, the parameters of the fractional‐order closed‐loop reference transfer function are specified based on the integral square error performance index within the specified stability region using a genetic algorithm. The time‐domain characteristics of the optimal fractional‐order closed‐loop reference transfer function are compared with those of the optimal second‐order integer closed‐loop reference transfer function. The fractional‐ and integer‐order controllers that are designed based on optimal closed‐loop reference transfer functions are implemented on a real‐time system. The performance of the fractional‐order controller outperforms that of the integer counterpart on the integral square error criterion. Moreover, the simulation and practical results are consistent with each other.