Low Integer-Order Approximation of Fractional-Order Systems Using Grey Wolf Optimizer-Based Cuckoo Search Algorithm

• Published in: Circuits, systems, and signal processing Vol. 41; no. 4; pp. 1869 - 1894
• Main Authors: Mouhou, Abdelaziz, Badri, Abdelmajid
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.04.2022; Springer Nature B.V
• Subjects: Approximation; Circuits and Systems; Electrical Engineering; Electronics and Microelectronics; Engineering; Frequency ranges; Heuristic methods; Instrumentation; Integers; Mathematical analysis; Model reduction; Search algorithms; Signal,Image and Speech Processing; Stability criteria; Transfer functions; Cuckoo search; Model order reduction; Fractional-order systems; Grey wolf optimizer; Oustaloup approximation
• ISSN: 0278-081X; 1531-5878
• DOI: 10.1007/s00034-021-01872-w

This paper presents a stable reduced order approximation method of fractional-order systems based on the grey wolf optimizer hybridized with cuckoo search algorithm (GWO-CS). The proposed method is applied to factional order transfer functions (FOTF) in order to obtain a low-order model exhibiting good fits to the Bode’s ideal transfer function (TF) of the original system, taking into account the stability criteria of the reduced model. In the first stage, the Oustaloup approximation of a given FOTF is applied to obtain a high integer-order TF that matches with the original FOTF. In the second stage, The GWO-CS method is compared with the frequency-limited balanced truncation method resulting from Oustaloup approximation of the original FOTF in a specified frequency range and other existing meta-heuristic based model order reduction approaches. Simulation of different numerical examples confirms and validates the effectiveness of the proposed approach.