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https://www.ias.ac.in/article/fulltext/sadh/045/0277

Model order reduction; fractional order system; genetic Algorithm; constrained optimization; commensurate; incommensurate; Hankel singular value.

In this paper, a new method is proposed for the reduced-order model approximation of commensurate/incommensurate fractional order (FO) systems. For integer order approximation, the model order is determined via Hankel singular values of the original system; while the order of FO approximations is determined via optimization. Unknown parameters of the reduced model are obtained by minimizing a fitness function via the genetic algorithm (GA). This fitness function is the weighted sum of differences of Integral Square Error (ISE), steady-state errors, maximum overshoots, and ISE of the magnitude of the frequency response of the FO system and the reduced-order model. Therefore, both time and frequency domain characteristics of the system considered in obtaining the reduced-order model. The stability criteria of the reducedordersystems were obtained in various cases and added to the cost function as constraints. Three fractional order systems were approximated by the proposed method and their properties were compared with famous approximation methods to show the out-performance of the proposed method

HASAN NASIRI SOLOKLO¹ NOOSHIN BIGDELI

1. Control Engineering Department, Imam Khomeini International University, Qazvin, Iran

Published

5 November 2020

Manuscript received

31 October 2018

Manuscript revised

19 July 2020

Accepted

23 September 2020