Direct approximation of fractional order systems as a reduced integer/fractional-order model by genetic algorithm
- PDF / 1,501,780 Bytes
- 15 Pages / 595.276 x 790.866 pts Page_size
- 111 Downloads / 237 Views
Sådhanå (2020) 45:277 https://doi.org/10.1007/s12046-020-01503-1
Sadhana(0123456789().,-volV)FT3](012345 6789().,-volV)
Direct approximation of fractional order systems as a reduced integer/ fractional-order model by genetic algorithm HASAN NASIRI SOLOKLO*
and NOOSHIN BIGDELI
Control Engineering Department, Imam Khomeini International University, Qazvin, Iran e-mail: [email protected]; [email protected] MS received 31 October 2018; revised 19 July 2020; accepted 23 September 2020 Abstract. 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 reducedorder systems 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. Keywords. Model order reduction; fractional order system; genetic Algorithm; constrained optimization; commensurate; incommensurate; Hankel singular value.
1. Introduction In the recent two decades, fractional calculus has received increasing attention in the description and modeling of natural and real-world phenomena [1]. Consequently, related issues such as the fractional-order system stability analysis [2–4], fractional order system identification [5, 6], and fractional-order system approximation [7–9], have been investigated, vastly, in the literature. Also, many controllers have been designed for real-world dynamic processes through fractional-order systems [10, 11]. However, the main disadvantages of the fractional-order models and controllers are their complicated analysis, difficult implementation, and mismatching with conventional science. Therefore, several methods have been proposed for the integer-order approximation of fractional order systems and controllers such as Oustaloup’s approximation algorithm [12], Matsuda’s approximation algorithm [13], and many more. Although these integer order approximations may be accurate enough for system description, they are not usually effective for controller design due to their high order. That is, accurate analysis and controller design for such high order systems are very difficult and time-consuming. Also, the implementation of these high order models and
Data Loading...
