A New Integer Order Approximation Table for Fractional Order Derivative Operators

• Published in: IFAC-PapersOnLine Vol. 50; no. 1; pp. 9736 - 9741
• Main Authors: Yüce, Ali, Deniz, Furkan N., Tan, Nusret
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.07.2017
• Subjects: Fractional order system; Inverse Fourier transform method; Laplace transform; Least-square fitting; Matsuda’s approximation method; Optimization; Oustaloup’s approximation method; Oustaloup’s approximation method; Inverse Fourier transform method; Fractional order system; Matsuda’s approximation method; Laplace transform; Least-square fitting; Optimization
• ISSN: 2405-8963; 2405-8963
• DOI: 10.1016/j.ifacol.2017.08.2177

There is considerable interest in the study of fractional order calculus in recent years because real world can be modelled better by fractional order differential equation. However, computing analytical time responses such as unit impulse and step responses is still a difficult problem in fractional order systems. Therefore, advanced integer order approximation table which gives satisfying results is very important for simulation and realization. In this paper, an integer order approximation table is presented for fractional order derivative operators (sa) where α ϵ R and 0 < α < 1 using exact time response functions computed with inverse Laplace transform solution technique. Thus, the time responses computed using the given table are almost the same with exact solution. The results are also compared with some well-known integer order approximation methods such as Oustaloup and Matsuda. It has been shown in numerical examples that the proposed method is very successful in comparison to Oustaloup’s and Matsuda’s methods.