A New Integer Order Approximation Table for Fractional Order Derivative Operators

Yuce A., DENİZ F. N., TAN N.

20th World Congress of the International-Federation-of-Automatic-Control (IFAC), Toulouse, Fransa, 9 - 14 Temmuz 2017, cilt.50, ss.9736-9741 identifier identifier

  • Yayın Türü: Bildiri / Tam Metin Bildiri
  • Cilt numarası: 50
  • Doi Numarası: 10.1016/j.ifacol.2017.08.2177
  • Basıldığı Şehir: Toulouse
  • Basıldığı Ülke: Fransa
  • Sayfa Sayıları: ss.9736-9741
  • Anahtar Kelimeler: Fractional order system, Matsuda's approximation method, Oustaloup's approximation method, Least-square fitting, Optimization, Inverse Fourier transform method, Laplace transform
  • İnönü Üniversitesi Adresli: Evet

Özet

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 (s(alpha)) where alpha is an element of R and 0 < alpha <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. (C) 2017, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved.