Indirect Methods for Discretizing Fractional Order Differentiator in Delta Domain—A Comparative Study

Abstract

In this paper, three indirect methods are presented for discretizing fractional order differentiator  in delta domain. To this aim, three extensively used discrete time approximation methods of -domains are reformulated in delta domain. As a first step of applying the indirect discretization method, rational approximation of a half order differentiator is obtained using the Oustaloup approximation method. Then, all of the proposed discretization methods are applied separately on the integer order approximant of . The resulting frequency responses of the discretized systems are compared for simulation studies using MATLAB software.

Keywords: Fractional Differentiator, Rational Approximation, Euler Transform, Tustin Transform, Al- Alaoui Transform, -operator

Cite this Article

Jaydeep Swarnakar, Prasanta Sarkar, Lairenlakpam Joyprakash Singh. Indirect Methods for Discretizing Fractional Order Differentiator in Delta Domain—A Comparative Study. Journal of Control & Instrumentation. 2017; 8(2): 27–34p.