Fractional Order Differentiators and Integrators Design using Transform Techniques

Abstract

The design of fractional order differentiators and integrators (FODI) using is the main objective of this paper. In this indirect discretization scheme based Al-Alaoui and Tustin operators used to design a novel FODIs. Firstly, fifth ordr rational approximations in the s-domain are used and finally, discretized using more popular s-to-z transforms to acheive the new FODIs. The performances of proposed FODIs are well compared with the continued fractionan expansion (CFE) approximation based ones. Fractional order differentiators and integrators of order 0.5 and 0.25 are designed by using indirect discretization. Matlab simulation software is used to obtain the magnitude, phase responses and normalized magnitude error (NME) plots of the digital differentiators and integrators.It is noted that the designed digital integrators and differentiators are accurate ntemd of magnitude and NME.