Performance Comparison of Fractional Digital Differentiators Using Various Approximation Models

An approximation of fractional differentiator <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$s^{1/2}$</tex> using various techniques and the corresponding fractional digital differentiator (DD) design is the main objective of this paper. In this rational transfer function in s-domain obtained by using Oustaloup, Matsuda and curve fitting approximation (CFA) approaches. The CFA fifth order approximation of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$s^{1/2}$</tex> gave better performance in required frequency range than Oustaloup and Matsuda based ones. The performance of these fractional analog approximations evaluated in terms of mean absolute error (MAE) and root mean square error (RMSE). By the application of CFA technique, fractional DDs designed by using the indirect discretization of interpolated transform, which provides more effective in the lower frequency region up to 1.57 rad. The magnitude, error plots are obtained with MATLAB software and performance of fractional DDs with CFA evaluated and compared in terms of maximum normalized magnitude error (MNME).