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Novel Digital Differentiator and Corresponding Fractional Order Differentiator Models

This paper proposes a novel first order digital differentiator. The differentiator is obtained by linear mixing of Al-Alaoui operator (Al-Alaoui, 1993) and wide band differentiator (Hsue, 2006). MATLAB simulation results of the proposed differentiator for various sampling frequencies have been presented. The magnitude results are in close conformity to the theoretical results for approximately 78% of the full range. The phase of the new differentiator is almost linear, with a maximum phase error of 8.24o. We have also proposed new operator based fractional order differentiator models. These models are obtained by performing the Taylor series expansion and continued fraction expansion of the proposed operator. Comparisons of the suggested models with the existing models of half differentiators show perceptible improvement in performance of the fractional order circuit. MATLAB simulation results show that the magnitude response of the proposed half differentiator matches with the theoretical results of continuous-time domain half differentiator for almost the whole frequency range and the phase approximates a constant group delay which is desirable for many applications. The major purpose of this paper is to emphasize that fractional order control systems are better than the conventional order systems as the system control performance is enhanced.