Curve Fitting-Based Approximation of Fractional Differentiator with Complex Orders

Abstract

This paper is focused on the design of fractional differentiator for complex orders of $\alpha+j\beta$ where $\alpha\in[0,1]$ and $\beta\in\Re$. Furthermore, for the practical realization of these fractional differentiators of complex orders, curve fitting-based approximation using Sanathanan-Koerner iteration is proposed. The fractional differentiator results with complex orders show that the proposed approximation is effectively handled both positive and negative imaginary parts of the complex orders. Furthermore, the results on fractional-integrator, PID controller, and low pass filter with complex orders show that the proposed technique has produced better approximation for the range $\omega$ in [$\omega_{l},\omega_{h}$]. The results also show that introducing an additional parameter has given more flexibility to obtain its robust performance.