Performance Evaluation of Two Analytical Discretization Methods for Implementation of Fractional Order Transfer Functions

Recent researches reported that fractional calculus provides more accurate modeling of real systems. For this reason, fractional order system models begun to utilized widely in numerical analysis and system simulations. However, due to high computational complexity of discrete time domain realization, there is need for accurate digital implementation of fractional order elements and transfer functions in operating ranges of applications. This study investigates frequency response matching properties of two analytical discrete approximation approaches for the application point of view: One is a direct discretization method, which is known as Tustin recursive approximation, and the other is an indirect disretization method, which benefits from continued fraction expansion (CFE) of fractional order derivative operator. Results of these two methods are compared and applicability of the methods are discussed on the bases of operating range requirements of control and filter realization applications