A unified direct approach for discretizing fractional-order differentiator in delta-domain

Fractional-order differentiator is a principal component of the fractional-order controller.Discretization of fractional-order differentiator is essential to implement the fractionalorder controller digitally.Discretization methods generally include indirect approach and direct approach to find the discrete-time approximation of fractional-order differentiator in the Z-domain as evident from the existing literature.In this paper,a direct approach is proposed for discretization of fractional-order differentiator in delta-domain instead of the conventional Z-domain as the delta operator unifies both analog system and digital system together at a high sampling frequency.The discretization of fractional-order differentiator is accomplished in two stages.In the first stage,the generating function is framed by reformulating delta operator using trapezoidal rule or Tustin approximation and in the next stage,the fractional-order differentiator has been approximated by expanding the generating function using continued fraction expansion method.The proposed method has been compared with two well-known direct discretization methods taken from the existing literature.Two examples are presented in this context to show the efficacy of the proposed discretization method using simulation results obtained from MATLAB.