A New Discretization Method for Fractonal Order Differentiators via the Bilinear Transformation

This work deals with the fractional order differentiator s^m and integrator s^-m (0<m<1) and its analogue and numerical implementation. A new method is proposed, first the fractional order differentiator s^m (0<m<1) is modeled by a fractional power zero (FPZ), in a given frequency band of practical interest. Next, this FPZ is approximated by a rational function, the same idea is used to model the fractional order differentiator s^-m (0<m<1) by a fractional power pole (FPP), using the rational function approximation of theses fractional order operators, we can derived simple analogue circuits which can serve as fractional order integrator, differentiator. For the numerical implementation and the computes of the output, we have discretized the obtained transfer function via the bilinear (trapezoidal, tustin) transformation in a given frequency band. Some examples are represented and compared. This method is tested and compared using some of the most recent functions, and some results are presented, discussed and compared with that of most recent methods of discretization of the fractional order differentiator s^-m.