Design of fractional order differentiators and integrators using indirect discretization scheme

This paper attempts to find the rational approximation of fractional order differentiators and integrators and their discretized transfer functions by using continued fraction expansion (CFE) based indirect discretization scheme. Schnieder 2^nd order rule and Al-alaoui's 2-segment rule are considered for indirect discretization approach and differentiators and integrators of order ½ and ¼ based on these two rules are presented. The rational transfer functions are first tested for minimum phase and stability then the resultant rational approximations are discretized by using s to z transforms. These discretized transfer functions are checked for stability again after performing approximation process. Simulation resultant curves are drawn with the help of MATLAB for the magnitude responses, absolute magnitude errors and the phase responses of the stabilized discrete transfer functions. These curves are then compared with each other and the corresponding ideal characteristics of differentiators and integrators.