Design of Fractional Order Differentiators and Integrators Using Indirect Discretization Approach

This paper deals with continued fraction expansion (CFE) based indirect discretization scheme for finding the rational approximation of fractional order differentiators and integrators and their discretized transfer functions. Indirect discretization approach is used for Al-Alaoui´s Optimized four segment rule and Simpson 1/3 rule based differentiators and integrators of order ½ and ¼. These rational transfer functions are first stabilized for minimum phase then the resultant rational approximation is discretized by using s to z transforms. The curves for their magnitude responses, absolute magnitude errors and the phase responses are drawn with the help of MATLAB. These curves are then compared with ideal characteristics of differentiators and integrators.