A New Method for Getting Rational Approximation for Fractional Order Differintegrals

In this paper a new algorithm is presented to calculate the poles and zeros to approximate a fractional order (FO) differintegral (s^±α,α∈(0,1)) by a rational function on a finite frequency band ω∈(ω_l,ω_h). The constant phase property of the FO differintegral is the basis for development of the algorithm. Interlacing of real poles and zeros is used to achieve the constant phase. The calculations are done using the asymptotic Bode phase plot. A brief investigation is made to get a good approximation for the Bode phase plot. Two design parameters are introduced to keep the average phase close to the desired phase angle and to keep the error within the allowed bounds. A study is done to empirically understand the relationship between the error and the design parameters. The results thus obtained help in the further calculations. The algorithm is computationally simple and inexpensive, and gives a fairly good approximation of fractance frequency response on the specified frequency band.