Design of Improved Fractional Order Integrators using Indirect Discretization Method

Abstract

paper has adopted rational approximation based on Regular Newton method, for frequency domain fitting of transfer functions of fractional order integrators (FOIs). Further, different discretized mathematical models of one-half, one-third and one-fourth order integrators based on Al-Alaoui operator and New optimized four segment operator have been also developed using these rational approximations by indirect discretization technique. All the proposed models of FOIs are found to be stable when investigated for stability. Simulation results of magnitude responses, phase responses and absolute magnitude errors show that the proposed FOIs obtained by approximations based on Regular Newton method, clearly outperform the other existing approximation techniques which have been used for designing fractional order operators. Results of absolute magnitude errors for all proposed fractional order integrators have been reported to be as low as 0.01, in range 0.35 ≤ ω ≤ 1 π radians of full band of normalized frequency. Among the proposed FOIs, the one-half, one-third and one- fourth order models based on Al-Alaoui operator (for 2 nd iterations) are noticeable with tremendously improved results with absolute magnitude errors of ≤ 0.004 in complete normalized frequency range.