Approximation of fractional-order low-pass filter

Approximation of fractional-order low-pass filter

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Optimal integer-order transfer function approximations to model the single fractance element-based fractional-order low-pass filter (FLF) for any arbitrary order α, where, 0 < α < 1, is proposed here. First of all, the integer-order filter coefficients for FLFs, with α varying from 0.01 to 0.99 in steps of 0.01, are directly obtained by using a metaheuristic algorithm called colliding bodies optimisation. For practical usability, the approximated FLF coefficients are explicitly provided in the form of analytical equations by employing a curve fitting on the optimised coefficients in the second step. The proposed approach provides a simpler design procedure in comparison to the reported literature which approximates the FLF by substituting an integer-order rational approximation of the sα operator in the transfer function of the ideal FLF. Simulations confirm the superior modelling accuracy of the proposed design over the recent literature.

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