Approximation of fractional‐order low‐pass filter.

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. [ABSTRACT FROM AUTHOR]