Optimal integer‐order rational approximation of α and α + β fractional‐order generalised analogue filters

Abstract

A new approach to determine the integer-order transfer function approximation for α and α + β, where 0 <; α , β <; 1, fractional-order analogue filters is presented. Reported works deal with this design problem by using techniques which are non-optimal. The proposed designs with guaranteed stability are obtained by employing a global search optimisation algorithm called colliding bodies optimisation (CBO). The modelling error is iteratively minimised by CBO in the least-squares sense directly in the frequency domain. The improved accuracy in the magnitude response of the proposed fractional-order low pass filters, fractional-order high pass filters, and fractional-order band pass filters as compared to the designs based on the Matsuda and the continued fractions expansion-based techniques is demonstrated. The efficacies of the proposed filters are also validated in SIMULINK platform.