Optimal design of wideband infinite impulse response fractional order digital integrators using colliding bodies optimisation algorithm

Abstract

This study presents a novel approach to design wideband infinite impulse response fractional order digital integrators (FODIs) for the half and one-fourth order integrators based on a parameter independent metaheuristic algorithm called colliding bodies optimisation (CBO). The performance of CBO-based FODIs have been compared with the designs based on three well-known benchmark evolutionary optimisation algorithms namely, real coded genetic algorithm (RGA), particle swarm optimisation (PSO), and differential evolution (DE) in terms of robustness, consistency, parameter sensitivity, convergence speed, and computational time. Simulations results confirm that the proposed CBO-based designed FODIs achieve consistently superior magnitude responses in a computationally efficient manner as compared with the designs based on RGA, PSO, and DE. The proposed CBO-based FODIs also significantly outperform all state-of-the-art designs reported in literature in terms of two different magnitude response error metrics. This research work underlines the potential of CBO as an efficient optimisation tool for the design of accurate digital approximations to the fractional order integrators.