Optimal and accurate design of fractional‐order digital differentiator – an evolutionary approach

Abstract

This study deals with the implementation of highly accurate, stable, minimum phase, and wideband fractional‐order digital differentiators (FODDs) in terms of infinite impulse response filters using an efficient evolutionary optimisation algorithm called adaptive Gbest‐guided gravitational search algorithm (GGSA). Performance evaluation of GGSA as compared with real coded genetic algorithm (RGA), particle swarm optimisation (PSO), and differential evolution (DE) based designs are carried out in terms of different magnitude and phase response error metrics, solution quality reliability, and convergence speed. Simulation results clearly demonstrate that GGSA significantly outperforms RGA, PSO, and DE in consistently achieving the most accurate FODDs in a computationally efficient manner. The proposed FODDs also significantly outperform all state‐of‐the‐art designs in terms of magnitude responses.