Optimal Design of Fractional-Order Digital Differentiator Using Flower Pollination Algorithm

Abstract

This paper presents an efficient approach to design wideband, accurate, stable, and minimum-phase fractional-order digital differentiators (FODDs) in terms of the infinite impulse response (IIR) filters using an evolutionary optimization technique called flower pollination algorithm (FPA). The efficiency comparisons of FPA with real-coded genetic algorithm (RGA), particle swarm optimization (PSO), and differential evolution (DE)-based designs are conducted with respect to different magnitude and phase response error metrics, parametric and nonparametric statistical hypotheses tests, computational time, and fitness convergence. Exhaustive simulation results clearly demonstrate that FPA significantly outperforms RGA, PSO, and DE in attaining the best solution quality consistently. Extensive analysis is also conducted in order to determine the role of control parameters of FPA on the performance of the designed FODDs. The proposed FPA-based FODDs outperform all the designs published in the recent literature with respect to the magnitude responses and also achieve a competitive performance in terms of the phase response.