MODELING AND CHARACTERISTIC ANALYSIS OF FRACTIONAL-ORDER BOOST CONVERTER BASED ON THE CAPUTO–FABRIZIO FRACTIONAL DERIVATIVES

Abstract

This paper presents a novel approach for modeling Boost converters using the Caputo–Fabrizio (C-F) definition-based fractional-order model to address singular characteristics in fractional-order definitions and enhance model accuracy. A small signal modeling method is proposed to improve the accuracy of circuit parameter design and to derive state-averaged models, state-space equations, and transfer functions. The influence of capacitor and inductor orders on steady-state characteristics is analyzed and the influence of fractional-order on ripple characteristics is investigated through simulation. When the fractional-order approaches 1, the output voltage increases and the inductance current decreases, with waveform jitter mitigation. Moreover, boundary conditions for continuous conduction mode operation are established based on ripple characteristics. The numerical and circuit-oriented simulations verify the correctness of the proposed model. Finally, the orders and accurate parameters of capacitors and inductors based on the C-F definition are determined and the experiments are conducted. The comparison between the experimental and simulation results demonstrates that the proposed model can accurately describe the steady-state characteristics of the practical circuit systems, which further validates the accuracy of the proposed method.