Modeling and Control of the Fractional Order Quadratic Boost Converter in PCCM

Abstract

Based on the fact that the inductors and capacitors are fractional order in nature, the four-order mathematical model of the fractional order quadratic Boost converter in PCCM is established by using the Caputo fractional calculus theory. According to the Lyapunov-like theorem of the fractional order system, a non-linear controller is designed. On the basis of the improved Oustaloup approximation algorithm and the equivalent circuit models of the fractional order inductor and capacitor, the influence of the orders on the performance of the quadratic Boost converter in PCCM and the efficiency of the proposed controller are demonstrated by numerical and circuit simulation.