A Lagrangian approach to average modeling of pulsewidth-modulation controlled DC-to-DC power converters

A Lagrangian approach is used for obtaining the average model of a switch regulated dc-to-dc Power Converter of the "Boost" type undergoing a Pulsewidth-Modulation (PWM) feedback strategy. A set of average Euler-Lagrange (EL) parameters, modulated by the duty ratio function, is proposed which recovers, under duty ratio saturation conditions, the individual EL formulations of the intervening circuit topologies. The obtained average PWM model coincides with, both the state average model and the infinite switching frequency average model, previously proposed in the literature and derived from entirely different viewpoints.