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Lagrangian modeling and control of switching networks with integrated coupled magnetics

In this paper a method is presented to build an Euler-Lagrange model for electrical networks, including switches and integrated (non-ideal) coupled-magnetics, in a structured general way. One of the advantages of emphasizing the physical structure of these systems is its functionality during the controller design stage. In a case a switching network contains coupled-inductor structures, an additional path for the energy transfer is introduced. For this reason, a basic building block is proposed that describes the dynamical behaviour of a pair of magnetically coupled-inductors. This building block is applicable to all types of switching converters, and easily predicts the existence of reduced or zero-ripple current. The switches make the dynamic models nonlinear. It is shown that under certain coupling conditions it is possible to design a globally stable controller. The approach is illustrated by means of the coupled-inductor Cuk converter with zero-output ripple, in closed loop with an adaptive passivity-based controller.