In this paper, a general and systematic method is presented to model topologically complete electrical networks, with or without multiple or single switches, within the Euler-Lagrange framework. Apart from the physical insight that can be obtained in this way, the framework has proven to be useful for the application of passivity-based control techniques, which on a case by case basis already has shown to be useful for the control of power converters within the class of switching electrical networks. The switches are assumed to be ideal, and pulse-width modulation is taken into account. Magnetic coupling of inductive elements is also included in the framework.
a.scherpen/d.jeltsema/j.b.klaassens @its.tudelft.nl Phone: +31-15-278/-6152/-4516/-2928, Fax: +3 1-15-278-6679 Absrrucr -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 case a switching network contains coupledinductor 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. For using the Lagrangian structure for controller design, the zero-dynamics for such switching network had to be studied. It is shown that under certain coupling conditions it will not be possible to design a globally stable controller. The approach is illustrated by means of the coupledinductor Cuk-converter with zero-output ripple, in closed loop with an adaptive passivity-based controller.
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