Lagrangian modeling and control of switching networks with integrated coupled magnetics

Abstract

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.

Lagrangian modeling of switching electrical networks

“…Application of the physical control design techniques to networks with realistic switching frequencies can be found in [6,11]. A thorough design analysis and physical tuning guideline are given in [6] for the damping injection of such controllers.…”

Tuning of Passivity-Preserving Controllers for Switched-Mode Power Converters

“…For circuits containing a single switch is defined as (3) with is the mixed-potential function for the switch position , and is the mixedpotential function for the switch position . The way the switch enters the potential function as defined in (3) differs from the definition of the switched Rayleigh dissipation function, as defined in [3], [7], and [12], in the sense that here we have used the concept of superposition of the power flows, where in the references the switch in the dissipation would enter via the dissipated energy. Although we have modified the mixed-potential function for the inclusion of one controllable switch, the approach is also suitable for circuits with more than one switch.…”

“…One particular PBC technique is based on the classical Euler-Lagrange (EL) equations. The application of EL-based PBC design to single-switch dc-to-dc power converters was first proposed by Sira-Ramírez et al [13] and is generalized to larger networks, like the coupled-inductor Ć uk converter, and three-phase rectifiers and inverters in e.g., [3], [7], and [12]. One of the major advantages of using the EL approach is that the physical structure (e.g., energy, dissipation, and interconnection), including the nonlinear phenomena and features, is explicitly incorporated in the model, and thus in the corresponding PBC.…”

“…It is hard to give a general answer to the first question since we are not able to give explicit formulations of the zero-dynamics for a general converter structure. Application of PBC to, for example, the boost, buck-boost [13] and the Ć uk [12] converter, leads to an indirect regulation scheme of the output voltage through regulation of the input current. Since there is no general answer to the first question yet, we continue with checking the stability of the zero-dynamics on a case by case basis.…”

Tuning rules for passivity-preserving controllers

“…Because the PBC relies on a partial system inversion we can not control the non-minimum phase states directly. Application of PBC to for qxample the boost, buck-boost [9] and the (coupled-inductor) Cuk [8] converters leads to an indirect regulation scheme of the output voltage through regulation of the input current.…”