Complementarity framework formulation from bond graphs to model a class of nonlinear systems and hybrid systems with fixed causality

Abstract

A systematic method for constructing models in the complementarity framework from a bond graph is proposed. Bond graphs with and without storage elements in derivative causality are considered. The proposed method allows the study of switching systems represented by a bond graph model of fixed causality. The proposed methodology allows the complementarity framework to be exploited in different engineering areas by using bond graphs. The idea of representing a unidirectional switch with a model that is essentially the same as a diode is presented. By employing a similar representation for diodes and switches, the modeling and simulation of power switching converters are simplified and become more intuitive. Two application examples are shown. A non-inverting buck-boost converter and a zeta converter with an element in derivative causality are simulated.