A Method for Minimizing the Set of Equations in Bond Graph Systems with Causal Loops

Abstract

This work presents a procedure for obtaining a reduced set for the dynamic equations of a system modeled with bond graphs including any type of topological loops and zero-order causal paths. This minimal set is composed only of differential equations expressed in terms of the degrees of freedom of the system. Initially, flows corresponding to inertances and displacements associated with compliances are used to establish the dynamic equations and to find the zero-order causal paths of the system. A new method is used to solve the ZCPs inverting the preferred causality for the energy storage elements. With this method, break variables disappear because variables associated with the energy storage elements are used directly to open the ZCPs. The procedure developed in this paper solves the problem originated with the introduction of break variables that imply the presence of new variables and constrain equations. This procedure, before numerical integration of the dynamic equations, converts the equations to a minimal set in order to gain computational efficiency. Several examples are also provided to illustrate the conversion steps.