Bond Graphs for Distributed System Models Admitting Mixed Causal Inputs

Abstract

Bond graphs are used for finite mode representations of distributed system dynamics. As long as all inputs to the system are “efforts” in a causal sense, then no formulation problems exist. However, if some of the system inputs are causal “flows”, then differential causality will exist and extremely tedious, often impossible, algebraic loops must be solved to formulate system equations. A procedure is developed which avoids these algebraic problems by including additional modal compliance in the system model without its associated modal inertia. The result of this approach is a finite mode distributed system model, devoid of artificially induced high frequencies, extremely accurate in a chosen frequency range, and capable of interacting with other distributed system models. The procedure is demonstrated through example.