On Gyrobondgraphs and Their Uses

Graphical representations of lumped-parameter models for physical and engineering systems have been in use for some time. A relatively recent arrival is the bond graph, which displays energy flow and energy structure explicitly. Bond graphs are finding increasing use in a variety of applications, including classical electromechanical, hydraulic, and thermal energy systems as well as chemical and biological processes. In addition, there has been some effort to extend the approach to energy-like macroeconomic systems. The standard bond graph approach uses the same basic elements commonly found in network theory, although the graphing scheme is different. This paper defines a specific type of bond graph—the gyrobondgraph—and shows how it serves as a canonical form for a large class of lumped-parameter multiport models. The gyrobondgraph is based on only five elements and a standard graph format. A transformation procedure is described for obtaining a gyrobondgraph from a standard bond graph. The formulation of system equations associated with a gyrobondgraph is discussed briefly, and, as a point of interest, Tellegen’s Theorem in quasi-power form is derived. The gyrobondgraph appears to be an important new tool for the exploration of multiport system theory; furthermore, it is a source of new techniques for the computer simulation of bond graph models.