Basis variables for linear junction structures

Abstract

The basis variables order of a bond graph junction structure is an important basic attribute. Results are available to predict the unique basis order for junction structures that do not contain any essential gyrator nodes. However, for junction structures containing one or more essential gyrator nodes, previous methods were unable to determine the basis properties. In this paper, a causality-oriented general linear junction structure is first converted to an associated gyrobondgraph form. That form is then abstracted into an associated gyrograph. Based on the gyrograph representation and the graph matching concept, an algorithm for determining the existence, the E-minimum and the E-maximum of basis order for a general junction structure is presented. The results should find applications in the effective solution of R-field, C-field, and I-field problems.