Essential gyrators and equivalence rules for 3-port function structures

It is shown that a theorem on essential gyrators presented by Rosenberg (1) and used in (2) claims too much and that the internal structure of the multiport elements of the system must be studied in order to be able to decide whether a gyrator is essentially contained in the system or not. Bond graph terminology is used (3)—(6) and a new theorem is formulated, which provides an algorithm to decide on the essentiality of a gyrator by immediate inspection of the bond graph.As a side-result of this approach some new methods for junction structure simplification can be formulated. The significance of junction 3-ports for the concept of the essential gyrator is elaborated by providing equivalence rules for all kinds of junction 3-ports and introducing a unit essential junction 3-port (ES) and a unit non-essential junction 3-port (NES). Finally the hydraulic junction is treated as an example of a physical non-potential junction, i.e. a junction congruent with an ES.     

Thermodynamic Bond Graphs and the Problem of Thermal Inertance

It is shown that an isolated thermal inertance does not obey the second law of thermodynamics. Consequently, such an element should not be used in physical systems theory. To eliminate the structural gap in the thermal domain of current physical systems theory, a new framework is introduced using Bond Graph concepts. These Thermodynamic Bond Graphs are the result of synthesis of methods used in thermodynamics and in mechanics.     

A bond graph algorithm to determine the equilibrium state of a system

An algorithm is presented which enables one to determine the nature of the equilibrium state of a system with constant inputs by direct inspection of its bond graph representation. The algorithm determines whether or not there exists a unique equilibrium state (within a certain region). If not, the system may have no (or infinitely many) equilibrium states in the linear case.     

Decomposition of multiport elements in a revised multibond graph notation

Decomposition rules are derived for multiport-transformers, -resistors, -storage elements and -gyrators into 1- and 2-port elements, junctions and bonds. It appears that it is useful to extend the vectorbond, or rather multibond, notation recently proposed by the author with a “multibond array”. Canonical forms are introduced on the basis of minimal realization, because decompositions of multiport elements are not unique. A new type of coupling factor (“directed coupling factor”) is introduced for multiport-resistors and capacitors.