Pieter C. Breedveld

Multibond graph elements in physical systems theory

The multibond graph notation turns out to be a natural and concise way to represent the behaviour of energy, power, entropy and other physical properties of macroscopic multiport systems. A global classification of the multiport elements in such a system is made on the basis of this (physical) behaviour in contrast with the usual classification on the basis of the (mathematical) form of the constitutive equations. Special attention is given to junction multiports.

Bond graph modelling for chemical reactors

In this paper we present a bond graph model of a continuous stirred tank reactor which represents the reaction kinetics as well as the heat and mass transport phenomena in the reactor. The consequences of reticulation of the phenomena and of the systematic use of the power conjugated variables on the formulation of the thermodynamic properties, the reaction kinetics and the energy and mass transport are shown. A classical example of chemical reaction is chosen to illustrate this approach: the equilibrated reaction of hydrogen and iodine in hydrogen iodide.

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.

Proposition for an Unambiguous Vector Bond Graph Notation

Notation and definitions of vector bonds and multiport elements are proposed. Multiport element arrays and junction arrays are introduced as well as the direct sum of vector bonds. The usefulness of these concepts is demonstrated by some examples: the lumped representation of distributed parameter systems, the representation of a 3-D mechanical system (coordinate transformations) and of a nonisothermal chemical reaction.

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.

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.

1985 Update of the bond graph bibliography

This bibliography augments and includes the bibliographies of V. D. Gebben, published in the Transactions of the ASME, Journal of Dynamic Systems, Measurement and Control, Vol. 99, No. 2, pp. 143-145, 1977 and in the Journal of the Franklin Institute, Vol. 308, No. 3, pp. 361-369, 1979. The publications are listed alphabetically according to the year in which they have appeared. Although the authors have tried to produce an exhaustive list of bond graph publications, it is most likely that there still are oversights. Since it is our intention to make periodical updates of the bibliography readers are invited to send full bibliographical details of any missing or new bond graph or related publication, to the following address: Twente University of Technology, Department of Electrical Engineering, P.O. Box 217, 7500 AE Enschede, The Netherlands.

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.

Qualitative reasoning about physical systems: an artificial intelligence perspective

Some interdisciplinary issues concerning artificial intelligence (AI) are explored in relation to modelling in physics and engineering. A short survey is given of automated qualitative reasoning about physical systems, which in recent years has become an active research area in AI, and has been partly influenced by system dynamics. The conceptual aspects of the AI approach to physical science are critically assessed, and the mutual relevance of the two disciplines is pointed out. In particular, we indicate how bond graphs can be interpreted as an AI knowledge representation language. On this basis, a knowledge-based approach, called qualitative bond analysis (QuBA), is discussed that exploits bond graphs such that a computational AI system is able to deduce qualitative information about physical systems.

On state-event constructs in physical system dynamics modeling

In this paper it will be shown that a common modeling approach based on extrapolation from standard (textbook) models may lead to the unnecessary use of the state-event construct. Although this may be hand-waved as the result of bad modeling practice, the running example discussed herein has been used for quite some time as a benchmark problem for event handling in the literature [F. Breitenecker, ‘Comparison 7: Constrained pendulum’, Simulation News Europe, No. 7, p. 29, March 1993, ARGESIM, Vienna University of Technology, Vienna, Austria (the benchmark proposed herein was used in several later issues of this journal)]. Unnecessary use of the state-event construct may be prevented by using a model representation that increases insight in the physical meaning of the state variables used in the model and in the way they are handled. Herein the mentioned benchmark problem is analyzed in order to demonstrate the problem and some guidelines are given which may increase this insight.