Port-Based Modeling of Dynamic Systems in Terms of Bond Graphs

Port-based modeling of dynamic systems is the topic of the first chapter of the book that will be one of the main results of the European project ‘Geometric Network Modeling and Control of Complex Physical Systems’ (GEOPLEX, IST-2001-34166, Key Action, Action line KAIV: Essential Technologies and Infrastructures, Action Line IV.4.2.1). In this chapter the reader is introduced to the concepts needed for port-based modeling, design and reasoning in order to prepare and motivate for the geometrical formulations of the port-based approach in the remainder of the book. After some general remarks about the modeling process, this is done from a historic perspective, which immediately relates the port concept to its original notation, the bond graph. Bond graph notation is discussed as well as the concept of causality, which allows one to combine physical and computational structure into one notation and provides important feedback on modeling decisions in the tradeoff between conceptual and computational complexity. Several simple examples of its use are presented and the details of many bond graph related transformations and analysis techniques are discussed in a series of appendices: conversion of an IPM into a bond graph, conversion of causal bond graphs into block diagrams, generation of a set of mixed algebraic and differential equations, direct linear analysis, impedance analysis using bond graphs, nonlinear mechanical systems (mechanisms), homogeneous functions and Euler’s theorem, homogeneous energy functions, Legendre transformations, co-energy functions, relations for co-energy functions, Legendre transforms in simple thermodynamics, Legendre transforms and causality, Maxwell reciprocity of constitutive relations.\ud \ud As it is impossible to fit all this material in this short contribution, two examples of the content are given that are more or less self-supporting/independent, viz. the Glossary, which provides a kind of bird’s eye view of the material, and the first Appendix that discusses basic model transformations. However, first the most important basis for the work on port-Hamiltonian systems, viz. the generalization of the bond graph representation into generalized bond graphs, is discussed shortly first.\u