Hierarchical Non-Linear Bond Graphs: A Unified Methodology for Modeling Complex Physical Systems

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Abstract

Bond graphs have been around for a quarter of a century. While originally intended for modeling mechanical systems, they have meanwhile found widespread applications in many areas of physical system modeling. Bond graphs are a very appealing tool for modeling physical systems, because they represent the flow of power through a system. Since energy and mass are the only tradable goods in our physical universe, a bond graph model is more likely to reflect physical reality than a model derived by use of any other modeling methodology. However, bond graphs, like all graphical techniques, become unwieldy when applied to complex systems. Also, bond graphs were traditionally used to model predominantly linear systems. This paper introduces new concepts for modeling complex physical systems through hierarchical bond graphs which can include arbitrary non-linearities. It introduces a software tool that can be used to implement these hierarchical non--linear bond graphs. Finally, a new application area for bond graphs will be discussed. It will be demonstrated how these hierarchical non-linear bond graphs can be used to model chemical reaction kinetics and chemical thermodynamics together in very general terms also farther away from equilibrium than traditional approaches would permit.

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Last modified: June 7, 2005 -- © François Cellier