Port-Hamiltonian Modeling of Multiphysics Systems and Object-Oriented Implementation With the Modelica Language

Abstract

In this article we present the implementation in Modelica language of a library with the fundamental components for modeling a wide variety of multiphysics systems. Modelica is an object-oriented modeling language, which allows to make a simple, systematic and elegant design of the library. The mechanisms of inheritance and composition of Modelica facilitate the modeling and reuse of components in different domains of Physics. To model the behavior of each component in a systematic framework we have used the theory of port-Hamiltonian systems, formulated mainly by means of differential geometry. The port-Hamiltonian approach allows a methodical definition of complex systems by connecting simple systems that exchange energy through connection ports. To graphically represent the components of a system and their connections, we have employed slightly modified bond graphs symbols for easier reading. The general and systematic applicability of the library is illustrated via two examples framed in different domains of Physics: the mechanical Sun-Earth-Moon system where we perform an analysis of errors that justifies the employed system of units, and the electrical nonlinear Chua circuit, modeled by composition of port-Hamiltonian subsystems. Both derived models have been built and simulated based on the more general models of mechanical and electrical systems, which are also part of the library developed with the port-Hamiltonian approach.

Keywords

• Bond graphs
• Dirac structures
• Modelica language
• multiphysics systems
• object oriented modeling
• port-Hamiltonian systems