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.
Highlights
CONTRIBUTIONS In this paper we propose an object-oriented library of the fundamental components for modeling and simulating multiphysics systems, rooted in the formal definitions of Dirac structures and port-Hamiltonian systems
For this purpose: i) we have implemented the components of our library with Modelica, a modern, expressive, and powerful object oriented language designed for system modeling; ii) we have founded such implementation on the concepts of Dirac structures and port-Hamiltonian systems, both of them formalized in terms of differential geometry; iii) to represent the fundamental components, we propose new symbols derived from the ones used in bond graphs, which are more expressive and make it easier to identify the constituent elements of the models
The following propositions formalize that the Dirac structures and the port-Hamiltonian systems meet a fundamental requirement for constructing complex system by interconnecting simpler ones: the composition of Dirac structures leads to another Dirac structure and, likewise, the interconnection of port-Hamiltonian systems provides again a port-Hamiltonian system
Summary
In the electrical engineering field; ii) Hamiltonian modeling, rooted in analytical mechanics; and iii) object oriented modeling of physical systems, an approach initiated in the late 1980s [4] For this purpose: i) we have implemented the components of our library with Modelica, a modern, expressive, and powerful object oriented language designed for system modeling; ii) we have founded such implementation on the concepts of Dirac structures and port-Hamiltonian systems, both of them formalized in terms of differential geometry; iii) to represent the fundamental components, we propose new symbols derived from the ones used in bond graphs (so that they remain recognizable by bond graph modelers), which are more expressive and make it easier to identify the constituent elements of the models.
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