Exergetic Port-Hamiltonian Systems Modeling Language

Mathematical modeling of real-world physical systems requires the consistent combination of a multitude of physical laws and phenomenological models. This challenging task can be greatly simplified by hierarchically decomposing systems. Moreover, the use of diagrams for expressing such decompositions helps make the process more intuitive and facilitates communication, even with non-experts. As an important requirement, models have to respect fundamental physical laws such as the first and the second law of thermodynamics. While some existing modeling frameworks can make such guarantees based on structural properties of their models, they lack a formal graphical syntax. We present a compositional and thermodynamically consistent modeling language with a graphical syntax. As its semantics, port-Hamiltonian systems are endowed with further structural properties and a fixed physical interpretation such that thermodynamic consistency is ensured in a way that is closely related to the GENERIC framework. While port-Hamiltonian systems are inspired by graphical modeling with bond graphs, neither the link between the two, nor bond graphs themselves, can be easily formalized. In contrast, our syntax is based on a refinement of the well-studied operad of undirected wiring diagrams. The language effectively decouples the construction of complex models via the graphical syntax from physical concerns, which are dealt with only at the level of primitive subsystems that represent elementary physical behaviors. As a consequence, reuse of models and substitution of their parts becomes possible. Finally, by construction, systems interact by exchanging exergy, i.e. energy that is available for doing work, so the language is particularly well suited for thermodynamic analysis and optimization.