Boundary controlled irreversible port-Hamiltonian systems

TL;DR

This paper extends boundary controlled port-Hamiltonian systems to irreversible thermodynamic systems, incorporating dissipation and ensuring passivity and thermodynamic principles are structurally satisfied.

Contribution

It introduces boundary controlled irreversible port-Hamiltonian systems (BC-IPHS) with a new boundary port variable framework for dissipative systems.

Findings

BC-IPHS are passive with respect to conjugated inputs and outputs.

The structure satisfies the first and second thermodynamic principles.

Several illustrative examples demonstrate the approach.

Abstract

Boundary controlled irreversible port-Hamiltonian systems (BC-IPHS) on 1-dimensional spatial domains are defined by extending the formulation of reversible BC-PHS to irreversible thermodynamic systems controlled at the boundaries of their spatial domains. The structure of BC-IPHS has clear physical interpretation, characterizing the coupling between energy storing and energy dissipating elements. By extending the definition of boundary port variables of BC-PHS to deal with the dissipative terms, a set of boundary port variables are defined such that BC-IPHS are passive with respect to a given set of conjugated inputs and outputs. As for finite dimensional IPHS, the first and second principle are satisfied as a structural property. Several examples are given to illustrate the proposed approach.