Towards Control by Interconnection of Port-Thermodynamic Systems

TL;DR

This paper explores controlling port-thermodynamic systems through their interconnection, ensuring stability via Lyapunov functions and canonical transformations, advancing the theoretical framework for thermodynamic control systems.

Contribution

It introduces a novel control approach by interconnecting port-thermodynamic systems and analyzes stability using generating functions and symplectized phase space transformations.

Findings

Interconnection preserves port-thermodynamic properties.

Lyapunov functions based on generating functions ensure stability.

Canonical point transformations facilitate analysis of interconnected systems.

Abstract

The power conserving interconnection of port-thermodynamic systems via their power ports results in another port-thermodynamic system, while the same holds for the rate of entropy increasing interconnection via their entropy flow ports. Control by interconnection of port-thermodynamic systems seeks to control a plant port-thermodynamic system by the interconnection with a controller port-thermodynamic system. The stability of the interconnected port-thermodynamic system is investigated by Lyapunov functions based on generating functions for the submanifold characterizing the state properties as well as additional conserved quantities. Crucial tool is the use of canonical point transformations on the symplectized thermodynamic phase space.