Geometric Modeling for Control of Thermodynamic Systems

Area of Science:

• Thermodynamics
• Control Theory
• Mathematical Physics

Background:

• Energy and entropy are fundamental thermodynamic properties.
• Understanding their behavior as storage functions is key to system analysis.
• Irreversible processes introduce complexities in thermodynamic modeling.

Purpose of the Study:

• To conceptualize energy and entropy as storage functions concerning supply rates.
• To explore the link between entropy production factorization and quasi-Hamiltonian formulations.
• To apply these formulations for stability analysis and control of thermodynamic systems.

Main Methods:

• Regarded energy and entropy as storage functions.
• Factorized irreversible entropy production.
• Utilized Liouville geometry and contact geometry.
• Developed port-thermodynamic systems framework.

Main Results:

• Demonstrated quasi-Hamiltonian formulations derived from entropy production factorization.
• Showcased the application of these formulations for stability analysis.
• Defined port-thermodynamic systems using Liouville geometry.
• Enabled control by interconnection of thermodynamic systems.

Conclusions:

• Energy and entropy can be effectively treated as storage functions.
• Quasi-Hamiltonian formulations offer a powerful tool for thermodynamic system analysis and control.
• The port-thermodynamic systems approach facilitates interconnection and control strategies.