Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR

Authors

Hector Ramirez, Bernhard Maschke, Daniel Sbarbaro

Abstract

In this paper we suggest a class of quasi-port-Hamiltonian systems called Irreversible port-Hamiltonian Systems, that expresses simultaneously the first and second principle of thermodynamics as a structural property. These quasi-port-Hamiltonian systems are defined with respect to a structure matrix and a modulating function which depends on the thermodynamic relation between state and co-state variables of the system. This modulating function itself is the product of some positive function γ and the Poisson bracket of the entropy and the energy function. This construction guarantees that the Hamiltonian function is a conserved quantity and simultaneously that the entropy function satisfies a balance equation containing an irreversible entropy creation term. In the second part of the paper, we suggest a lift of the Irreversible Port-Hamiltonian Systems to control contact systems defined on the Thermodynamic Phase Space which is canonically endowed with a contact structure associated with Gibbs’ relation. For this class of systems we have suggested a lift which avoids any singularity of the contact Hamiltonian function and defines a control contact system on the complete Thermodynamic Phase Space, in contrast to the previously suggested lifts of such systems. Finally we derive the formulation of the balance equations of a CSTR model as an Irreversible Port-Hamiltonian System and give two alternative lifts of the CSTR model to a control contact system defined on the complete Thermodynamic Phase Space.

Keywords

Irreversible thermodynamics; Entropy; Port-Hamiltonian system; Contact structure; System theory; Chemical reactor

Citation

• Journal: Chemical Engineering Science
• Year: 2013
• Volume: 89
• Issue:
• Pages: 223–234
• Publisher: Elsevier BV
• DOI: 10.1016/j.ces.2012.12.002

BibTeX

@article{Ramirez_2013,
  title={{Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR}},
  volume={89},
  ISSN={0009-2509},
  DOI={10.1016/j.ces.2012.12.002},
  journal={Chemical Engineering Science},
  publisher={Elsevier BV},
  author={Ramirez, Hector and Maschke, Bernhard and Sbarbaro, Daniel},
  year={2013},
  pages={223--234}
}

Download the bib file

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