An irreversible port-Hamiltonian formulation of distributed diffusion processes

Authors

Hector Ramirez, Yann Le Gorrec

Abstract

An infinite dimensional formulation of IPHS is proposed for a general class of mass and heat diffusion processes. The structure of the system is derived from the expression of the internal entropy creation, and just as for the lumped case the IPHS structure is expressed as a function of the distributed thermodynamic driving forces and a positive definite function containing the thermodynamic parameters of the different diffusion processes. The distributed thermodynamic driving forces are expressed as the evaluation of the internal energy density and entropy density on a pseudo-Poisson bracket defined by the skew-adjoint differential operator defining the coupling between the different energy domains. This is analogous to the case of lumped IPHS, where the pseudo-Poisson bracket is defined not by differential operators but by constant (canonical) skew-symmetric matrices.

Keywords

Port-Hamiltonian systems; irreversible thermodynamics; infinite dimensional systems

Citation

• Journal: IFAC-PapersOnLine
• Year: 2016
• Volume: 49
• Issue: 24
• Pages: 46–51
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2016.10.752
• Note: 2th IFAC Workshop on Thermodynamic Foundations for a Mathematical Systems Theory TFMST 2016- Vigo, Spain, 28—30 September 2016

BibTeX

@article{Ramirez_2016,
  title={{An irreversible port-Hamiltonian formulation of distributed diffusion processes}},
  volume={49},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2016.10.752},
  number={24},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Ramirez, Hector and Gorrec, Yann Le},
  year={2016},
  pages={46--51}
}

Download the bib file

References

• Alonso, A. A. & Ydstie, B. E. Stabilization of distributed systems using irreversible thermodynamics. Automatica vol. 37 1739–1755 (2001) – 10.1016/s0005-1098(01)00140-6
• Alonso, A. A., Ydstie, B. E. & Banga, J. R. From irreversible thermodynamics to a robust control theory for distributed process systems. Journal of Process Control vol. 12 507–517 (2002) – 10.1016/s0959-1524(01)00017-8
• Duindam, (2009)
• Eberard, D., Maschke, B. M. & van der Schaft, A. J. An extension of Hamiltonian systems to the thermodynamic phase space: Towards a geometry of nonreversible processes. Reports on Mathematical Physics vol. 60 175–198 (2007) – 10.1016/s0034-4877(07)00024-9
• Grmela, M. & Öttinger, H. C. Dynamics and thermodynamics of complex fluids.  I. Development of a general formalism. Physical Review E vol. 56 6620–6632 (1997) – 10.1103/physreve.56.6620
• Hermann, (1973)
• Keenan, J. H. Availability and irreversibility in thermodynamics. British Journal of Applied Physics vol. 2 183–192 (1951) – 10.1088/0508-3443/2/7/302
• Kondepudi, (1998)
• Maschke, B. M., Van Der Schaft, A. J. & Breedveld, P. C. An intrinsic hamiltonian formulation of network dynamics: non-standard poisson structures and gyrators. Journal of the Franklin Institute vol. 329 923–966 (1992) – 10.1016/s0016-0032(92)90049-m
• Mrugała, R. Continuous contact transformations in thermodynamics. Reports on Mathematical Physics vol. 33 149–154 (1993) – 10.1016/0034-4877(93)90050-o
• Mrugala, R., Nulton, J. D., Christian Schön, J. & Salamon, P. Contact structure in thermodynamic theory. Reports on Mathematical Physics vol. 29 109–121 (1991) – 10.1016/0034-4877(91)90017-h
• Öttinger, H. C. & Grmela, M. Dynamics and thermodynamics of complex fluids.  II. Illustrations of a general formalism. Physical Review E vol. 56 6633–6655 (1997) – 10.1103/physreve.56.6633
• Ramirez, H., Maschke, B. & Sbarbaro, D. Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR. Chemical Engineering Science vol. 89 223–234 (2013) – 10.1016/j.ces.2012.12.002
• Ramirez, H., Maschke, B. & Sbarbaro, D. Modelling and control of multi-energy systems: An irreversible port-Hamiltonian approach. European Journal of Control vol. 19 513–520 (2013) – 10.1016/j.ejcon.2013.09.009
• Ramirez, (2014)
• Ramírez, H., Le Gorrec, Y., Maschke, B. & Couenne, F. On the passivity based control of irreversible processes: A port-Hamiltonian approach. Automatica vol. 64 105–111 (2016) – 10.1016/j.automatica.2015.07.002
• Willems, J. C. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis vol. 45 321–351 (1972) – 10.1007/bf00276493