Authors

Hector Ramirez, Yann Le Gorrec, Bernhard Maschke, Françoise Couenne

Abstract

The frameworks of thermodynamic availability function and irreversible port Hamiltonian systems are used to derive passivity based control strategies for irreversible thermodynamic systems. An energy based availability function is defined using as generating function the internal energy. This is a variation with respect to previous works where the total entropy usually corresponds to the generating function. The specific structure of irreversible port-Hamiltonian systems then permits to elegantly derive stability conditions for open and closed thermodynamic systems. The results are illustrated on two classical thermodynamic examples: The heat exchanger and the continuous stirred tank reactor.

Keywords

Irreversible port Hamiltonian systems; Passivity based control; Irreversible thermodynamics; Entropy creation; CSTR

Citation

  • Journal: IFAC Proceedings Volumes
  • Year: 2013
  • Volume: 46
  • Issue: 14
  • Pages: 84–89
  • Publisher: Elsevier BV
  • DOI: 10.3182/20130714-3-fr-4040.00012
  • Note: 1st IFAC Workshop on Thermodynamic Foundations of Mathematical Systems Theory

BibTeX

@article{Ramirez_2013,
  title={{Passivity Based Control of Irreversible Port Hamiltonian Systems}},
  volume={46},
  ISSN={1474-6670},
  DOI={10.3182/20130714-3-fr-4040.00012},
  number={14},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Ramirez, Hector and Gorrec, Yann Le and Maschke, Bernhard and Couenne, Françoise},
  year={2013},
  pages={84--89}
}

Download the bib file

References

  • Aeyels, D. On stabilization by means of the Energy-Casimir method. Systems & Control Letters 18, 325–328 (1992) – 10.1016/0167-6911(92)90021-j
  • Banaszuk, A. & Hauser, J. Approximate Feedback Linearization: A Homotopy Operator Approach. SIAM J. Control Optim. 34, 1533–1554 (1996) – 10.1137/s0363012994261306
  • Birtea, P., Boleantu, M., Puta, M. & Tudoran, R. M. Asymptotic stability for a class of metriplectic systems. Journal of Mathematical Physics 48, (2007) – 10.1063/1.2771420
  • Bloch, A. M. & Marsden, J. E. Stabilization of rigid body dynamics by the Energy-Casimir method. Systems & Control Letters 14, 341–346 (1990) – 10.1016/0167-6911(90)90055-y
  • Callen, (1985)
  • Cheng, D., Shen, T. & Tarn, T. J. Pseudo-Hamiltonian realization and its application. Communications in Information and Systems 2, 91–120 (2002) – 10.4310/cis.2002.v2.n2.a1
  • Cortés, J., van der Schaft, A. & Crouch, P. E. Characterization of Gradient Control Systems. SIAM J. Control Optim. 44, 1192–1214 (2005) – 10.1137/s0363012903425568
  • Edelen, (2005)
  • Favache, A. & Dochain, D. Power-shaping control of reaction systems: The CSTR case. Automatica 46, 1877–1883 (2010) – 10.1016/j.automatica.2010.07.011
  • Favache, A., Dochain, D. & Maschke, B. An entropy-based formulation of irreversible processes based on contact structures. Chemical Engineering Science 65, 5204–5216 (2010) – 10.1016/j.ces.2010.06.019
  • Flanders, (1989)
  • Grmela, M. & Öttinger, H. C. Dynamics and thermodynamics of complex fluids.  I. Development of a general formalism. Phys. Rev. E 56, 6620–6632 (1997) – 10.1103/physreve.56.6620
  • Guay, Representation and control of Brayton–Moser systems using a geometric decomposition. (2012)
  • Guha, P. Metriplectic structure, Leibniz dynamics and dissipative systems. Journal of Mathematical Analysis and Applications 326, 121–136 (2007) – 10.1016/j.jmaa.2006.02.023
  • Hudon, Construction of control Lyapunov functions for damping stabilization of control affine systems. (2009)
  • Hudon, Equivalence to dissipative Hamiltonian realization. (2008)
  • Jurdjevic, V. & Quinn, J. P. Controllability and stability. Journal of Differential Equations 28, 381–389 (1978) – 10.1016/0022-0396(78)90135-3
  • Kaufman, A. N. Dissipative hamiltonian systems: A unifying principle. Physics Letters A 100, 419–422 (1984) – 10.1016/0375-9601(84)90634-0
  • Kiehn, R. M. An extension of Hamilton’s principle to include dissipative systems. Journal of Mathematical Physics 15, 9–13 (1974) – 10.1063/1.1666514
  • Lee, (2006)
  • Malisoff, (2009)
  • Morita, (2001)
  • Morrison, P. J. A paradigm for joined Hamiltonian and dissipative systems. Physica D: Nonlinear Phenomena 18, 410–419 (1986) – 10.1016/0167-2789(86)90209-5
  • Ortega, R., van der Schaft, A., Maschke, B. & Escobar, G. Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38, 585–596 (2002) – 10.1016/s0005-1098(01)00278-3
  • Öttinger, H. C. & Grmela, M. Dynamics and thermodynamics of complex fluids.  II. Illustrations of a general formalism. Phys. Rev. E 56, 6633–6655 (1997) – 10.1103/physreve.56.6633
  • Roels, Sur la décomposition locale d’un champ de vecteurs d’une surface symplectique en un gradient et un champ hamiltonien. C. R. Acad. Sci. Paris Sér. A (1974)
  • van der Schaft, (2000)
  • Mendes, R. V. & Duarte, J. T. Decomposition of vector fields and mixed dynamics. Journal of Mathematical Physics 22, 1420–1422 (1981) – 10.1063/1.525063
  • Warner, (1983)
  • Ydstie, B. E. & Alonso, A. A. Process systems and passivity via the Clausius-Planck inequality. Systems & Control Letters 30, 253–264 (1997) – 10.1016/s0167-6911(97)00023-6