From Brayton-Moser formulation to Port Hamiltonian representation: the CSTR case study

Authors

H. Hoang, F. Couenne, D. Dochain, Y. Le Gorrec

Abstract

This paper shows that any thermodynamic potential fulfilling some thermodynamic stability criterion (e.g. the chemical affinity or the ectropy) can be used as a potential function for the dissipative (pseudo) Port Hamiltonian formulation of the non isothermal Continuous Stirred Tank Reactor (CSTR) model. Besides Brayton-Moser formulation is used to obtain some dissipative Port Hamiltonian representation.

Keywords

Irreversible thermodynamics; CSTR; Port Hamiltonian systems; Brayton-Moser formulation; Passivity

Citation

• Journal: IFAC Proceedings Volumes
• Year: 2011
• Volume: 44
• Issue: 1
• Pages: 1628–1633
• Publisher: Elsevier BV
• DOI: 10.3182/20110828-6-it-1002.02464
• Note: 18th IFAC World Congress

BibTeX

@article{Hoang_2011,
  title={{From Brayton-Moser formulation to Port Hamiltonian representation: the CSTR case study}},
  volume={44},
  ISSN={1474-6670},
  DOI={10.3182/20110828-6-it-1002.02464},
  number={1},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Hoang, H. and Couenne, F. and Dochain, D. and Le Gorrec, Y.},
  year={2011},
  pages={1628--1633}
}

Download the bib file

References

• Alonso, A. A. & Erik Ydstie, B. Process systems, passivity and the second law of thermodynamics. Computers & Chemical Engineering 20, S1119–S1124 (1996) – 10.1016/0098-1354(96)00194-9
• Alonso, A. A. & Ydstie, B. E. Stabilization of distributed systems using irreversible thermodynamics. Automatica 37, 1739–1755 (2001) – 10.1016/s0005-1098(01)00140-6
• Bao, (2007)
• Brayton, R. K. & Moser, J. K. A theory of nonlinear networks. I. Quart. Appl. Math. 22, 1–33 (1964) – 10.1090/qam/169746
• Brogliato, (2007)
• Callen, (1985)
• Couenne, F., Jallut, C., Maschke, B., Breedveld, P. C. & Tayakout, M. Bond graph modelling for chemical reactors. Mathematical and Computer Modelling of Dynamical Systems 12, 159–174 (2006) – 10.1080/13873950500068823
• De Groot, (1962)
• Dörfler, F., Johnsen, J. K. & Allgöwer, F. An introduction to interconnection and damping assignment passivity-based control in process engineering. Journal of Process Control 19, 1413–1426 (2009) – 10.1016/j.jprocont.2009.07.015
• 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 60, 175–198 (2007) – 10.1016/s0034-4877(07)00024-9
• Favache, Power-shaping control of an exothermic continuous stirred tank reactor (CSTR). (2009)
• 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
• Glansdorff, (1971)
• Hangos, K. M., Bokor, J. & Szederkényi, G. Hamiltonian view on process systems. AIChE Journal 47, 1819–1831 (2001) – 10.1002/aic.690470813
• Hoang, Lyapunov based control for non isothermal continuous stirred tank reactor. (2008)
• Hoang, Thermodynamic approach for Lyapunov based control. (2009)
• Hoang, Hamiltonian formulation and IDA-PBC control of non isothermal continuous stirred tank reactors. (2010)
• Hoang, Port Hamiltonian based modeling and control of exothermic Continuous Stirred Tank Reactors. (2010)
• Hudon, Equivalence to dissipative Hamiltonian realization. (2008)
• Jillson, K. R. & Erik Ydstie, B. Process networks with decentralized inventory and flow control. Journal of Process Control 17, 399–413 (2007) – 10.1016/j.jprocont.2006.12.006
• Maschke, Energy based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE TAC (2000)
• 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
• Otero-Muras, I., Szederkényi, G., Alonso, A. A. & Hangos, K. M. Local dissipative Hamiltonian description of reversible reaction networks. Systems & Control Letters 57, 554–560 (2008) – 10.1016/j.sysconle.2007.12.003
• Ramírez, H., Sbarbaro, D. & Ortega, R. On the control of non-linear processes: An IDA–PBC approach. Journal of Process Control 19, 405–414 (2009) – 10.1016/j.jprocont.2008.06.018
• Ruszkowski, M., Garcia‐Osorio, V. & Ydstie, B. E. Passivity based control of transport reaction systems. AIChE Journal 51, 3147–3166 (2005) – 10.1002/aic.10543
• Sandler, (1999)
• van der Schaft, Port-controlled Hamiltonian systems: towards a theory for control and design of nonlinear physical systems. SICE J (2000)
• van der Schaft, (2000)
• Tarbell, J. M. A thermodynamic Liapunov function for the near equilibrium CSTR. Chemical Engineering Science 32, 1471–1476 (1977) – 10.1016/0009-2509(77)80244-3
• 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