On the relaxing dissipation of dissipative pseudo Hamiltonian models

Authors

N. Ha Hoang, T. Phong Mai, Denis Dochain

Abstract

This paper further explores the link between irreversible thermodynamics and system theory, and its use for port-based modeling for reaction systems. More specifically we show here that a pseudo Hamiltonian representation with R(x) > 0 can be obtained by considering the Brayton-Moser formulation via a unified potential function that verifies a thermodynamic evolution criterion. As a consequence, it gives additional degrees of freedom (i.e. to construct alternate pseudo Hamiltonian models with new passive outputs) usable for further studies on the control design. A representative example of irreversible processes via the non isothermal continuous stirred tank reactor model is used to illustrate the theoretical developments.

Keywords

Port controlled Hamiltonian systems; Brayton-Moser formulation; CSTR

Citation

• Journal: IFAC-PapersOnLine
• Year: 2015
• Volume: 48
• Issue: 8
• Pages: 1051–1056
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2015.09.107
• Note: 9th IFAC Symposium on Advanced Control of Chemical Processes ADCHEM 2015- Whistler, Canada, 7–10 June 7 – 10, 2015

BibTeX

@article{Hoang_2015,
  title={{On the relaxing dissipation of dissipative pseudo Hamiltonian models}},
  volume={48},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2015.09.107},
  number={8},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Hoang, N. Ha and Mai, T. Phong and Dochain, Denis},
  year={2015},
  pages={1051--1056}
}

Download the bib file

References

• Antonelli, R. & Astolfi, A. Continuous stirred tank reactors: easy to stabilise? Automatica 39, 1817–1827 (2003) – 10.1016/s0005-1098(03)00177-8
• 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)
• Dammers, W. R. & Tels, M. Thermodynamic stability and entropy production in adiabatic stirred flow reactors. Chemical Engineering Science 29, 83–90 (1974) – 10.1016/0009-2509(74)85033-5
• 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, 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. & Winkin, J. J. Power-shaping control: Writing the system dynamics into the Brayton–Moser form. Systems & Control Letters 60, 618–624 (2011) – 10.1016/j.sysconle.2011.04.021
• García-Canseco, E., Jeltsema, D., Ortega, R. & Scherpen, J. M. A. Power-based control of physical systems. Automatica 46, 127–132 (2010) – 10.1016/j.automatica.2009.10.012
• Haddad, (2005)
• Hangos, K. M., Bokor, J. & Szederkényi, G. Hamiltonian view on process systems. AIChE Journal 47, 1819–1831 (2001) – 10.1002/aic.690470813
• Hoang, H., Couenne, F., Jallut, C. & Le Gorrec, Y. The port Hamiltonian approach to modeling and control of Continuous Stirred Tank Reactors. Journal of Process Control 21, 1449–1458 (2011) – 10.1016/j.jprocont.2011.06.014
• Hoang, H., Couenne, F., Dochain, D. & Le Gorrec, Y. From Brayton-Moser formulation to Port Hamiltonian representation: the CSTR case study. IFAC Proceedings Volumes 44, 1628–1633 (2011) – 10.3182/20110828-6-it-1002.02464
• Hoang, H., Couenne, F., Jallut, C. & Le Gorrec, Y. Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamics. Journal of Process Control 22, 412–422 (2012) – 10.1016/j.jprocont.2011.12.007
• Hoang, N. H. & Dochain, D. On an evolution criterion of homogeneous multi-component mixtures with chemical transformation. Systems & Control Letters 62, 170–177 (2013) – 10.1016/j.sysconle.2012.11.013
• Hudon, N., Hoffner, K. & Guay, M. Equivalence to dissipative Hamiltonian realization. 2008 47th IEEE Conference on Decision and Control 3163–3168 (2008) doi:10.1109/cdc.2008.4739446 – 10.1109/cdc.2008.4739446
• Khalil, (2002)
• Maschke, B., Ortega, R. & Van Der Schaft, A. J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Trans. Automat. Contr. 45, 1498–1502 (2000) – 10.1109/9.871758
• 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
• Ortega, R., Jeltsema, D. & Scherpen, J. M. A. Power shaping: A new paradigm for stabilization of nonlinear RLC circuits. IEEE Trans. Automat. Contr. 48, 1762–1767 (2003) – 10.1109/tac.2003.817918
• Ortega, R., van der Schaft, A., Castanos, F. & Astolfi, A. Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Trans. Automat. Contr. 53, 2527–2542 (2008) – 10.1109/tac.2008.2006930
• 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
• Ramirez, H., Maschke, B. & Sbarbaro, D. Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR. Chemical Engineering Science 89, 223–234 (2013) – 10.1016/j.ces.2012.12.002
• 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
• 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
• Van Der Schaft, Port-controlled Hamiltonian systems: Towards a theory for control and design of nonlinear physical systems. J. Soc. Instr. Control Eng. Japan (2000)
• Van Der Schaft, (2000)
• Warden, An analysis of chemical reactor stability and control - VIII. The direct method of Lyapunov. Introduction and applications to simple reactions in stirred vessels. Chem. Eng. Sci. (1964)
• Willems, (1970)
• Willems, Dissipative dynamical systems. Part I: General theory. Arch. Rat. Mech. and Analysis (1972)
• Xu, S. J., Darouach, M. & Schaefers, J. Expansion of det(A+B) and robustness analysis of uncertain state space systems. IEEE Trans. Automat. Contr. 38, 1671–1675 (1993) – 10.1109/9.262036
• 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