The port Hamiltonian approach to modeling and control of Continuous Stirred Tank Reactors

Authors

H. Hoang, F. Couenne, C. Jallut, Y. Le Gorrec

Abstract

Abstract This paper proposes a thermodynamical pseudo-Hamiltonian formulation of Continuous Stirred Tank Reactor model in which takes place some chemical reaction. This is done both in the isothermal and non isothermal cases. It is shown that the Gibbs free energy and the opposite of entropy can be chosen as Hamiltonian function respectively. For the non isothermal case, the so-called Interconnection and Damping Assignment Passivity Based Control method is applied to stabilize the system at a desired state. For this general reaction scheme, the control problem is shown to be easy to solve as soon as the closed loop Hamiltonian function is chosen to be proportional to the so-called thermodynamic availability function. Simulation results based on a simple first order reaction and operating conditions leading to multiple steady states of the CSTR are given to validate the proposed control design procedure.

Keywords

Port Hamiltonian systems; Lyapunov stability; Thermodynamics; IDA-PBC control; Chemical reactors

Citation

Journal: Journal of Process Control
Year: 2011
Volume: 21
Issue: 10
Pages: 1449–1458
Publisher: Elsevier BV
DOI: 10.1016/j.jprocont.2011.06.014
Note: Special Issue:Selected Papers From Two Joint IFAC Conferences: 9th International Symposium on Dynamics and Control of Process Systems and the 11th International Symposium on Computer Applications in Biotechnology, Leuven, Belgium, July 5-9, 2010.

BibTeX

@article{Hoang_2011,
  title={{The port Hamiltonian approach to modeling and control of Continuous Stirred Tank Reactors}},
  volume={21},
  ISSN={0959-1524},
  DOI={10.1016/j.jprocont.2011.06.014},
  number={10},
  journal={Journal of Process Control},
  publisher={Elsevier BV},
  author={Hoang, H. and Couenne, F. and Jallut, C. and Le Gorrec, Y.},
  year={2011},
  pages={1449--1458}
}

Download the bib file

References

Alonso, A. A. & Erik Ydstie, B. Process systems, passivity and the second law of thermodynamics. Computers & Chemical Engineering vol. 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 vol. 37 1739–1755 (2001) – 10.1016/s0005-1098(01)00140-6
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 vol. 12 159–174 (2006) – 10.1080/13873950500068823
Dörfler, F., Johnsen, J. K. & Allgöwer, F. An introduction to interconnection and damping assignment passivity-based control in process engineering. Journal of Process Control vol. 19 1413–1426 (2009) – 10.1016/j.jprocont.2009.07.015
Eberard, Port contact systems for irreversible thermodynamical systems. (2005)
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
Favache, Power-shaping control of an exothermic continuous stirred tank reactor (CSTR). (2009)
Favache, A. & Dochain, D. Thermodynamics and chemical systems stability: The CSTR case study revisited. Journal of Process Control vol. 19 371–379 (2009) – 10.1016/j.jprocont.2008.07.007
Glansdorff, (1971)
de Groot, (1962)
Hangos, K. M., Alonso, A. A., Perkins, J. D. & Ydstie, B. E. Thermodynamic approach to the structural stability of process plants. AIChE Journal vol. 45 802–816 (1999) – 10.1002/aic.690450414
Hangos, K. M., Bokor, J. & Szederkényi, G. Hamiltonian view on process systems. AIChE Journal vol. 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 reactor. (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 vol. 17 399–413 (2007) – 10.1016/j.jprocont.2006.12.006
McLachlan, R. I., Quispel, G. R. W. & Robidoux, N. Unified Approach to Hamiltonian Systems, Poisson Systems, Gradient Systems, and Systems with Lyapunov Functions or First Integrals. Physical Review Letters vol. 81 2399–2403 (1998) – 10.1103/physrevlett.81.2399
Maschke, B., Ortega, R. & Van Der Schaft, A. J. Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation. IEEE Transactions on Automatic Control vol. 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 vol. 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 vol. 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 vol. 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 vol. 51 3147–3166 (2005) – 10.1002/aic.10543
van der Schaft, Port-controlled Hamiltonian systems: towards a theory for control and design of nonlinear physical systems. SICE Journal (2000)
van der Schaft, (2000)
Wang, Y., Li, C. & Cheng, D. Generalized Hamiltonian realization of time-invariant nonlinear systems. Automatica vol. 39 1437–1443 (2003) – 10.1016/s0005-1098(03)00132-8
Ydstie, B. E. & Alonso, A. A. Process systems and passivity via the Clausius-Planck inequality. Systems & Control Letters vol. 30 253–264 (1997) – 10.1016/s0167-6911(97)00023-6