Bond graph model and Port-Hamiltonian formulation of an enzymatic reaction in a CSTR

Authors

Abstract

This paper proposes a chemical Port-Hamiltonian formulation of a well-mixed CSTR model considering that the chemical reaction is taking place at constant pressure and temperature. More focus is put on chemical reaction network theory and its inclusion in the formulation to achieve synchronization between concentration space and reaction space. It is made clear that Gibbs free energy is an apt Hamiltonian function for such cases. The same concept is applied on a basic enzyme reaction. The Bond Graph models related to Hamiltonian formulation for both types of reactions are given in order to show its ability of pictorial representation and intuitive solution.

Citation

Journal: 2nd International Conference on Systems and Computer Science
Year: 2013
Volume:
Issue:
Pages: 68–73
Publisher: IEEE
DOI: 10.1109/icconscs.2013.6632025

BibTeX

@inproceedings{Makka_2013,
  title={{Bond graph model and Port-Hamiltonian formulation of an enzymatic reaction in a CSTR}},
  DOI={10.1109/icconscs.2013.6632025},
  booktitle={{2nd International Conference on Systems and Computer Science}},
  publisher={IEEE},
  author={Makka, Mohit and Dieulot, Jean-Yves},
  year={2013},
  pages={68--73}
}

Download the bib file

References

ould bouamama, Procds thermodynamiques et chimiques. Les Bond Graphs (2000)
Oster, G. & Perelson, A. Chemical reaction networks. IEEE Trans. Circuits Syst. 21, 709–721 (1974) – 10.1109/tcs.1974.1083946
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
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
Oster, G. F. & Perelson, A. S. Chemical reaction dynamics. Arch. Rational Mech. Anal. 55, 230–274 (1974) – 10.1007/bf00281751
ortega, Passivity-based control of euler-lagrange systems. Mechanical Electrical and Electromechanical Applications (1998)
Putting energy back in control. IEEE Control Syst. 21, 18–33 (2001) – 10.1109/37.915398
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. & Spong, M. W. Adaptive motion control of rigid robots: A tutorial. Automatica 25, 877–888 (1989) – 10.1016/0005-1098(89)90054-x
Perelson, A. S. & Oster, G. F. Chemical reaction dynamics part II: Reaction networks. Arch. Rational Mech. Anal. 57, 31–98 (1974) – 10.1007/bf00287096
Ould-Bouamama, B., El Harabi, R., Abdelkrim, M. N. & Ben Gayed, M. K. Bond graphs for the diagnosis of chemical processes. Computers & Chemical Engineering 36, 301–324 (2012) – 10.1016/j.compchemeng.2011.07.008
Perelson, A. S. Network thermodynamics. An overview. Biophysical Journal 15, 667–685 (1975) – 10.1016/s0006-3495(75)85847-4
Ramirez, H., Maschke, B. & Sbarbaro, D. On the Hamiltonian formulation of the CSTR. 49th IEEE Conference on Decision and Control (CDC) 3301–3306 (2010) doi:10.1109/cdc.2010.5717317 – 10.1109/cdc.2010.5717317
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
Roman, M., Selisteanu, D., Bobasu, E., Petre, E. & Sendrescu, D. Bond graph modelling of a wastewater biodegradation bioprocess. 2009 IEEE International Conference on Automation and Logistics 1501–1506 (2009) doi:10.1109/ical.2009.5262736 – 10.1109/ical.2009.5262736
Thomaseth, K. Multidisciplinary modelling of biomedical systems. Computer Methods and Programs in Biomedicine 71, 189–201 (2003) – 10.1016/s0169-2607(02)00095-0
van der Schaft, A. & Maschke, B. A Port-Hamiltonian Formulation of Open Chemical Reaction Networks. Lecture Notes in Control and Information Sciences 339–348 (2010) doi:10.1007/978-3-642-16135-3_27 – 10.1007/978-3-642-16135-3_27
zhang, Bond graph modeling of an integrated biological wastewater treatment system. Proceedings of the American Inst of Chemical Eng Annual Meeting Session Advanced Comp and Numerical Models in Water Technology and Resource Management-II (2006)
zwart, The Port-Hamiltonian Approach to Physical System Modeling and Control (2008)
Delgado, M. & Pichardo, C. Use of MATLAB and 20-sim to simulate a flash separator. Simulation Practice and Theory 7, 515–530 (1999) – 10.1016/s0928-4869(99)00016-6
brown, Bond graph modeling and simulation of thermodynamic systems. Plenary Session ICBGM Conference (2007)
karnopp, System Dynamics A Unified Approach (1975)
bailey, Biochemical Engineering Fundamentals (1986)
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
Hangos, K. M., Bokor, J. & Szederkényi, G. Hamiltonian view on process systems. AIChE Journal 47, 1819–1831 (2001) – 10.1002/aic.690470813
Favache, A., Dochain, D. & Maschke, B. A geometric perspective to open irreversible thermodynamic systems: GENERIC, Matrix and port-contact systems. Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference 8387–8392 (2009) doi:10.1109/cdc.2009.5399977 – 10.1109/cdc.2009.5399977
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
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
hoang, From brayton-moser formulation to port-hamiltonian representation: The CSTR case study. 18th World Congress of the International Federation of Automatic Control (2012)