On the Port-Hamiltonian Models of some Electrochemical Processes
Authors
Abstract
Electrochemical processes play an important role in many natural and technological processes; such as, mineral refining, water purification, energy storage and generation. The port-Hamiltonian framework has been widely used for modeling and control design of mechanical and electro-mechanical systems. It has demonstrated to be an important tool to analyze and integrate models of different domains. This work discusses the modeling of isothermal electrochemical processes as port-Hamiltonian systems. Port-Hamiltonian models based on the Gibbs energy function are derived for two examples. They illustrate the main steps to obtain a port-Hamiltonian representation from molar and charge balance equations. Further work will consider non isothermal reactions and the analysis of system considering also diffusion phenomena.
Keywords
Electrochemical reactions; port Hamiltonian; Modeling
Citation
- Journal: IFAC-PapersOnLine
- Year: 2018
- Volume: 51
- Issue: 3
- Pages: 38–43
- Publisher: Elsevier BV
- DOI: 10.1016/j.ifacol.2018.06.010
- Note: 6th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2018
BibTeX
@article{Sbarbaro_2018,
title={{On the Port-Hamiltonian Models of some Electrochemical Processes}},
volume={51},
ISSN={2405-8963},
DOI={10.1016/j.ifacol.2018.06.010},
number={3},
journal={IFAC-PapersOnLine},
publisher={Elsevier BV},
author={Sbarbaro, Daniel},
year={2018},
pages={38--43}
}
References
- Auslander, D. M., Oster, G. F., Perelson, A. & Clifford, G. On Systems With Coupled Chemical Reaction and Diffusion. Journal of Dynamic Systems, Measurement, and Control vol. 94 239–248 (1972) – 10.1115/1.3426594
- 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
- Couenne, F., Jallut, C., Maschke, B., Tayakout, M. & Breedveld, P. Bond graph for dynamic modelling in chemical engineering. Chemical Engineering and Processing: Process Intensification vol. 47 1994–2003 (2008) – 10.1016/j.cep.2007.09.006
- Donaire, A. & Junco, S. Energy shaping, interconnection and damping assignment, and integral control in the bond graph domain. Simulation Modelling Practice and Theory vol. 17 152–174 (2009) – 10.1016/j.simpat.2008.02.012
- Donaire, A. & Junco, S. Derivation of Input-State-Output Port-Hamiltonian Systems from bond graphs. Simulation Modelling Practice and Theory vol. 17 137–151 (2009) – 10.1016/j.simpat.2008.02.007
- Duindam, (2009)
- García-Sandoval, J. P., Hudon, N. & Dochain, D. Generalized Hamiltonian representation of thermo-mechanical systems based on an entropic formulation. Journal of Process Control vol. 51 18–26 (2017) – 10.1016/j.jprocont.2016.09.011
- Golo, Hamiltonian formulation of bond graphs. in A. Rantzer R.. (2003)
- Hjelmfelt, A., Schreiber, I. & Ross, J. Efficiency of power production in simple nonlinear electrochemical systems. The Journal of Physical Chemistry vol. 95 6048–6053 (1991) – 10.1021/j100168a062
- Hoang, N. H. & Dochain, D. On an evolution criterion of homogeneous multi-component mixtures with chemical transformation. Systems & Control Letters vol. 62 170–177 (2013) – 10.1016/j.sysconle.2012.11.013
- Hoang, N. H., Dochain, D., Couenne, F. & Le Gorrec, Y. Dissipative pseudo-Hamiltonian realization of chemical systems using irreversible thermodynamics. Mathematical and Computer Modelling of Dynamical Systems vol. 23 135–155 (2016) – 10.1080/13873954.2016.1237973
- 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 vol. 21 1449–1458 (2011) – 10.1016/j.jprocont.2011.06.014
- Karnopp, D. Bond graph models for electrochemical energy storage : electrical, chemical and thermal effects. Journal of the Franklin Institute vol. 327 983–992 (1990) – 10.1016/0016-0032(90)90073-r
- Kondepudi, (1999)
- Oster, G. F., Perelson, A. S. & Katchalsky, A. Network thermodynamics: dynamic modelling of biophysical systems. Quarterly Reviews of Biophysics vol. 6 1–134 (1973) – 10.1017/s0033583500000081
- Ramirez, H., Maschke, B. & Sbarbaro, D. Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR. Chemical Engineering Science vol. 89 223–234 (2013) – 10.1016/j.ces.2012.12.002
- Shiner, J. S. Algebraic symmetry in chemical reaction systems at stationary states arbitrarily far from thermodynamic equilibrium. The Journal of Chemical Physics vol. 87 1089–1094 (1987) – 10.1063/1.453341
- Shiner, (1996)
- Tofighi, A. & Kalantar, M. Passivity-based control of PEM fuel cell/battery hybrid power source. 2011 IEEE Energy Conversion Congress and Exposition 902–908 (2011) doi:10.1109/ecce.2011.6063867 – 10.1109/ecce.2011.6063867
- van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
- van der Schaft, A., Rao, S. & Jayawardhana, B. On the Mathematical Structure of Balanced Chemical Reaction Networks Governed by Mass Action Kinetics. SIAM Journal on Applied Mathematics vol. 73 953–973 (2013) – 10.1137/11085431x
- van der Schaft, (2011)
- Zárate-Navarro, M. A., García-Sandoval, J. P., Dochain, D. & Hudon, N. Effect of mesoscopic conservative phenomena in the dynamics of chemical reactions at the macroscopic scale. Physica A: Statistical Mechanics and its Applications vol. 486 79–91 (2017) – 10.1016/j.physa.2017.05.029