Control of non-isothermal chemical reaction networks using irreversible port-Hamiltonian systems

Authors

Abstract

In this work irreversible port-Hamiltonian systems are used to derive a passivity based controller which shapes the total energy of a non-isothermal reaction network and renders it asymptotically stable with respect to a desired dynamic equilibrium configuration. The closed-loop system is in IPHS form, hence it can be identified with a desired reaction network and the control parameters are related with thermodynamic variables, such as the reaction rates. A complex reaction network is used to illustrate the approach: the van der Vusse reaction mechanism.

Keywords

Irreversible port-Hamiltonian systems; non-isothermal reaction networks; passivity based control

Citation

Journal: IFAC-PapersOnLine
Year: 2017
Volume: 50
Issue: 1
Pages: 576–581
Publisher: Elsevier BV
DOI: 10.1016/j.ifacol.2017.08.079
Note: 20th IFAC World Congress

BibTeX

@article{Ramirez_2017,
  title={{Control of non-isothermal chemical reaction networks using irreversible port-Hamiltonian systems}},
  volume={50},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2017.08.079},
  number={1},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Ramirez, Hector and Le Gorrec, Yann},
  year={2017},
  pages={576--581}
}

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References

Angeli, D. A Tutorial on Chemical Reaction Network Dynamics. European Journal of Control vol. 15 398–406 (2009) – 10.3166/ejc.15.398-406
ARIS, R. What is Chemical Reactor Analysis? Elementary Chemical Reactor Analysis 1–7 (1989) doi:10.1016/b978-0-409-90221-1.50007-4 – 10.1016/b978-0-409-90221-1.50007-4
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
Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
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
Feinberg, M. Chemical reaction network structure and the stability of complex isothermal reactors—I. The deficiency zero and deficiency one theorems. Chemical Engineering Science vol. 42 2229–2268 (1987) – 10.1016/0009-2509(87)80099-4
Hangos, K. M., Bokor, J. & Szederkényi, G. Hamiltonian view on process systems. AIChE Journal vol. 47 1819–1831 (2001) – 10.1002/aic.690470813
Horn, F. & Jackson, R. General mass action kinetics. Archive for Rational Mechanics and Analysis vol. 47 81–116 (1972) – 10.1007/bf00251225
Niemiec, Nonlinear model-state feedback control for nonminimum-phase processes. Automatica (2003)
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
Oster, G. F. & Perelson, A. S. Chemical reaction dynamics. Archive for Rational Mechanics and Analysis vol. 55 230–274 (1974) – 10.1007/bf00281751
Perelson, A. S. & Oster, G. F. Chemical reaction dynamics part II: Reaction networks. Archive for Rational Mechanics and Analysis vol. 57 31–98 (1974) – 10.1007/bf00287096
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
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
Ramirez, H., Maschke, B. & Sbarbaro, D. Modelling and control of multi-energy systems: An irreversible port-Hamiltonian approach. European Journal of Control vol. 19 513–520 (2013) – 10.1016/j.ejcon.2013.09.009
Ramirez, (2014)
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
Ramírez, H., Le Gorrec, Y., Maschke, B. & Couenne, F. On the passivity based control of irreversible processes: A port-Hamiltonian approach. Automatica vol. 64 105–111 (2016) – 10.1016/j.automatica.2015.07.002
van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
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
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