On the passivity of inventory control in the Port Hamiltonian framework

Authors

null Ngoc-Ha Hoang, null Du Juan, B. Erik Ydstie

Abstract

This paper proposes an extensive connection between passivity based control and inventory control in the Port Hamiltonian framework to stabilize a non-isothermal reactor. This homogeneous multi-reaction system is described by ordinary differential equations with affine inputs. Numerical simulations for the first order reaction system with multiple steady states support the theoretical development. A generalization to chemical reaction networks without specifying reaction kinetics is also presented.

Citation

• Journal: 2013 American Control Conference
• Year: 2013
• Volume:
• Issue:
• Pages: 1639–1644
• Publisher: IEEE
• DOI: 10.1109/acc.2013.6580070

BibTeX

@inproceedings{Ngoc_Ha_Hoang_2013,
  title={{On the passivity of inventory control in the Port Hamiltonian framework}},
  DOI={10.1109/acc.2013.6580070},
  booktitle={{2013 American Control Conference}},
  publisher={IEEE},
  author={Ngoc-Ha Hoang and Du Juan and Ydstie, B. Erik},
  year={2013},
  pages={1639--1644}
}

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References

• khalil, Nonlinear Systems (2002)
• 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
• Brogliato, B., Maschke, B., Lozano, R. & Egeland, O. Dissipative Systems Analysis and Control. Communications and Control Engineering (Springer London, 2007). doi:10.1007/978-1-84628-517-2 – 10.1007/978-1-84628-517-2
• 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
• 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
• 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
• 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
• hoang, Passivity based controller and observer for exothermic chemical reactors. IFAC ADCHEM (2012)
• hoang, Thermodynamics based stabilization of CSTR networks. IEEE-CDC (2012)
• juan, The measurement selection of inventory control. American Control Conference (2010)
• Bruns, D. D. & Bailey, J. E. Process operation near an unstable steady state using nonlinear feedback control. Chemical Engineering Science 30, 755–762 (1975) – 10.1016/0009-2509(75)85103-7
• Ruszkowski, M., Garcia‐Osorio, V. & Ydstie, B. E. Passivity based control of transport reaction systems. AIChE Journal 51, 3147–3166 (2005) – 10.1002/aic.10543
• Antonelli, R. & Astolfi, A. Continuous stirred tank reactors: easy to stabilise? Automatica 39, 1817–1827 (2003) – 10.1016/s0005-1098(03)00177-8
• Jillson, K. R. & Erik Ydstie, B. Process networks with decentralized inventory and flow control. Journal of Process Control 17, 399–413 (2007) – 10.1016/j.jprocont.2006.12.006
• Christofides, P. D. Nonlinear and Robust Control of Parabolic PDE Systems with Time-Dependent Spatial Domains. Systems & Control: Foundations & Applications 123–151 (2001) doi:10.1007/978-1-4612-0185-4_6 – 10.1007/978-1-4612-0185-4_6
• luyben, Process Modeling Simulation and Control for Chemical Engineers (1990)
• ydstie, From thermodynamics to process control. Proc Eng Syst Symp (1994)
• 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
• Farschman, C. A., Viswanath, K. P. & Erik Ydstie, B. Process systems and inventory control. AIChE Journal 44, 1841–1857 (1998) – 10.1002/aic.690440814
• favache, Towards power-shaping control of the CSTR: From thermodynamics to the Brayton-Moser formulation of the dynamics. Proc IFAC DYCOPS6 (2010)
• 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
• Alvarez, J., Alvarez-Ramirez, J., Espinosa-Perez, G. & Schaum, A. Energy shaping plus damping injection control for a class of chemical reactors. Chemical Engineering Science 66, 6280–6286 (2011) – 10.1016/j.ces.2011.09.002
• Viel, F., Jadot, F. & Bastin, G. Global stabilization of exothermic chemical reactors under input constraints. Automatica 33, 1437–1448 (1997) – 10.1016/s0005-1098(97)00071-x
• 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, Thermodynamic Approach for the Stabilization of Chemical Reactors (2009)