Passivity-based nonlinear control of CSTR via asymptotic observers

Authors

N. Ha Hoang, F. Couenne, Y. Le Gorrec, C.L. Chen, B. Erik Ydstie

Abstract

This work makes use of a passivity-based approach (PBA) and tools from Lyapunov theory to design a nonlinear controller for the asymptotic stabilization of a class of nonisothermal Continuous Stirred Tank Reactors (CSTR) around any desired stationary point. The convergence and stability proofs are derived in the port Hamiltonian framework. Asymptotic observers that do not require knowledge of reaction kinetics are also proposed for a system with incomplete state measurement. Numerical simulations are given to illustrate the application of the theoretical results to a CSTR with multiple steady states.

Citation

• Journal: Annual Reviews in Control
• Year: 2013
• Volume: 37
• Issue: 2
• Pages: 278–288
• Publisher: Elsevier BV
• DOI: 10.1016/j.arcontrol.2013.09.007

BibTeX

@article{Ha_Hoang_2013,
  title={{Passivity-based nonlinear control of CSTR via asymptotic observers}},
  volume={37},
  ISSN={1367-5788},
  DOI={10.1016/j.arcontrol.2013.09.007},
  number={2},
  journal={Annual Reviews in Control},
  publisher={Elsevier BV},
  author={Ha Hoang, N. and Couenne, F. and Le Gorrec, Y. and Chen, C.L. and Ydstie, B. Erik},
  year={2013},
  pages={278--288}
}

Download the bib file

References

• 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 vol. 66 6280–6286 (2011) – 10.1016/j.ces.2011.09.002
• Alvarez-Ramírez, J. Observers for a class of continuous tank reactors via temperature measurement. Chemical Engineering Science vol. 50 1393–1399 (1995) – 10.1016/0009-2509(94)00506-m
• Alvarez-Ramirez, J. & Morales, A. PI control of continuously stirred tank reactors: stability and performance. Chemical Engineering Science vol. 55 5497–5507 (2000) – 10.1016/s0009-2509(00)00173-1
• Antonelli, R. & Astolfi, A. Continuous stirred tank reactors: easy to stabilise? Automatica vol. 39 1817–1827 (2003) – 10.1016/s0005-1098(03)00177-8
• Brogliato, (2007)
• Bruns, D. D. & Bailey, J. E. Process operation near an unstable steady state using nonlinear feedback control. Chemical Engineering Science vol. 30 755–762 (1975) – 10.1016/0009-2509(75)85103-7
• 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
• Dochain, D. State and parameter estimation in chemical and biochemical processes: a tutorial. Journal of Process Control vol. 13 801–818 (2003) – 10.1016/s0959-1524(03)00026-x
• Dochain, D., Couenne, F. & Jallut, C. Enthalpy based modelling and design of asymptotic observers for chemical reactors. International Journal of Control vol. 82 1389–1403 (2009) – 10.1080/00207170802236085
• Dochain, Asymptotic observers for stirred tank reactors. Chemical Engineering Science (1992)
• 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
• Farschman, C. A., Viswanath, K. P. & Erik Ydstie, B. Process systems and inventory control. AIChE Journal vol. 44 1841–1857 (1998) – 10.1002/aic.690440814
• Favache, A. & Dochain, D. Power-shaping control of reaction systems: The CSTR case. Automatica vol. 46 1877–1883 (2010) – 10.1016/j.automatica.2010.07.011
• Favache, A., Dochain, D. & Winkin, J. J. Power-shaping control: Writing the system dynamics into the Brayton–Moser form. Systems & Control Letters vol. 60 618–624 (2011) – 10.1016/j.sysconle.2011.04.021
• Georgakis, C. On the use of extensive variables in process dynamics and control. Chemical Engineering Science vol. 41 1471–1484 (1986) – 10.1016/0009-2509(86)85232-0
• Gibon-Fargeot, A. M., Hammouri, H. & Celle, F. Nonlinear observers for chemical reactors. Chemical Engineering Science vol. 49 2287–2300 (1994) – 10.1016/s0009-2509(94)85061-5
• Hangos, K. M., Bokor, J. & Szederkényi, G. Hamiltonian view on process systems. AIChE Journal vol. 47 1819–1831 (2001) – 10.1002/aic.690470813
• 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
• 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 vol. 22 412–422 (2012) – 10.1016/j.jprocont.2011.12.007
• Hoang, H., Couenne, F., Le Gorrec, Y., Chen, C.-L. & Ydstie, B. E. Passivity based controller and observer of exothermic chemical reactors. IFAC Proceedings Volumes vol. 45 377–384 (2012) – 10.3182/20120710-4-sg-2026.00051
• Hudon, N. & Bao, J. Dissipativity-based decentralized control of interconnected nonlinear chemical processes. Computers & Chemical Engineering vol. 45 84–101 (2012) – 10.1016/j.compchemeng.2012.05.013
• Hudon, N., Hoffner, K. & Guay, M. Equivalence to dissipative Hamiltonian realization. 2008 47th IEEE Conference on Decision and Control 3163–3168 (2008) doi:10.1109/cdc.2008.4739446 – 10.1109/cdc.2008.4739446
• Jeltsema, D., Ortega, R. & M.A. Scherpen, J. An energy-balancing perspective of interconnection and damping assignment control of nonlinear systems. Automatica vol. 40 1643–1646 (2004) – 10.1016/j.automatica.2004.04.007
• Khalil, (2002)
• Kravaris, C., Hahn, J. & Chu, Y. Advances and selected recent developments in state and parameter estimation. Computers & Chemical Engineering vol. 51 111–123 (2013) – 10.1016/j.compchemeng.2012.06.001
• Luyben, (1990)
• 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
• Moreno, J. A. & Dochain, D. Global observability and detectability analysis of uncertain reaction systems and observer design. International Journal of Control vol. 81 1062–1070 (2008) – 10.1080/00207170701636534
• P. Niemiec, M. & Kravaris, C. Nonlinear model-state feedback control for nonminimum-phase processes. Automatica vol. 39 1295–1302 (2003) – 10.1016/s0005-1098(03)00103-1
• Ortega, R., Jeltsema, D. & Scherpen, J. M. A. Power shaping: A new paradigm for stabilization of nonlinear RLC circuits. IEEE Transactions on Automatic Control vol. 48 1762–1767 (2003) – 10.1109/tac.2003.817918
• Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
• 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
• 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
• Soroush, M. Nonlinear state-observer design with application to reactors. Chemical Engineering Science vol. 52 387–404 (1997) – 10.1016/s0009-2509(96)00391-0
• Srinivasan, B., Amrhein, M. & Bonvin, D. Reaction and flow variants/invariants in chemical reaction systems with inlet and outlet streams. AIChE Journal vol. 44 1858–1867 (1998) – 10.1002/aic.690440815
• van der Schaft, (2000)
• van der Schaft, Port-controlled Hamiltonian systems: Towards a theory for control and design of nonlinear physical systems. SICE Journal (2000)
• van de Vusse, J. G. Plug-flow type reactor versus tank reactor. Chemical Engineering Science vol. 19 994–996 (1964) – 10.1016/0009-2509(64)85109-5
• Viel, F., Jadot, F. & Bastin, G. Global stabilization of exothermic chemical reactors under input constraints. Automatica vol. 33 1437–1448 (1997) – 10.1016/s0005-1098(97)00071-x
• Willems, J. C. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis vol. 45 321–351 (1972) – 10.1007/bf00276493
• 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