Integration of inventory control into the port‐Hamiltonian framework for dissipative stabilization of chemical reactors

Authors

Abstract

This work integrates passivity‐based inventory control with the port‐Hamiltonian framework to design stabilizing feedback laws for lumped parameter chemically reacting systems. A static state feedback law with admissible controls is developed using an inventory‐related storage function as a closed loop Hamiltonian function. The control gain matrix is derived from the interconnection and damping matrices of the resulting Hamiltonian representation. Consequently, the proposed controller globally and exponentially stabilizes the system at a desired set‐point (including the open loop unstable equilibrium point) without restrictions on the reaction kinetics. Numerical simulations illustrate the application of the theory to a nonisothermal, continuous stirred tank reactor with the steady‐state multiplicity. The proposed approach is compared with the thermodynamic availability‐based control approach in terms of amplitude and variation rate to show its performance and effectiveness.

Citation

Journal: Asian Journal of Control
Year: 2022
Volume: 24
Issue: 5
Pages: 2490–2504
Publisher: Wiley
DOI: 10.1002/asjc.2668

BibTeX

@article{Hoang_2022,
  title={{Integration of inventory control into the port‐Hamiltonian framework for dissipative stabilization of chemical reactors}},
  volume={24},
  ISSN={1934-6093},
  DOI={10.1002/asjc.2668},
  number={5},
  journal={Asian Journal of Control},
  publisher={Wiley},
  author={Hoang, N. Ha and Ydstie, B. Erik},
  year={2022},
  pages={2490--2504}
}

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References

Glansdorff P., Thermodynamic Theory of Structure, Stability and Fluctuations (1971)
Alonso, A. A. & Erik Ydstie, B. Process systems, passivity and the second law of thermodynamics. Computers & Chemical Engineering vol. 20 S1119–S1124 (1996) – 10.1016/0098-1354(96)00194-9
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
Hangos, K. M., Alonso, A. A., Perkins, J. D. & Ydstie, B. E. Thermodynamic approach to the structural stability of process plants. AIChE Journal vol. 45 802–816 (1999) – 10.1002/aic.690450414
Asbjørnsen, O. A. & Field, M. Response modes of continuous stirred tank reactors. Chemical Engineering Science vol. 25 1627–1636 (1970) – 10.1016/0009-2509(70)80054-9
Rodrigues, D., Srinivasan, S., Billeter, J. & Bonvin, D. Variant and invariant states for chemical reaction systems. Computers & Chemical Engineering vol. 73 23–33 (2015) – 10.1016/j.compchemeng.2014.10.009
Haddad W. M., Thermodynamics—A Dynamical Systems Approach (2005)
Bao J., Process Control: The Passive Systems Approach (2007)
Hoang, N. H. & Dochain, D. A comment on thermodynamically consistent feasibility condition of asymptotic observers. Chemical Engineering Science vol. 199 258–274 (2019) – 10.1016/j.ces.2019.01.010
Jillson, K. R. & Erik Ydstie, B. Process networks with decentralized inventory and flow control. Journal of Process Control vol. 17 399–413 (2007) – 10.1016/j.jprocont.2006.12.006
Otero-Muras, I., Szederkényi, G., Hangos, K. M. & Alonso, A. A. Dynamic analysis and control of biochemical reaction networks. Mathematics and Computers in Simulation vol. 79 999–1009 (2008) – 10.1016/j.matcom.2008.02.019
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
Ederer, M., Dieter Gilles, E. & Sawodny, O. The Glansdorff–Prigogine stability criterion for biochemical reaction networks. Automatica vol. 47 1097–1104 (2011) – 10.1016/j.automatica.2011.01.072
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
Grmela, M. Geometry of Multiscale Nonequilibrium Thermodynamics. Entropy vol. 17 5938–5964 (2015) – 10.3390/e17095938
García-Sandoval, J. P., Hudon, N., Dochain, D. & González-Álvarez, V. Stability analysis and passivity properties of a class of thermodynamic processes: An internal entropy production approach. Chemical Engineering Science vol. 139 261–272 (2016) – 10.1016/j.ces.2015.07.039
van der Schaft, A. J., Rao, S. & Jayawardhana, B. A network dynamics approach to chemical reaction networks. International Journal of Control vol. 89 731–745 (2015) – 10.1080/00207179.2015.1095353
Ydstie, B. E. Stability of Multi-Phase Systems Evolving on an Equilibrium Manifold. IFAC-PapersOnLine vol. 49 943–948 (2016) – 10.1016/j.ifacol.2016.07.321
Ramirez, H., Maschke, B. & Sbarbaro, D. Partial Stabilization of Input-Output Contact Systems on a Legendre Submanifold. IEEE Transactions on Automatic Control vol. 62 1431–1437 (2017) – 10.1109/tac.2016.2572403
Luyben W. L., Process Modeling, Simulation, and Control for Chemical Engineers (1990)
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
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
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
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
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
Hoang, N. H., Couenne, F., Jallut, C. & Le Gorrec, Y. Thermodynamics based stability analysis and its use for nonlinear stabilization of the CSTR. Computers & Chemical Engineering vol. 58 156–177 (2013) – 10.1016/j.compchemeng.2013.06.016
Kravaris, C. & Kantor, J. C. Geometric methods for nonlinear process control. 1. Background. Industrial & Engineering Chemistry Research vol. 29 2295–2310 (1990) – 10.1021/ie00108a001
Kravaris, C. & Kantor, J. C. Geometric methods for nonlinear process control. 2. Controller synthesis. Industrial & Engineering Chemistry Research vol. 29 2310–2323 (1990) – 10.1021/ie00108a002
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
Afsi, N. et al. Model predictive control for continuous lactide ring‐opening polymerization processes. Asian Journal of Control vol. 23 92–104 (2020) – 10.1002/asjc.2453
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
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
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
Fang, Z. & Gao, C. Stabilization of Input-Disturbed Stochastic Port-Hamiltonian Systems Via Passivity. IEEE Transactions on Automatic Control vol. 62 4159–4166 (2017) – 10.1109/tac.2017.2676619
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
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
Keenan, J. H. Availability and irreversibility in thermodynamics. British Journal of Applied Physics vol. 2 183–192 (1951) – 10.1088/0508-3443/2/7/302
Alonso, A. A. & Ydstie, B. E. Stabilization of distributed systems using irreversible thermodynamics. Automatica vol. 37 1739–1755 (2001) – 10.1016/s0005-1098(01)00140-6
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
De Persis, C. & Monshizadeh, N. Bregman Storage Functions for Microgrid Control. IEEE Transactions on Automatic Control vol. 63 53–68 (2018) – 10.1109/tac.2017.2709246
Ferguson, J., Donaire, A. & Middleton, R. H. Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation. IEEE Transactions on Automatic Control vol. 62 5947–5953 (2017) – 10.1109/tac.2017.2700995
Brockett, R. W. Thermodynamics with time: Exergy and passivity. Systems & Control Letters vol. 101 44–49 (2017) – 10.1016/j.sysconle.2016.06.009
Fang, Z., Ydstie, B. E. & Gao, C. Thermodynamic Potentials from Stationary Probabilities. IFAC-PapersOnLine vol. 52 96–102 (2019) – 10.1016/j.ifacol.2019.07.017
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
Ruszkowski, M., Garcia‐Osorio, V. & Ydstie, B. E. Passivity based control of transport reaction systems. AIChE Journal vol. 51 3147–3166 (2005) – 10.1002/aic.10543
Nguyen, T. S., Hoang, N. H. & Azlan Hussain, M. Feedback passivation plus tracking-error-based multivariable control for a class of free-radical polymerisation reactors. International Journal of Control vol. 92 1970–1984 (2018) – 10.1080/00207179.2017.1423393
Nguyen, T. S., Hoang, N. H., Hussain, M. A. & Tan, C. K. Tracking-error control via the relaxing port-Hamiltonian formulation: Application to level control and batch polymerization reactor. Journal of Process Control vol. 80 152–166 (2019) – 10.1016/j.jprocont.2019.05.014
Juan Du, Laird, C. M. & Ydstie, B. E. The measurement selection of inventory control. Proceedings of the 2010 American Control Conference 3555–3560 (2010) doi:10.1109/acc.2010.5530854 – 10.1109/acc.2010.5530854
Ngoc-Ha Hoang, Du Juan & Ydstie, B. E. On the passivity of inventory control in the Port Hamiltonian framework. 2013 American Control Conference 1639–1644 (2013) doi:10.1109/acc.2013.6580070 – 10.1109/acc.2013.6580070
Kuhlmann, A. & Bogle, D. Study on nonminimum phase behaviour and optimal operation. Computers & Chemical Engineering vol. 21 S397–S402 (1997) – 10.1016/s0098-1354(97)87534-5
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
Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
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
Wu, D., Ortega, R. & Duan, G. On universal stabilization property of Interconnection and Damping Assignment Control. Automatica vol. 119 109087 (2020) – 10.1016/j.automatica.2020.109087
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
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
Ha Hoang, N., Couenne, F., Le Gorrec, Y., Chen, C. L. & Ydstie, B. E. Passivity-based nonlinear control of CSTR via asymptotic observers. Annual Reviews in Control vol. 37 278–288 (2013) – 10.1016/j.arcontrol.2013.09.007
Schaft A. J., Port‐controlled Hamiltonian systems: Towards a theory for control and design of nonlinear physical systems. SICE J. (2000)
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
Khalil H. K., Nonlinear Systems (2002)
Willems, J. C. Dissipative dynamical systems part I: General theory. Archive for Rational Mechanics and Analysis vol. 45 321–351 (1972) – 10.1007/bf00276493
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
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 vol. 60 175–198 (2007) – 10.1016/s0034-4877(07)00024-9
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
Callen H. B., Thermodynamics and An Introduction to Thermostatics (1985)
Romo-Hernández, A., Hudon, N., Ydstie, B. E. & Dochain, D. Thermodynamic Analysis and Feedback Stabilization for Irreversible Liquid–Vapor Systems. Industrial & Engineering Chemistry Research vol. 59 2252–2260 (2020) – 10.1021/acs.iecr.9b04869
Bahroun, S., Couenne, F., Jallut, C. & Valentin, C. Thermodynamics-Based Nonlinear Control of a Three-Phase Slurry Catalytic Fed-Batch Reactor. IEEE Transactions on Control Systems Technology vol. 21 360–371 (2013) – 10.1109/tcst.2011.2181173
Hoang, N. H. & Dochain, D. On the equivalence of storage functions in controlled thermodynamic systems. IFAC-PapersOnLine vol. 49 579–584 (2016) – 10.1016/j.ifacol.2016.07.405