A perturbed Port-Hamiltonian approach for the stabilization of homogeneous reaction systems via the control of vessel extents

Authors

T. Sang Nguyen, C.K. Tan, N. Ha Hoang, M.A. Hussain, D. Bonvin

Abstract

The paper proposes a tracking-error passivity-based control scheme for the asymptotic stabilization of homogeneous reaction systems. The approach uses the concept of vessel extents in the Port-Hamiltonian (PH) framework. Concretely, the extent-based representation that is obtained by linear time-invariant transformation of the reaction model is expressed as a perturbed PH system, whereby the reaction rates constitute unmatched time-varying disturbances. Two scenarios are considered. The first one assumes that the molar numbers of all species and the reaction temperature are measured and, furthermore, the kinetic model is known, while the second scenario relaxes these assumptions and requires only the measurements of a subset of the molar numbers and of the reactor temperature, but no knowledge of reaction kinetics. For the first scenario, the passivity-based method is used to compensate the disturbances, while preserving the PH structure of the error system via simple matrix factorization of the disturbances. For the second scenario, a constructive procedure is proposed to complete the space of vessel extents with the aim of computing an appropriate damping injection for the closed-loop system. It is shown that the proposed strategies guarantee that the system trajectories converge towards the desired setpoints without the need of state observation. A reaction system exhibiting non-minimum phase behavior is used to illustrate the theoretical developments. The closed-loop performance is discussed and compared to that of a PI controller.

Keywords

Chemical reaction; Vessel extents; Disturbance compensation; Port-Hamiltonian formulation; Tracking-error passivity-based control

Citation

Journal: Computers & Chemical Engineering
Year: 2021
Volume: 154
Issue:
Pages: 107458
Publisher: Elsevier BV
DOI: 10.1016/j.compchemeng.2021.107458

BibTeX

@article{Nguyen_2021,
  title={{A perturbed Port-Hamiltonian approach for the stabilization of homogeneous reaction systems via the control of vessel extents}},
  volume={154},
  ISSN={0098-1354},
  DOI={10.1016/j.compchemeng.2021.107458},
  journal={Computers &amp; Chemical Engineering},
  publisher={Elsevier BV},
  author={Nguyen, T. Sang and Tan, C.K. and Hoang, N. Ha and Hussain, M.A. and Bonvin, D.},
  year={2021},
  pages={107458}
}

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References

Alvarez-Ramirez, J. & Puebla, H. On classical PI control of chemical reactors. Chemical Engineering Science vol. 56 2111–2121 (2001) – 10.1016/s0009-2509(00)00471-1
Alvarez-Ramírez, J., Suárez, R. & Femat, R. Control of continuous-stirred tank reactors: Stabilization with unknown reaction rates. Chemical Engineering Science vol. 51 4183–4188 (1996) – 10.1016/0009-2509(96)00240-0
Amrhein, M., Bhatt, N., Srinivasan, B. & Bonvin, D. Extents of reaction and flow for homogeneous reaction systems with inlet and outlet streams. AIChE Journal vol. 56 2873–2886 (2010) – 10.1002/aic.12125
Asbjørnsen, O. A. Reaction invariants in the control of continuous chemical reactors. Chemical Engineering Science vol. 27 709–717 (1972) – 10.1016/0009-2509(72)85007-3
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
Bhatt, N., Amrhein, M. & Bonvin, D. Extents of Reaction, Mass Transfer and Flow for Gas−Liquid Reaction Systems. Industrial & Engineering Chemistry Research vol. 49 7704–7717 (2010) – 10.1021/ie902015t
Billeter, J., Rodrigues, D., Srinivasan, S., Amrhein, M. & Bonvin, D. On decoupling rate processes in chemical reaction systems – Methods and applications. Computers & Chemical Engineering vol. 114 296–305 (2018) – 10.1016/j.compchemeng.2017.09.021
Donaire, A. & Junco, S. On the addition of integral action to port-controlled Hamiltonian systems. Automatica vol. 45 1910–1916 (2009) – 10.1016/j.automatica.2009.04.006
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
Fjeld, M., Asbjørnsen, O. A. & Åström, K. J. Reaction invariants and their importance in the analysis of eigenvectors, state observability and controllability of the continuous stirred tank reactor. Chemical Engineering Science vol. 29 1917–1926 (1974) – 10.1016/0009-2509(74)85009-8
Fradkov, A., Ortega, R. & Bastin, G. Semi‐adaptive control of convexly parametrized systems with application to temperature regulation of chemical reactors. International Journal of Adaptive Control and Signal Processing vol. 15 415–426 (2001) – 10.1002/acs.634
Fujimoto, K., Sakurama, K. & Sugie, T. Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica vol. 39 2059–2069 (2003) – 10.1016/j.automatica.2003.07.005
Hammarström, L. G. Control of chemical reactors in the subspace of reaction and control variants. Chemical Engineering Science vol. 34 891–899 (1979) – 10.1016/0009-2509(79)85146-5
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, 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
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
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
Hoang, On the computation of extents of reaction with a limited number of measurements. Comput. Chem. Eng. (2020)
Ha Hoang, N., Rodrigues, D. & Bonvin, D. Revisiting the concept of extents for chemical reaction systems using an enthalpy balance. Computers & Chemical Engineering vol. 136 106652 (2020) – 10.1016/j.compchemeng.2019.106652
Khalil, (2002)
Lucia, S., Finkler, T. & Engell, S. Multi-stage nonlinear model predictive control applied to a semi-batch polymerization reactor under uncertainty. Journal of Process Control vol. 23 1306–1319 (2013) – 10.1016/j.jprocont.2013.08.008
Luyben, (1990)
Marquez-Ruiz, A., Mendez-Blanco, C. S. & Özkan, L. Control of Homogeneous Reaction Systems using Extent-Based LPV Models. IFAC-PapersOnLine vol. 51 548–553 (2018) – 10.1016/j.ifacol.2018.09.367
Marquez-Ruiz, A., Loonen, M., Saltık, M. B. & Özkan, L. Model Learning Predictive Control for Batch Processes: A Reactive Batch Distillation Column Case Study. Industrial & Engineering Chemistry Research vol. 58 13737–13749 (2019) – 10.1021/acs.iecr.8b06474
Marquez-Ruiz, A., Méndez-Blanco, C. S. & Özkan, L. Modeling of reactive batch distillation processes for control. Computers & Chemical Engineering vol. 121 86–98 (2019) – 10.1016/j.compchemeng.2018.10.010
Marquez-Ruiz, A., Mendez-Blanco, C. & Özkan, L. Constrained Control and Estimation of Homogeneous Reaction Systems Using Extent-Based Linear Parameter Varying Models. Industrial & Engineering Chemistry Research vol. 59 2242–2251 (2020) – 10.1021/acs.iecr.9b04412
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
Nguyen, T. S., Tan, C. K., Hoang, N. H. & Hussain, M. A. Tracking-error-based control of a chemical reactor using decoupled dynamic variables. IFAC-PapersOnLine vol. 52 74–79 (2019) – 10.1016/j.ifacol.2019.07.013
Thanh Sang, N., Chee Keong, T., Ngoc Ha, H. & Hussain, M. A. Control of reaction systems using decoupled dynamics via perturbed Hamiltonian formulation. IFAC-PapersOnLine vol. 53 11527–11532 (2020) – 10.1016/j.ifacol.2020.12.628
Nunna, K., Sassano, M. & Astolfi, A. Constructive Interconnection and Damping Assignment for Port-Controlled Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 60 2350–2361 (2015) – 10.1109/tac.2015.2400663
Ortega, R. & Romero, J. G. Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances. Systems & Control Letters vol. 61 11–17 (2012) – 10.1016/j.sysconle.2011.09.015
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
Prakash, J. & Srinivasan, K. Design of nonlinear PID controller and nonlinear model predictive controller for a continuous stirred tank reactor. ISA Transactions vol. 48 273–282 (2009) – 10.1016/j.isatra.2009.02.001
Rasmuson, (2014)
Rawlings, (2015)
Rodrigues, Control of reaction systems via rate estimation and feedback linearization. (2015)
Rodrigues, D., Billeter, J. & Bonvin, D. Maximum-likelihood estimation of kinetic parameters via the extent-based incremental approach. Computers & Chemical Engineering vol. 122 152–171 (2019) – 10.1016/j.compchemeng.2018.05.024
Rodrigues, D. & Bonvin, D. On reducing the number of decision variables for dynamic optimization. Optimal Control Applications and Methods vol. 41 292–311 (2019) – 10.1002/oca.2543
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
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
Srinivasan, S., Billeter, J., Narasimhan, S. & Bonvin, D. Data reconciliation for chemical reaction systems using vessel extents and shape constraints. Computers & Chemical Engineering vol. 101 44–58 (2017) – 10.1016/j.compchemeng.2017.02.003
Viel, F., Busvelle, E. & Gauthier, J. P. Stability of polymerization reactors using I/O linearization and a high-gain observer. Automatica vol. 31 971–984 (1995) – 10.1016/0005-1098(95)00009-l
Viel, F., Jadot, F. & Bastin, G. Robust feedback stabilization of chemical reactors. IEEE Transactions on Automatic Control vol. 42 473–481 (1997) – 10.1109/9.566657
Waller, K. V. & Makila, P. M. Chemical reaction invariants and variants and their use in reactor modeling, simulation, and control. Industrial & Engineering Chemistry Process Design and Development vol. 20 1–11 (1981) – 10.1021/i200012a001
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
Yaghmaei, A. & Yazdanpanah, M. J. Trajectory tracking for a class of contractive port Hamiltonian systems. Automatica vol. 83 331–336 (2017) – 10.1016/j.automatica.2017.06.039
Zerari, Robust adaptive neural network prescribed performance control for uncertain CSTR system with input nonlinearities and external disturbance. Neural Comput. Appl. (2019)
Zhang, M., Ortega, R., Liu, Z. & Su, H. A new family of interconnection and damping assignment passivity-based controllers. International Journal of Robust and Nonlinear Control vol. 27 50–65 (2016) – 10.1002/rnc.3557