Adaptive Proportional-Integral Control Design for a Class of Continuous Stirred Tank Reactors with Uncertain Parameters
Corressponding author's email:
ntsang@hcmute.edu.vnDOI:
https://doi.org/10.54644/jte.2024.1570Keywords:
Chemical reactor, Temperature regulation, Control theory, Lyapunov function, Non-isothermal reactorAbstract
Mathematical model of reaction systems contains experimental parameters such as reaction enthalpies, which may be inaccurate and, therefore, severely affect the computation as well as the implementation of feedback control laws. This paper aims to design an adaptive PI-like controller to regulate a chemical reaction system by means of the Lyapunov theory. More precisely, uncertain model parameters are updated online by solving a set of ordinary differential equations while the global asymptotic convergence of closed-loop system trajectories towards the desired equilibrium is ensured by using the proposed adaptive PI-like controller under the assumption of stability of isothermal conditions. The applicability of theoretical developments is illustrated with an irreversible first-order reaction system having multiple steady states and taking place in a non-isothermal continuous stirred tank reactor. Simulation results show that system trajectories initiated at different conditions are asymptotically stabilized at the desired values and the closed-loop system is robust against the uncertainty of heat exchange coefficient and dilution rate.
Downloads: 0
References
W. L. Luyben, Process Modeling, Simulation, and Control for Chemical Engineers, second ed. (Chemical Engineering Series). McGraw-Hill Higher Education, 1990.
B. W. Bequette, Process dynamics: Modeling, analysis and simulation, first ed. (Prentice Hall International Series in The Physical and Chemical Engineering Studies). New Jersey: Prentice Hall PTR, Upper Saddle River, 1998.
A. Favache and D. Dochain, "Power-shaping control of reaction systems: The CSTR case," Automatica, vol. 46, no. 11, pp. 1877-1883, 2010. DOI: https://doi.org/10.1016/j.automatica.2010.07.011
N. H. Hoang, F. Couenne, Y. Le Gorrec, C. L. Chen, and B. E. Ydstie, "Passivity-based nonlinear control of CSTR via asymptotic observers," Annual Reviews in Control, vol. 37, no. 2, pp. 278-288, 2013. DOI: https://doi.org/10.1016/j.arcontrol.2013.09.007
K. J. Astrom, "Limitations on control system performance," European Journal of Control, vol. 6, pp. 2-20, 2006.
D. D. Bruns and J. E. Bailey, "Process operation near an unstable steady state using nonlinear feedback control," Chemical Engineering Science, vol. 30, pp. 755-762, 1975. DOI: https://doi.org/10.1016/0009-2509(75)85103-7
A. Uppal and W. H. Ray, "On the dynamic behavior of continuous stirred tank reactors," Chemical Engineering Science., vol. 29, pp. 967-985, 1974. DOI: https://doi.org/10.1016/0009-2509(74)80089-8
C. Van Heerden, "Autothermic processes. Properties and reactor design," Industrial & Engineering Chemistry Research, vol. 45, no. 6, pp. 1242-1247, 1953. DOI: https://doi.org/10.1021/ie50522a030
N. T. Sang, H. N. M. Ha, and M. A. Hussain, "Feedback passivation plus tracking-error-based multivariable control for a class of free-radical polymerisation reactors," International Journal of Control, vol. 92, no. 9, pp. 1970-1984, 2019. DOI: https://doi.org/10.1080/00207179.2017.1423393
N. H. Hoang, F. Couenne, C. Jallut, and Y. Le Gorrec, "Lyapunov-based control of non isothermal continuous stirred tank reactors using irreversible thermodynamics," Journal of Process Control, vol. 22, no. 2, pp. 412-422, 2012. DOI: https://doi.org/10.1016/j.jprocont.2011.12.007
N. H. Hoang, F. Couenne, C. Jallut, and Y. Le Gorrec, "Thermodynamics based stability analysis and its use for nonlinear stabilization of the CSTR," Computers & Chemical Engineering, vol. 58, pp. 156-177, 2013. DOI: https://doi.org/10.1016/j.compchemeng.2013.06.016
C. Panjapornpon, M. Soroush, and W. D. Seider, "Model-based controller design for unstable, non-minimum-phase, nonlinear processes," Industrial & Engineering Chemistry Research, vol. 45, pp. 2758-2768, 2006. DOI: https://doi.org/10.1021/ie050724p
S. I. Sandler, Chemical, biochemical, and engineering thermodynamics. John Wiley & Sons, 2017.
T. S. Nguyen, "A port-Hamiltonian Framework for control of chemical reaction systems with variant and invariant states," Ph.D., Chemical Engineering, Universiti Malaya, Faculty of Engineering, 2023.
N. H. Hoang, D. Rodrigues, and D. Bonvin, "Revisiting the concept of extents for chemical reaction systems using an enthalpy balance," Computers & Chemical Engineering, vol. 136, p. 106652, 2020. DOI: https://doi.org/10.1016/j.compchemeng.2019.106652
J. Alvarez, J. A. Ramirez, G. E. Perez, and A. Schaum, "Energy shaping plus damping injection control for a class of chemical reactors," Chemical Engineering Science, vol. 66, no. 23, pp. 6280-6286, 2011. DOI: https://doi.org/10.1016/j.ces.2011.09.002
H. K. Khalil, Nonlinear systems, third ed. Prentice Hall, 2002.
Downloads
Published
How to Cite
License
Copyright (c) 2024 Journal of Technical Education Science
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.
Copyright © JTE.
