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Model predictive control of a CSTR: A hybrid modeling approach

  • Michal Kvasnica EMAIL logo , Martin Herceg , Ľuboš Čirka and Miroslav Fikar
Published/Copyright: March 31, 2010
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Abstract

This paper presents a case study of model predictive control (MPC) applied to a continuous stirred tank reactor (CSTR). It is proposed to approximate nonlinear behavior of a plant by several local linear models, enabling a piecewise affine (PWA) description of the model used to predict and optimize future evolution of the reactor behavior. Main advantage of the PWA model over traditional approaches based on single linearization is a significant increase of model accuracy which leads to a better control quality. It is also illustrated that, by adopting the PWA modeling framework, MPC strategy can be implemented using significantly less computational power compared to nonlinear MPC setups.

[1] Aurenhammer, F. (1991). Voronoi diagrams — survey of a fundamental geometric data structure. ACM Computing Surveys, 23, 345–405. DOI: 10.1145/116873.116880. http://dx.doi.org/10.1145/116873.11688010.1145/116873.116880Search in Google Scholar

[2] Bakošovál, P., & Závacká, J. (2009). Robust stabilization of a chemical reactor. Chemical Papers, 63, 527–536. DOI: 10.2478/s11696-009-0046-2. http://dx.doi.org/10.2478/s11696-009-0046-210.2478/s11696-009-0046-2Search in Google Scholar

[3] Bemporad, A., & Morari, M. (1999). Control of systems integrating logic, dynamics, and constraints. Automatica, 35, 407–427. DOI: 10.1016/S0005-1098(98)00178-2. http://dx.doi.org/10.1016/S0005-1098(98)00178-210.1016/S0005-1098(98)00178-2Search in Google Scholar

[4] Du, J. Song, C., & Li, P. (2009). Application of gap metric to model bank determination in multilinear model approach. Journal of Process Control, 19, 231–240, DOI: 10.1016/j.jprocont.2008.04.015. http://dx.doi.org/10.1016/j.jprocont.2008.04.01510.1016/j.jprocont.2008.04.015Search in Google Scholar

[5] Du, J., Song, C., & Li, P. (2007). Modeling and control of a continuous stirred tank reactor based on a mixed logical dynamical model. Chinese Journal of Chemical Engineering, 15, 533–538. DOI: 10.1016/S1004-9541(07)60120-7. http://dx.doi.org/10.1016/S1004-9541(07)60120-710.1016/S1004-9541(07)60120-7Search in Google Scholar

[6] Fletcher, R., & Leyffer, S. (1998). Numerical experience with lower bounds for MIQP branch-and-bound. SIAM Journal on Optimization, 8, 604–616. DOI: 10.1137/S1052623494268 455. http://dx.doi.org/10.1137/S1052623494268455Search in Google Scholar

[7] Graichen, K., Hagenmeyer, V., & Zeitz, M. (2009). Design of adaptive feedforward control under input constraints for a benchmark CSTR based on a BVP solver. Computers & Chemical Engineering, 33, 473–483. DOI: 10.1016/j.compchemeng.2008.11.002. http://dx.doi.org/10.1016/j.compchemeng.2008.11.00210.1016/j.compchemeng.2008.11.002Search in Google Scholar

[8] ILOG Inc. (2006). CPLEX User Manual. ILOG Inc., Gentilly Cedex, France. Retrieved October, 2007, from http://www.ilog.fr/products/cplex Search in Google Scholar

[9] Klatt, K.-U., & Engell, S. (1998). Gain-scheduling trajectory control of a continuous stirred tank reactor. Computers & Chemical Engineering, 22, 491–502. DOI: 10.1016/S0098-1354(97)00261-5. http://dx.doi.org/10.1016/S0098-1354(97)00261-510.1016/S0098-1354(97)00261-5Search in Google Scholar

[10] Kvasnica, M., Grieder, P., Baotic, M., & Morari, M. (2004). Multi-parametric toolbox (MPT). In Hybrid systems: Computation and control (pp. 121–124). Berlin/Heidelberg, Germany: Springer. DOI: 10.1007/b96398. 10.1007/b96398Search in Google Scholar

[11] Kvasnica, M., Herceg, M., Čirka, Lș., & Fikar, M. (2009). Model predictive control of a CSTR. Institute of Information Engineering, Automation and Mathematics, Slovak University of Technology in Bratislava, Slovak Republic. (Technical report). Search in Google Scholar

[12] Löfberg, J. (2004). YALMIP: A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference, 2–4 September 2004 (pp. 284–289). Taipei, Taiwan. 10.1109/CACSD.2004.1393890Search in Google Scholar

[13] Maciejowski, J. M. (2002). Predictive control: with constraints. Harlow, UK: Prentice Hall. Search in Google Scholar

[14] Makhorin, A. (2001). GLPK — GNU linear programming kit. Retrieved from http://www.gnu.org/directory/libs/glpk.html Search in Google Scholar

[15] Melo, D. N. C., Costa, C. B. B, de Toledo, E. C. V., Santos, M. M., Maciel, M. R. W., & Filho, R. M. (2008). Evaluation of control algorithms for three-phase hydrogenation catalytic reactor. Chemical Engineering Journal, 141, 250–263. DOI: 10.1016/j.cej.2007.12.026. http://dx.doi.org/10.1016/j.cej.2007.12.02610.1016/j.cej.2007.12.026Search in Google Scholar

[16] Qin, S. J., & Badgwell, T. A. (2003). A survey of industrial model predictive control technology. Control Engineering Practice, 11, 733–764. DOI: 10.1016/S0967-0661(02)00186-7. http://dx.doi.org/10.1016/S0967-0661(02)00186-710.1016/S0967-0661(02)00186-7Search in Google Scholar

[17] Raman, R., & Grossmann, I. E. (1991). Relation between MILP modeling and logical inference for chemical process synthesis. Computers & Chemical Engineering, 15, 73–84. DOI: 10.1016/0098-1354(91)87007-V. http://dx.doi.org/10.1016/0098-1354(91)87007-V10.1016/0098-1354(91)87007-VSearch in Google Scholar

[18] Sakakura, Y., Noda, M., Nishitani, H., Yamashita, Y., Yoshida, M., & Matsumoto, S. (2006). Application of a hybrid control approach to highly nonlinear chemical processes. In W. Marquardt C. Pantelides (Eds.), Proceedings of the 16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering (Vol. 21, Part 2, pp. 1515–1520). Amsterdam, The Netherlands: Elsevier. DOI: 10.1016/S1570-7946(06)80262-2. http://dx.doi.org/10.1016/S1570-7946(06)80262-210.1016/S1570-7946(06)80262-2Search in Google Scholar

[19] Sontag, E. D. (1981). Nonlinear regulation: The piecewise linear approach. IEEE Transactions on Automatic Control, 26, 346–358. http://dx.doi.org/10.1109/TAC.1981.110259610.1109/TAC.1981.1102596Search in Google Scholar

[20] Utz, T., Hagenmeyer, V., & Mahn, B. (2007). Comparative evaluation of nonlinear model predictive and flatness-based two-degree-of-freedom control design in view of industrial application. Journal of Process Control, 17, 129–141. DOI: 10.1016/j.jprocont.2006.09.002. http://dx.doi.org/10.1016/j.jprocont.2006.09.00210.1016/j.jprocont.2006.09.002Search in Google Scholar

[21] Zavala, V. M., & Biegler, L. T. (2009). The advanced-step NMPC controller: Optimality, stability and robustness. Automatica, 45, 86–93. DOI: 10.1016/j.automatica.2008.06.011. http://dx.doi.org/10.1016/j.automatica.2008.06.01110.1016/j.automatica.2008.06.011Search in Google Scholar

Published Online: 2010-3-31
Published in Print: 2010-6-1

© 2009 Institute of Chemistry, Slovak Academy of Sciences

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