Efficient solution of nonlinear model predictive control by a restricted enumeration method
DOI:
https://doi.org/10.29019/enfoqueute.v9n4.393Keywords:
restricted enumeration method, nonlinear program (NLP), nonlinear model predictive control (NMPC), pH controlAbstract
This work presents an alternative method to solve the nonlinear program (NLP) for nonlinear model predictive control (NMPC) problems. The NLP is the most computational demanding task in NMPC, which limits the industrial implementation of this control strategy. Therefore, it is important to consider algorithms that can solve the nonlinear program, not only in real time but also guaranteeing feasibility. In this work, the restricted enumeration method is proposed as alternative to solve the NLP for NMPC problems, showing successful results for pH control in a sugar cane process plant. This method enumerates in restricted way a set of final control element possible positions around the current one. Next, it tests all positions in that set to find the best one, taken as the optimization solution.
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References
Alkan, M., Erkmen, A. M., & Erkmen, I. (1994). Fuzzy dynamic programming. In Proceedings of MELECON ’94. Mediterranean Electrotechnical Conference (pp. 723–726). IEEE. https://doi.org/10.1109/MELCON.1994.380904
Alvarez, H. (2000). Control predictivo basado en modelo borroso para el control de pH (Temas de Automática, 10). Editorial Fundación UNSJ, San Juan, Argentina.
Aydin, E., Bonvin, D., & Sundmacher, K. (2017). Dynamic optimization of constrained semi-batch processes using Pontryagin’s minimum principle - An effective quasi-Newton approach. Computers & Chemical Engineering, 99, 135–144.
Binder, T., Cruse, A., Villar, C. A. C., & Marquardt, W. (2000). Dynamic optimization using a wavelet based adaptive control vector parameterization strategy. Computers & Chemical Engineering, 24(2), 1201–1207.
Camacho, E. F., & Bordons, C. (Carlos). (2007). Model predictive control. Springer.
Chen, H., & Allgöwer, F. (1998). Nonlinear Model Predictive Control Schemes with Guaranteed Stability. In Nonlinear Model Based Process Control (pp. 465–494). Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-94-011-5094-1_16
Darby, M. L., & Nikolaou, M. (2012). MPC: Current practice and challenges. Control Engineering Practice, 20(4), 328–342.
De Oliveira, S. L. (1996). Model predictive control (MPC) for constrained nonlinear systems. Retrieved from https://thesis.library.caltech.edu/5069/
Holland, J. H. (John H. (1992). Adaptation in natural and artificial systems : an introductory analysis with applications to biology, control, and artificial intelligence. MIT Press.
Isaza, J. A., & Alvarez, H. (2011). Selección de parámetros para un sistema de inferencia borrosa Takagi-Sugeno con conjuntos borroso multidimensionales. In Proceedings of XIV Reunión de Trabajo en Procesamiento de la Información y Control RPIC.
Luus, R. (1996). Numerical Convergence Properties of Iterative Dynamic-Programming When Applied to High-Dimensional Systems. Chemical Engineering Research & Design, 74(1), 55–62.
Mayne, D. Q. (2000). Nonlinear Model Predictive Control. In F. Allgöwer & A. Zheng (Eds.) (pp. 23–44). Birkhäuser.
Mishra, S. K. (Ed.). (2011). Topics in Nonconvex Optimization (Vol. 50). New York, NY: Springer New York. https://doi.org/10.1007/978-1-4419-9640-4
Rao, C. V., & Rawlings, J. B. (2000). Linear programming and model predictive control. Journal of Process Control, 10(2–3), 283–289. https://doi.org/10.1016/S0959-1524(99)00034-7
Richalet, J. (1993). Industrial applications of model based predictive control. Automatica, 29(5), 1251–1274. https://doi.org/10.1016/0005-1098(93)90049-Y
Vatter, V. (2008). Enumeration Schemes for Restricted Permutations. Combinatorics, Probability and Computing, 17(1), 137–159. https://doi.org/10.1017/S0963548307008516
Xi, Y. G., Li, D. W., & Lin, S. (2013). Model Predictive Control - Status and Challenges. Acta Automatica Sinica, 39(3), 222–236.
Zenem, Y. O., Chehade, H., & Yalaoui, A. (2012). New restricted enumeration method for production line design optimization. In IFAC Proceedings Volumes (Vol. 45, pp. 1347–1352).
Alvarez, H. (2000). Control predictivo basado en modelo borroso para el control de pH (Temas de Automática, 10). Editorial Fundación UNSJ, San Juan, Argentina.
Aydin, E., Bonvin, D., & Sundmacher, K. (2017). Dynamic optimization of constrained semi-batch processes using Pontryagin’s minimum principle - An effective quasi-Newton approach. Computers & Chemical Engineering, 99, 135–144.
Binder, T., Cruse, A., Villar, C. A. C., & Marquardt, W. (2000). Dynamic optimization using a wavelet based adaptive control vector parameterization strategy. Computers & Chemical Engineering, 24(2), 1201–1207.
Camacho, E. F., & Bordons, C. (Carlos). (2007). Model predictive control. Springer.
Chen, H., & Allgöwer, F. (1998). Nonlinear Model Predictive Control Schemes with Guaranteed Stability. In Nonlinear Model Based Process Control (pp. 465–494). Dordrecht: Springer Netherlands. https://doi.org/10.1007/978-94-011-5094-1_16
Darby, M. L., & Nikolaou, M. (2012). MPC: Current practice and challenges. Control Engineering Practice, 20(4), 328–342.
De Oliveira, S. L. (1996). Model predictive control (MPC) for constrained nonlinear systems. Retrieved from https://thesis.library.caltech.edu/5069/
Holland, J. H. (John H. (1992). Adaptation in natural and artificial systems : an introductory analysis with applications to biology, control, and artificial intelligence. MIT Press.
Isaza, J. A., & Alvarez, H. (2011). Selección de parámetros para un sistema de inferencia borrosa Takagi-Sugeno con conjuntos borroso multidimensionales. In Proceedings of XIV Reunión de Trabajo en Procesamiento de la Información y Control RPIC.
Luus, R. (1996). Numerical Convergence Properties of Iterative Dynamic-Programming When Applied to High-Dimensional Systems. Chemical Engineering Research & Design, 74(1), 55–62.
Mayne, D. Q. (2000). Nonlinear Model Predictive Control. In F. Allgöwer & A. Zheng (Eds.) (pp. 23–44). Birkhäuser.
Mishra, S. K. (Ed.). (2011). Topics in Nonconvex Optimization (Vol. 50). New York, NY: Springer New York. https://doi.org/10.1007/978-1-4419-9640-4
Rao, C. V., & Rawlings, J. B. (2000). Linear programming and model predictive control. Journal of Process Control, 10(2–3), 283–289. https://doi.org/10.1016/S0959-1524(99)00034-7
Richalet, J. (1993). Industrial applications of model based predictive control. Automatica, 29(5), 1251–1274. https://doi.org/10.1016/0005-1098(93)90049-Y
Vatter, V. (2008). Enumeration Schemes for Restricted Permutations. Combinatorics, Probability and Computing, 17(1), 137–159. https://doi.org/10.1017/S0963548307008516
Xi, Y. G., Li, D. W., & Lin, S. (2013). Model Predictive Control - Status and Challenges. Acta Automatica Sinica, 39(3), 222–236.
Zenem, Y. O., Chehade, H., & Yalaoui, A. (2012). New restricted enumeration method for production line design optimization. In IFAC Proceedings Volumes (Vol. 45, pp. 1347–1352).
Published
2018-12-21
Issue
Section
Automation and Control, Mechatronics, Electromechanics, Automotive
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How to Cite
Efficient solution of nonlinear model predictive control by a restricted enumeration method. (2018). Enfoque UTE, 9(4), pp. 13 - 23. https://doi.org/10.29019/enfoqueute.v9n4.393
