Reference Trajectory Optimization Under Constrained Predictive Control
Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specification and operational constraints. However, direct implementation of optimal input trajectories would, in general, result in offset in th...
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| Vydané v: | Canadian journal of chemical engineering Ročník 85; číslo 4; s. 454 - 464 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Wiley Subscription Services, Inc., A Wiley Company
01.08.2007
Wiley Blackwell Publishing Limited, a company of John Wiley & Sons, Inc |
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| ISSN: | 0008-4034, 1939-019X |
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| Abstract | Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specification and operational constraints. However, direct implementation of optimal input trajectories would, in general, result in offset in the presence of disturbances and plant/model mismatch. This paper considers reference trajectory optimization of processes controlled by constrained model predictive control (MPC). Consideration of the closed‐loop dynamics of the MPC‐controlled process in the reference trajectory optimization results in a multi‐level optimization problem. A solution strategy is applied in which the MPC quadratic programming subproblems are replaced by their Karush‐Kuhn‐Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints (MPCC). The performance of the method is illustrated through application to two case studies, the second of which considers economically optimal grade transitions in a polymerization process.
Les systèmes de procédés chimiques doivent souvent répondre à des changements de production fréquents. Ceci motive la détermination de transitions optimales, soumises à des contraintes de spécification et de fonctionnement. Toutefois, l'implantation directe de trajectoires d'entrée optimales entraîne, en général, un décalage en présence de perturbations et d'une incompatibilité installation/modèle. Cet article porte sur l'optimisation des trajectoires pour des procédés contrôlés par le contrôle prédictif par modèle contraint (MPC). Le fait de considérer la dynamique en boucle fermée du procédé contrôlé par MPC dans l'optimisation des trajectoires de référence cause un problème d'optimisation à plusieurs niveaux. Une stratégie de solution est appliquée dans laquelle les sous‐problèmes de programmation quadratique du MPC sont remplacés par des conditions d'optimalité de Karush‐Kuhn‐Tucker. On obtient ainsi un programme mathématique à niveau unique associé à des contraintes de complémentarité (MPCC). La performance de la méthode est illustrée par l'application de deux études de cas, le second considérant les transitions de grade optimales en termes économiques dans un procédé de polymérisation. |
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| AbstractList | Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specification and operational constraints. However, direct implementation of optimal input trajectories would, in general, result in offset in the presence of disturbances and plant/model mismatch. This paper considers reference trajectory optimization of processes controlled by constrained model predictive control (MPC). Consideration of the closed‐loop dynamics of the MPC‐controlled process in the reference trajectory optimization results in a multi‐level optimization problem. A solution strategy is applied in which the MPC quadratic programming subproblems are replaced by their Karush‐Kuhn‐Tucker optimality conditions, resulting in a single‐level mathematical program with complementarity constraints (MPCC). The performance of the method is illustrated through application to two case studies, the second of which considers economically optimal grade transitions in a polymerization process.
Les systèmes de procédés chimiques doivent souvent répondre à des changements de production fréquents. Ceci motive la détermination de transitions optimales, soumises à des contraintes de spécification et de fonctionnement. Toutefois, l'implantation directe de trajectoires d'entrée optimales entraîne, en général, un décalage en présence de perturbations et d'une incompatibilité installation/modèle. Cet article porte sur l'optimisation des trajectoires pour des procédés contrôlés par le contrôle prédictif par modèle contraint (MPC). Le fait de considérer la dynamique en boucle fermée du procédé contrôlé par MPC dans l'optimisation des trajectoires de référence cause un problème d'optimisation à plusieurs niveaux. Une stratégie de solution est appliquée dans laquelle les sous‐problèmes de programmation quadratique du MPC sont remplacés par des conditions d'optimalité de Karush‐Kuhn‐Tucker. On obtient ainsi un programme mathématique à niveau unique associé à des contraintes de complémentarité (MPCC). La performance de la méthode est illustrée par l'application de deux études de cas, le second considérant les transitions de grade optimales en termes économiques dans un procédé de polymérisation. Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specification and operational constraints. However, direct implementation of optimal input trajectories would, in general, result in offset in the presence of disturbances and plant/model mismatch. This paper considers reference trajectory optimization of processes controlled by constrained model predictive control (MPC). Consideration of the closed-loop dynamics of the MPC-controlled process in the reference trajectory optimization results in a multi-level optimization problem. A solution strategy is applied in which the MPC quadratic programming subproblems are replaced by their Karush-Kuhn-Tucker optimality conditions, resulting in a single-level mathematical program with complementarity constraints (MPCC). The performance of the method is illustrated through application to two case studies, the second of which considers economically optimal grade transitions in a polymerization process. Les systemes de procedes chimiques doivent souvent repondre a des changements de production frequents. Ceci motive la determination de transitions optimales, soumises a des contraintes de specification et de fonctionnement. Toutefois, l'implantation directe de trajectoires d'entree optimales entraine, en general, un decalage en presence de perturbations et d'une incompatibilite installation/modele. Cet article porte sur l'optimisation des trajectoires pour des procedes controles par le controle predictif par modele contraint (MPC). Le fait de considerer la dynamique en boucle fermee du procede controle par MPC dans l'optimisation des trajectoires de reference cause un probleme d'optimisation a plusieurs niveaux. Une strategie de solution est appliquee dans laquelle les sous-problemes de programmation quadratique du MPC sont remplaces par des conditions d'optimalite de Karush-Kuhn-Tucker. On obtient ainsi un programme mathematique a niveau unique associe a des contraintes de complementarite (MPCC). La performance de la methode est illustree par l'application de deux etudes de cas, le second considerant les transitions de grade optimales en termes economiques dans un procede de polymerisation. Keywords: reference trajectory optimization, model predictive control, dynamic optimization, steady state transitions Chemical process systems often need to respond to frequently changing product demands. This motivates the determination of optimal transitions, subject to specification and operational constraints. However, direct implementation of optimal input trajectories would, in general, result in offset in the presence of disturbances and plant/model mismatch. This paper considers reference trajectory optimization of processes controlled by constrained model predictive control (MPC). Consideration of the closed-loop dynamics of the MPC-controlled process in the reference trajectory optimization results in a multi-level optimization problem. A solution strategy is applied in which the MPC quadratic programming subproblems are replaced by their Karush-Kuhn-Tucker optimality conditions, resulting in a single-level mathematical program with complementarity constraints (MPCC). The performance of the method is illustrated through application to two case studies, the second of which considers economically optimal grade transitions in a polymerization process. |
| Audience | Academic |
| Author | Le Swartz, Christopher Baker, Rhoda Lam, David K. |
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| Keywords | model predictive control Closed loop steady state transitions Polymerization dynamic optimization Forecast model Quadratic programming Modeling Steady state Optimization Offset reference trajectory optimization Mathematical programming Predictive control |
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| References | Muske, K. R. and J. B., Rawlings, "Model Predictive Control with Linear Models," AIChE J. 39 (2), 262-287 (1993). Bemporad, A., A., Casavola and E. Mosca, "Nonlinear Control of Constrained Linear Systems via Predictive Reference Management," IEEE Trans. Auto. Control 42 (3), 340-349 (1997). Bemporad, A. and E., Mosca, "Fulfilling Hard Constraints in Uncertain Linear Systems by Reference Managing," Automatica 34 (4), 451-461 (1998). Asteasuain, M., A., Bandoni, C. Sarmoria and A. Brandolin, "Simultaneous Process and Control System Design for Grade Transition in Styrene Polymerization," Chem. Eng. Sci. 61, 3362-3378 (2006). Chatzidoukas, C., J. D., Perkins, E. N. Pistikopoulos and C. Kiparissides, "Optimal Grade Transition and Selection of Closed-Loop Controllers in a Gas-Phase Olefin Polymerization Fluidized Bed Reactor," Chem. Eng. Sci. 58, 3643-3658 (2003). Qin, S. J. and T. A., Badgwell, "A Survey of Industrial Model Predictive Control Technology," Control Eng. Prac. 11, 733-764 (2003). Ralph, D. and S. J., Wright, "Some Properties of Regularization and Penalization Schemes for MPECs," Optimization Methods and Software 19 (5), 527-556 (2004). Wang, Y., H., Seki, S. Ohyama, K. Akamatsu, M. Ogawa and M. Ohshima, "Optimal Grade Transition Control for Polymerization Reactors," Comp. Chem. Eng. 24, 1555-1561 (2000). Maciejowski, J. M., "Predictive Control with Constraints," Prentice Hall (2002). McAuley, K. B. and J. F., MacGregor, "Nonlinear Product Property Control in Industrial Gas-Phase Polyethylene Reactors," AIChE J. 39 (5), 855-866 (1993). Luyben, M. L. and C. A., Floudas, "Analyzing the Interaction of Design and Control - 1. A Multiobjective Framework and Application to Binary Distillation Synthesis," Comp. Chem. Eng. 18 (10), 933-969 (1994). Zafiriou, E., "Robust Model Predictive Control of Processes with Hard Constraints," Comp. Chem. Eng. 14, 359-371 (1990). Maner, B. R., F. J. Doyle III, B. A. Ogunnaike and R. K. Pearson, "Nonlinear Model Predictive Control of a Simulated Multivariable Polymerization Reactor using Second-Order Volterra Models," Automatica 32 (9), 1285-1301 (1996). Flores-Tlacuahuac, A., L. T., Biegler and E. Saldivar-Guerra, "Optimal Grade Transitions in the High-Impact Polystyrene Polymerization Process," Ind. Eng. Chem. Res. 45, 6175-6189 (2006). McAuley, K. B. and J. F., MacGregor, "Optimal Grade Transitions in a Gas Phase Polyethylene Reactor," AIChE J. 38 (10), 1564-1576 (1992). Takeda, M. and W. H., Ray, "Optimal-Grade Transition Strategies for Multistage Polyolefin Reactors," AIChE J. 45 (8), 1776-1793 (1999). Cervantes, A. M., S., Tonelli, A. Brandolin, J. A. Bandoni and L. T. Biegler, "Large-Scale Dynamic Optimization for Grade Transitions in a Low Density Polyethylene Plant," Comp. Chem. Eng. 26, 227-237 (2002). Wright, S. J., "Primal-Dual Interior Point Methods," SIAM, Philadelphia, PA (1997). Kadam, J. V., W., Marquardt, B. Srinivasan and D. Bonvin, "Optimal Grade Transition in Industrial Polymerization Processes via NCO Tracking," AIChE J. 53 (3), 627-639 (2007). Raghunathan, A. U. and L. T., Biegler, "Mathematical Programs with Equlibrium Constraints (MPECs) in Process Engineering," Comp. Chem. Eng. 27, 1381-1392 (2003). 2002; 26 2006; 61 1993; 39 1990; 14 2006; 45 2001 2004; 19 1997; 42 2000; 24 1998 2003; 58 1999; 45 1997 2003; 27 2005 2003 1994; 18 2002 1992; 38 2007; 53 1998; 34 1996; 32 1979 2003; 11 e_1_2_1_20_1 e_1_2_1_23_1 e_1_2_1_24_1 e_1_2_1_21_1 e_1_2_1_22_1 e_1_2_1_27_1 e_1_2_1_25_1 Maciejowski J. M. (e_1_2_1_14_1) 2002 e_1_2_1_26_1 e_1_2_1_7_1 e_1_2_1_8_1 e_1_2_1_5_1 e_1_2_1_6_1 e_1_2_1_3_1 e_1_2_1_12_1 e_1_2_1_4_1 e_1_2_1_13_1 e_1_2_1_10_1 e_1_2_1_2_1 e_1_2_1_11_1 e_1_2_1_16_1 e_1_2_1_17_1 e_1_2_1_15_1 e_1_2_1_9_1 e_1_2_1_18_1 e_1_2_1_19_1 |
| References_xml | – reference: Chatzidoukas, C., J. D., Perkins, E. N. Pistikopoulos and C. Kiparissides, "Optimal Grade Transition and Selection of Closed-Loop Controllers in a Gas-Phase Olefin Polymerization Fluidized Bed Reactor," Chem. Eng. Sci. 58, 3643-3658 (2003). – reference: Asteasuain, M., A., Bandoni, C. Sarmoria and A. Brandolin, "Simultaneous Process and Control System Design for Grade Transition in Styrene Polymerization," Chem. Eng. Sci. 61, 3362-3378 (2006). – reference: Muske, K. R. and J. B., Rawlings, "Model Predictive Control with Linear Models," AIChE J. 39 (2), 262-287 (1993). – reference: Bemporad, A. and E., Mosca, "Fulfilling Hard Constraints in Uncertain Linear Systems by Reference Managing," Automatica 34 (4), 451-461 (1998). – reference: Flores-Tlacuahuac, A., L. T., Biegler and E. Saldivar-Guerra, "Optimal Grade Transitions in the High-Impact Polystyrene Polymerization Process," Ind. Eng. Chem. Res. 45, 6175-6189 (2006). – reference: McAuley, K. B. and J. F., MacGregor, "Nonlinear Product Property Control in Industrial Gas-Phase Polyethylene Reactors," AIChE J. 39 (5), 855-866 (1993). – reference: Luyben, M. L. and C. A., Floudas, "Analyzing the Interaction of Design and Control - 1. A Multiobjective Framework and Application to Binary Distillation Synthesis," Comp. Chem. Eng. 18 (10), 933-969 (1994). – reference: Kadam, J. V., W., Marquardt, B. Srinivasan and D. Bonvin, "Optimal Grade Transition in Industrial Polymerization Processes via NCO Tracking," AIChE J. 53 (3), 627-639 (2007). – reference: Zafiriou, E., "Robust Model Predictive Control of Processes with Hard Constraints," Comp. Chem. Eng. 14, 359-371 (1990). – reference: Wang, Y., H., Seki, S. Ohyama, K. Akamatsu, M. Ogawa and M. Ohshima, "Optimal Grade Transition Control for Polymerization Reactors," Comp. Chem. Eng. 24, 1555-1561 (2000). – reference: Raghunathan, A. U. and L. T., Biegler, "Mathematical Programs with Equlibrium Constraints (MPECs) in Process Engineering," Comp. Chem. Eng. 27, 1381-1392 (2003). – reference: Ralph, D. and S. J., Wright, "Some Properties of Regularization and Penalization Schemes for MPECs," Optimization Methods and Software 19 (5), 527-556 (2004). – reference: Bemporad, A., A., Casavola and E. Mosca, "Nonlinear Control of Constrained Linear Systems via Predictive Reference Management," IEEE Trans. Auto. Control 42 (3), 340-349 (1997). – reference: McAuley, K. B. and J. F., MacGregor, "Optimal Grade Transitions in a Gas Phase Polyethylene Reactor," AIChE J. 38 (10), 1564-1576 (1992). – reference: Maciejowski, J. M., "Predictive Control with Constraints," Prentice Hall (2002). – reference: Maner, B. R., F. J. Doyle III, B. A. Ogunnaike and R. K. 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| SubjectTerms | Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization Applied sciences Chemical engineering dynamic optimization Exact sciences and technology model predictive control reference trajectory optimization steady state transitions |
| Title | Reference Trajectory Optimization Under Constrained Predictive Control |
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