Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System
This paper studies the application of proper orthogonal decomposition (POD) to reduce the order of distributed reactor models with axial and radial diffusion and the implementation of model predictive control (MPC) based on discrete-time linear time invariant (LTI) reduced-order models. In this pape...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Control Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2013/763165 |
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| author | Alejandro Marquez Jairo José Espinosa Oviedo Darci Odloak |
| author_facet | Alejandro Marquez Jairo José Espinosa Oviedo Darci Odloak |
| author_sort | Alejandro Marquez |
| collection | DOAJ |
| description | This paper studies the application of proper orthogonal decomposition (POD) to reduce the order of distributed reactor models with axial and radial diffusion and the implementation of model predictive control (MPC) based on discrete-time linear time invariant (LTI) reduced-order models. In this paper, the control objective is to keep the operation of the reactor at a desired operating condition in spite of the disturbances in the feed flow. This operating condition is determined by means of an optimization algorithm that provides the optimal temperature and concentration profiles for the system. Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. POD and Galerkin projection are used to derive the low-order linear model that captures the dominant dynamics of the PDEs, which are subsequently used for controller design. An MPC formulation is constructed on the basis of the low-order linear model. The proposed approach is tested through simulation, and it is shown that the results are good with regard to keep the operation of the reactor. |
| format | Article |
| id | doaj-art-0272037935fa48419a67057d7165d539 |
| institution | Kabale University |
| issn | 1687-5249 1687-5257 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Control Science and Engineering |
| spelling | doaj-art-0272037935fa48419a67057d7165d5392025-02-03T05:48:29ZengWileyJournal of Control Science and Engineering1687-52491687-52572013-01-01201310.1155/2013/763165763165Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor SystemAlejandro Marquez0Jairo José Espinosa Oviedo1Darci Odloak2Faculty of Minas, National University of Colombia, 050041 Medellín, ColombiaFaculty of Minas, National University of Colombia, 050041 Medellín, ColombiaChemical Engineering Department, University of São Paulo, 05508-900 São Paulo, SP, BrazilThis paper studies the application of proper orthogonal decomposition (POD) to reduce the order of distributed reactor models with axial and radial diffusion and the implementation of model predictive control (MPC) based on discrete-time linear time invariant (LTI) reduced-order models. In this paper, the control objective is to keep the operation of the reactor at a desired operating condition in spite of the disturbances in the feed flow. This operating condition is determined by means of an optimization algorithm that provides the optimal temperature and concentration profiles for the system. Around these optimal profiles, the nonlinear partial differential equations (PDEs), that model the reactor are linearized, and afterwards the linear PDEs are discretized in space giving as a result a high-order linear model. POD and Galerkin projection are used to derive the low-order linear model that captures the dominant dynamics of the PDEs, which are subsequently used for controller design. An MPC formulation is constructed on the basis of the low-order linear model. The proposed approach is tested through simulation, and it is shown that the results are good with regard to keep the operation of the reactor.http://dx.doi.org/10.1155/2013/763165 |
| spellingShingle | Alejandro Marquez Jairo José Espinosa Oviedo Darci Odloak Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System Journal of Control Science and Engineering |
| title | Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System |
| title_full | Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System |
| title_fullStr | Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System |
| title_full_unstemmed | Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System |
| title_short | Model Reduction Using Proper Orthogonal Decomposition and Predictive Control of Distributed Reactor System |
| title_sort | model reduction using proper orthogonal decomposition and predictive control of distributed reactor system |
| url | http://dx.doi.org/10.1155/2013/763165 |
| work_keys_str_mv | AT alejandromarquez modelreductionusingproperorthogonaldecompositionandpredictivecontrolofdistributedreactorsystem AT jairojoseespinosaoviedo modelreductionusingproperorthogonaldecompositionandpredictivecontrolofdistributedreactorsystem AT darciodloak modelreductionusingproperorthogonaldecompositionandpredictivecontrolofdistributedreactorsystem |