Model reduction through identification – Application to some diffusion–convection problems in heat transfer, with an extension towards control strategies

Yassine Rouizi; Yann Favennec; Yvon Jarny; Daniel Petit

doi:10.1016/j.crme.2013.09.005

Model reduction through identification – Application to some diffusion–convection problems in heat transfer, with an extension towards control strategies

Yassine Rouizi ^1,² ; Yann Favennec ³ ; Yvon Jarny ³ ; Daniel Petit ²

¹ Laboratoire de mécanique et dʼénergétique dʼÉvry, 40, rue du Pelvoux, CE1455 Courcouronnes, 91020 Évry cedex, France
² Institut Pʼ CNRS–ENSMA–Université de Poitiers, UPR 3346, Département Fluides, Thermique, Combustion, ENSMA – Téléport 2, 1, avenue Clément-Ader, BP 40109, 86961 Futuroscope-Chasseneuil-du-Poitou cedex, France
³ Laboratoire de thermocinétique de Nantes, UMR–CNRS 6607, École polytechnique de lʼuniversité de Nantes, La Chantrerie, 44306 Nantes cedex 3, France

Comptes Rendus. Mécanique, Volume 341 (2013) no. 11-12, pp. 776-792.

Résumé

The simulation of heat convection problems usually leads to very large matrix systems because both Navier–Stokes equations and the energy equations are to be taken into account and discretized. Of course, such large matrix systems cannot be used for on-line control algorithms due to memory limitations and computation time. On-line control algorithms should rather consider much smaller matrix systems. Bearing this in mind, model reduction techniques present a large interest to obtain a suitable low-order model that can further be used in control processes. In this paper, reduced models are obtained through the modal identification method. This method relies on the solution of an optimization problem of parameter estimation following the steps: (i) the structure of the state model is first defined, (ii) the related vectors and matrices are estimated through the minimization of a corresponding functional, (iii) the reduced order model then must be validated with input data different from those used within the identification process. These steps being completed, other control algorithms can “plug” such reduced models. Among linear control algorithms, the feedback control laws considered in this paper are based either on the reduced state or on the output. A Kalman filter evaluates the state through a limited number of measurements. The developed numerical application deals with a temperature field within a 2D stationary flow over a backward-facing step. The goal is to keep the outlet temperature as close as possible to a given temperature profile downstream from the step, whatever the pipe inlet temperature fluctuations. One thus searches some “optimal” heat fluxes upstream from the step that counteract the inlet temperature variations.

Reçu le : 2013-04-05
Accepté le : 2013-09-27
Publié le : 2013-11-01

DOI : 10.1016/j.crme.2013.09.005

Mots clés : Feedback control, Model reduction, Modal identification method, Optimization, Backward-facing step flow, Heat transfer convection

Affiliations des auteurs :

Yassine Rouizi ^{1, 2} ; Yann Favennec ³ ; Yvon Jarny ³ ; Daniel Petit ²

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     title = {Model reduction through identification {\textendash} {Application} to some diffusion{\textendash}convection problems in heat transfer, with an extension towards control strategies},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {776--792},
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     volume = {341},
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     year = {2013},
     doi = {10.1016/j.crme.2013.09.005},
     language = {en},
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Yassine Rouizi; Yann Favennec; Yvon Jarny; Daniel Petit. Model reduction through identification – Application to some diffusion–convection problems in heat transfer, with an extension towards control strategies. Comptes Rendus. Mécanique, Volume 341 (2013) no. 11-12, pp. 776-792. doi : 10.1016/j.crme.2013.09.005. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2013.09.005/

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