The decay of stabilizability with Reynolds number in a linear model of spatially developing flows

Abstract : This article characterizes the gradual decay of stabilizability with Reynolds number in the linear complex Ginzburg-Landau model of spatially developing flow systems when a single spatially-localized actuator is used to apply the control forcing. It is shown that, technically, the system considered is linearly stabilizable for all actuator locations at any Reynolds number. However, as the Reynolds number is increased and an increasing number of modes of the open-loop system become unstable, the control authority on some of these open-loop unstable modes is found to be exponentially small. Using finite-precision arithmetic and any given numerical method for computing the feedback gains, an effective upper bound on the Reynolds number is reached, above which it is not possible to compute a linearly stabilizing control algorithm. This 'effective upper bound', however, is not a fundamental characteristic of the system; rather, it is a persistent artefact of the numerical precision used in the controller calculation. The most suitable location for the actuator as the Reynolds number is increased is well predicted by analysis of the domain of support of the open-loop adjoint eigenfunctions. Further understanding is provided by analysis of the closed-loop system eigenfunctions, which are shown to become increasingly non-normal as the Reynolds number is increased.
Type de document :
Article dans une revue
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2003, 459 (2036), pp.2077-2095. 〈10.1098/rspa.2002.1116〉
Liste complète des métadonnées

Littérature citée [28 références]  Voir  Masquer  Télécharger

https://hal-polytechnique.archives-ouvertes.fr/hal-01024924
Contributeur : Denis Roura <>
Soumis le : vendredi 8 décembre 2017 - 20:57:03
Dernière modification le : jeudi 10 mai 2018 - 02:03:35

Fichier

ELTB1.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Eric Lauga, Thomas Bewley. The decay of stabilizability with Reynolds number in a linear model of spatially developing flows. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Royal Society, The, 2003, 459 (2036), pp.2077-2095. 〈10.1098/rspa.2002.1116〉. 〈hal-01024924〉

Partager

Métriques

Consultations de la notice

92

Téléchargements de fichiers

15