EDP Sciences Journals List
Advanced Search
Subscriber Authentication Point
Home All issues Volume 25 Article
Free access article

Issue ESAIM: Proc.
Volume 25, 2008
Paris-sud working group on modelling and scientific computing 2007-2008
Page(s) 19 - 28
DOI http://dx.doi.org/10.1051/proc:082502
Published online 16 January 2009

ESAIM: Proc., 2008, Vol. 25, pp. 19-28
DOI: 10.1051/proc:082502

Exact controllability and output feedback stabilization of a bimorph mirror

Pierre Le Gall1, Christophe Prieur2 and Lionel Rosier1

1  Institut Elie Cartan, Université Henri Poincaré Nancy 1, B.P. 239, 54506 Vandœuvre-lès-Nancy Cedex, France
2  LAAS-CNRS, Université de Toulouse, 7 avenue du colonel Roche, 31077 Toulouse, France


Published online: 16 January 2009

Abstract
We consider a large bimorph mirror which is composed of three layers: a purely elastic layer, a layer equipped with a distribution of sensor piezoelectric inclusions, and a layer equipped with a distribution of actuator piezoelectric inclusions. Such a device is modelized by a system of two coupled PDE, the first one involving a second-order operator without time derivative, and the second one being a plate equation. The controllability properties are investigated for both the 1D model and the 2D model, and an output feedback law is proposed for the stabilization of the 1D model.


Résumé
Nous considérons un miroir bimorphe qui est composé de trois couches: une couche purement élastique, une couche munie d'une distribution de capteurs piézoélectriques, et une autre munie d'une distribution d'actionneurs piézoélectriques. Un tel équipement est modélisé par un système de deux EDP couplées, la première étant écrite à l'aide d'un opérateur du second ordre sans dérivation en temps, et la deuxième étant l'équation des plaques. Nous étudions la contrôlabilité des modèles 1D et 2D, et nous proposons un retour de sortie stabilisant le modèle 1D.



© EDP Sciences, ESAIM 2008


What is OpenURL?

The OpenURL standard is a protocol for transmission of metadata describing the resource that you wish to access. An OpenURL link contains article metadata and directs it to the OpenURL server of your choice. The OpenURL server can provide access to the resource and also offer complementary services (specific search engine, export of references...). The OpenURL link can be generated by different means.
  • If your librarian has set up your subscription with an OpenURL resolver, OpenURL links appear automatically on the abstract pages.
  • You can define your own OpenURL resolver with your EDPS Account. In this case your choice will be given priority over that of your library.
  • You can use an add-on for your browser (Firefox or I.E.) to display OpenURL links on a page (see http://www.openly.com/openurlref/). You should disable this module if you wish to use the OpenURL server that you or your library have defined.