Nonlinear Feedback Stabilization of a Rotating Body-Beam Without Damping

This paper deals with nonlinear feedback stabilization problem of a exible beam clamped at a rigid body and free at the other end. We assume that there is no damping. The feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a nonlinear boundary control moment or a nonlinear boundary control force or both of them applied to the free end of the beam. This nonlinear feedback, which insures the exponential decay of the beam vibrations, extends the linear case studied by Laousy et al. to a more general class of controls. This new class of controls is in particular of the interest to be robust. Key-words: Rotating body-beam, Nonlinear control, Exponential stability. INRIA-Lorraine (projet Cong e) & URA CNRS 399 (MMAS) ISGMP, Bât. A, Universit e de Metz, Ile de Saulcy 57045 Metz cedex 01 t el. : 03 87 54 72 76 { fax : 03 87 54 72 77 e-mail : fchentouf,couchour [email protected] Unité de recherche INRIA Lorraine Technopôle de Nancy-Brabois, Campus scientifique, 615 rue de Jardin Botanique, BP 101, 54600 VILLERS LÈS NANCY (France) Téléphone : (33) 83 59 30 30 – Télécopie : (33) 83 27 83 19 Antenne de Metz, technopôle de Metz 2000, 4 rue Marconi, 55070 METZ Téléphone : (33) 87 20 35 00 – Télécopie : (33) 87 76 39 77 2 Boumedi ene CHENTOUF & Jean-Fran cois COUCHOURON