### Abstract

This paper deals with feedback stabilization of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the rigid body rotates with a nonconstant angular velocity. To stabilize this system, we propose a feedback law which consists of a control torque applied on the rigid body and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. Then it is shown that the closed loop system is well posed and exponentially stable provided that the actuators, which generate the boundary controls, satisfy some classical assumptions and the angular velocity is smaller than a critical one.

Original language | English |
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Pages (from-to) | 107-126 |

Number of pages | 20 |

Journal | Journal of Applied Mathematics |

Volume | 2004 |

Issue number | 2 |

DOIs | |

Publication status | Published - 2004 |

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### ASJC Scopus subject areas

- Applied Mathematics

### Cite this

*Journal of Applied Mathematics*,

*2004*(2), 107-126. https://doi.org/10.1155/S1110757X04312027

**Dynamic boundary controls of a rotating body-beam system with time-varying angular velocity.** / Chentouf, Boumediène.

Research output: Contribution to journal › Article

*Journal of Applied Mathematics*, vol. 2004, no. 2, pp. 107-126. https://doi.org/10.1155/S1110757X04312027

}

TY - JOUR

T1 - Dynamic boundary controls of a rotating body-beam system with time-varying angular velocity

AU - Chentouf, Boumediène

PY - 2004

Y1 - 2004

N2 - This paper deals with feedback stabilization of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the rigid body rotates with a nonconstant angular velocity. To stabilize this system, we propose a feedback law which consists of a control torque applied on the rigid body and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. Then it is shown that the closed loop system is well posed and exponentially stable provided that the actuators, which generate the boundary controls, satisfy some classical assumptions and the angular velocity is smaller than a critical one.

AB - This paper deals with feedback stabilization of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the rigid body rotates with a nonconstant angular velocity. To stabilize this system, we propose a feedback law which consists of a control torque applied on the rigid body and either a dynamic boundary control moment or a dynamic boundary control force or both of them applied at the free end of the beam. Then it is shown that the closed loop system is well posed and exponentially stable provided that the actuators, which generate the boundary controls, satisfy some classical assumptions and the angular velocity is smaller than a critical one.

UR - http://www.scopus.com/inward/record.url?scp=20444406522&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=20444406522&partnerID=8YFLogxK

U2 - 10.1155/S1110757X04312027

DO - 10.1155/S1110757X04312027

M3 - Article

AN - SCOPUS:20444406522

VL - 2004

SP - 107

EP - 126

JO - Journal of Applied Mathematics

JF - Journal of Applied Mathematics

SN - 1110-757X

IS - 2

ER -