### Abstract

In this article, the stabilization problem of a rotating disk-beam system is addressed. It is assumed that the flexible beam is free at one end, whereas the other end is attached to the center of the rotating disk whose angular velocity is time-varying. The proposed feedback law consists of a torque control which acts on the disk, whereas a delayed boundary force control is exerted at the free end of the beam. Thereafter, it is proved that the presence of such controls in the system guarantees the exponential stability of the system under a realistic smallness condition on the angular velocity of the disk as well as the feedback gain in the delay term. This result is illustrated by numerical examples.

Original language | English |
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Pages (from-to) | 2249-2259 |

Number of pages | 11 |

Journal | Nonlinear Dynamics |

Volume | 78 |

Issue number | 3 |

DOIs | |

Publication status | Published - Oct 22 2014 |

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### Keywords

- Delayed boundary force control
- Exponential stability
- Nonlinear system
- Rotating flexible structure
- Torque control

### ASJC Scopus subject areas

- Applied Mathematics
- Mechanical Engineering
- Aerospace Engineering
- Ocean Engineering
- Electrical and Electronic Engineering
- Control and Systems Engineering

### Cite this

*Nonlinear Dynamics*,

*78*(3), 2249-2259. https://doi.org/10.1007/s11071-014-1592-x

**Stabilization of the rotating disk-beam system with a delay term in boundary feedback.** / Chentouf, Boumediene.

Research output: Contribution to journal › Article

*Nonlinear Dynamics*, vol. 78, no. 3, pp. 2249-2259. https://doi.org/10.1007/s11071-014-1592-x

}

TY - JOUR

T1 - Stabilization of the rotating disk-beam system with a delay term in boundary feedback

AU - Chentouf, Boumediene

PY - 2014/10/22

Y1 - 2014/10/22

N2 - In this article, the stabilization problem of a rotating disk-beam system is addressed. It is assumed that the flexible beam is free at one end, whereas the other end is attached to the center of the rotating disk whose angular velocity is time-varying. The proposed feedback law consists of a torque control which acts on the disk, whereas a delayed boundary force control is exerted at the free end of the beam. Thereafter, it is proved that the presence of such controls in the system guarantees the exponential stability of the system under a realistic smallness condition on the angular velocity of the disk as well as the feedback gain in the delay term. This result is illustrated by numerical examples.

AB - In this article, the stabilization problem of a rotating disk-beam system is addressed. It is assumed that the flexible beam is free at one end, whereas the other end is attached to the center of the rotating disk whose angular velocity is time-varying. The proposed feedback law consists of a torque control which acts on the disk, whereas a delayed boundary force control is exerted at the free end of the beam. Thereafter, it is proved that the presence of such controls in the system guarantees the exponential stability of the system under a realistic smallness condition on the angular velocity of the disk as well as the feedback gain in the delay term. This result is illustrated by numerical examples.

KW - Delayed boundary force control

KW - Exponential stability

KW - Nonlinear system

KW - Rotating flexible structure

KW - Torque control

UR - http://www.scopus.com/inward/record.url?scp=84910149779&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84910149779&partnerID=8YFLogxK

U2 - 10.1007/s11071-014-1592-x

DO - 10.1007/s11071-014-1592-x

M3 - Article

AN - SCOPUS:84910149779

VL - 78

SP - 2249

EP - 2259

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 3

ER -