Boundary feedback stabilization of a rotating body-beam system

Laousy, H.; Xu, Cheng-Zhong; Sallet, Gauthier

doi:10.1109/9.481526

Cited by 63 publications

(45 citation statements)

References 6 publications

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“…Then, as in the linear case [16] it will be shown that, in our case, the equilibrium point of (1.1) is still exponentially stabilizable.…”

supporting

confidence: 57%

“…The stabilization problem of similar systems has been studied in [17,18] and [19]. Recently, for the body-beam system without damping, exponential stabilization was established in [16] as soon as at least one of two linear boundary controls (force or moment) is present at the free end of the beam with, in addition, a control torque of the disk. The last result on this subject has been obtained by Coron and d'Andréa-Novel [9]: without damping nor controls on the free boundary of the beam, the authors found a torque control which insured the strong stability of the system but not the exponential one.…”

mentioning

confidence: 99%

“…The contribution of this paper consists in extending the class of controls proposed in [16] for the system without damping to a nonlinear one. In fact, this work is motivated by two arguments: first, the interest of such an extension is to highlight the robustness of controls which is a very desirable property.…”

mentioning

confidence: 99%

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Nonlinear feedback stabilization of a rotating body-beam without damping

Chentouf

Couchouron

1999

ESAIM: COCV

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Abstract. This paper deals with nonlinear feedback stabilization problem of a flexible beam clamped at a rigid body and free at the other end. We assume that there is no damping and the feedback law proposed here consists of a nonlinear control torque applied to the rigid body and either a 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.Résumé. On aborde dans cet article un problème de stabilisation par feedback non linéaire d'un système constitué d'une poutre flexible fixéeà l'une de ses extrémitésà un corps rigide et libreà l'autre extrémité. On suppose qu'il n'y a pas de frottements; on propose alors une loi de commande composée d'une part d'un contrôle de couple exercé sur le disque et d'autre part d'un contrôle de force et/ou d'un contrôle de moment appliquéà l'extrémité libre de la poutre. On montre ici que cette loi de commande non linéaire assure l'amortissement exponentiel des vibrations de la poutre. Cette conclusion est une extension des résultats antérieurs obtenus avec des contrôles linéaires dans le sens où notre classe de contrôle est plus large.

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“…Then, as in the linear case [16] it will be shown that, in our case, the equilibrium point of (1.1) is still exponentially stabilizable.…”

supporting

confidence: 57%

mentioning

confidence: 99%

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Nonlinear feedback stabilization of a rotating body-beam without damping

Chentouf

Couchouron

1999

ESAIM: COCV

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“…Laousy et al [14] proved the exponentially stability of the system (without amortization) for two boundary linear controls at the free extremity of the beam (Γ 1 (t) = −αu tx (L, t); Γ 2 (t) = βu tx (L, t)) and a control of moment type (Γ 3 (t) = −γ(ω(t) − w * ). Chentouf and Couchouron [6] extended the results of [14] by a class of non linear boundary controls…”

Section: Introductionmentioning

confidence: 99%

Attachment observability of a rotating body-beam

Deguenon

Bărbulescu

2013

Analele Universitatii "Ovidius" Constanta - Seria Matematica

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In this article we analyze the admissibility and the exact observability of a body-beam system when the output is taken in a point of attachment from the beam to the body. The single output case chosen here is the practical measurement of the strength, its velocity or its moment. We prove the exact observability for the moment and the admissibility for the other cases. These results are obtained by the spectral properties of rotating body beam system operator and Ingham's inequalities.

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“…[2,3,6,15]) u tt (x, t) + u xxxx (x, t) = ω 2 (t)u(x, t) i n ( 0 , 1) × (0, T ), ( e.g. [5,6,9,15]) to globally asymptotically stabilize the equilibrium point (0,ω) provided ω ∈ (−ω c , ω c ), (1.5) where ω c is an explicit critical angular velocity (see, e.g. [6,15]).…”

Section: Introductionmentioning

confidence: 99%

Optimal Control of a Rotating Body Beam

Liu

2002

ESAIM: COCV

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Abstract. In this paper we consider the problem of optimal control of the model for a rotating body beam, which describes the dynamics of motion of a beam attached perpendicularly to the center of a rigid cylinder and rotating with the cylinder. The control is applied on the cylinder via a torque to suppress the vibrations of the beam. We prove that there exists at least one optimal control and derive a necessary condition for the control. Furthermore, on the basis of iteration method, we propose numerical approximation scheme to calculate the optimal control and give numeric examples.Mathematics Subject Classification. 49K20, 35L75, 74K10.

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Boundary feedback stabilization of a rotating body-beam system

Cited by 63 publications

References 6 publications

Nonlinear feedback stabilization of a rotating body-beam without damping

Nonlinear feedback stabilization of a rotating body-beam without damping

Attachment observability of a rotating body-beam

Optimal Control of a Rotating Body Beam

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