Absolute boundary stabilization for an axially moving Kirchhoff beam. (July 2021)

• Record Type: Journal Article
• Authors: Cheng, Yi; Wu, Yuhu; Guo, Bao-Zhu
• Is Part Of: Automatica. Volume 129(2021)
• Publication Date: 2021-07
• Subjects: Axially moving Kirchhoff beam -- Boundary control -- Exponential stability -- Absolute stabilization; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2021.109667
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: In this paper, we consider absolute stability for an axially moving Kirchhoff beam under nonlinear boundary feedback controls. The nonlinear boundary control which satisfies a slope-restricted condition is a negative feedback of the transverse velocity at the right eyelet of the moving beam. First, the well-posedness of the resulting closed-loop system is established by means of the Faedo–Galerkin approximation combined with some priori estimates. By invoking the integral-type multiplier method, the exponential stability of the closed-loop is developed. The numerical simulations by the finite element method are presented to demonstrate the effectiveness of the proposed controller.