Boundary Stability Criterion for a Nonlinear Axially Moving Beam

• 成果类型: Article
• 署名作者: Cheng, Yi; Wu, Yuhu; Guo, Bao-Zhu
• 署名单位: Bohai University; Dalian University of Technology; Dalian University of Technology; North China Electric Power University; Chinese Academy of Sciences; Academy of Mathematics & System Sciences, CAS
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3124754
• 发表日期: 2022
• 页码: 5714-5729
• 关键词: mathematical models; Stability criteria; Structural beams; vibrations; strain; Numerical stability; Feedback control; Absolute stabilization; axially moving beam; boundary control; exponential stability

摘要

This article deals with, in the framework of absolute stability, boundary stabilization for a nonlinear axially moving beam under boundary velocity feedback controls. The nonlinear boundary control that satisfies a slope-sector condition covering many types of nonlinear control schemes is a negative feedback of the transverse velocity at the right eyelet of the moving beam. Under the nonlinear control scheme, the well-posedness of the nonlinear partial differential equation, which depends continuously on the initial value is investigated by means of the Faedo-Galerkin approximation and priori estimates. By exploiting the integral-type multiplier method, the exponential stability of the closed-loop system is established, where a novel energy like function is constructed. The numerical simulation examples using the finite element method are presented to illustrate the effectiveness of the established criterion of the controller.