Boundary Stability Criterion for a Nonlinear Axially Moving Beam

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...

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Bibliographic Details
Published in:IEEE transactions on automatic control 2022-11, Vol.67 (11), p.5714-5729
Main Authors: Cheng, Yi, Wu, Yuhu, Guo, Bao-Zhu
Format: Article
Language:English
Subjects:
Absolute stabilization
axially moving beam
Boundary control
exponential stability
Feedback control
Finite element method
Mathematical analysis
Mathematical models
Negative feedback
Nonlinear control
Nonlinear differential equations
Numerical stability
Partial differential equations
Stability criteria
Strain
Structural beams
Vibrations
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Summary: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.
ISSN:0018-9286
1558-2523
DOI:10.1109/TAC.2021.3124754