Stability of a nonlinear axially moving string

Authors:
S. M. Shahruz;Ahmed H. El-Shaer
Affiliations:
Berkeley Engineering Research Institute, Berkeley, CA;Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA
Venue:
ACC'09 Proceedings of the 2009 conference on American Control Conference
Year:
2009

Citing 2
Cited 0

Stability and Stabilization of Infinite Dimensional Systems with Applications

Stability and Stabilization of Infinite Dimensional Systems with Applications
Technical Communique: Boundary Control of the Axially Moving Kirchhoff String

Automatica (Journal of IFAC)

Quantified Score

Hi-index	0.00

Visualization

Abstract

In this paper, a nonlinear axially moving string with the Kelvin-Voigt damping is considered. It is proved that the string is stable, i.e., its transversal displacement converges to zero when the axial speed of the string is less than a certain critical value. The proof is established by showing that a Lyapunov function corresponding to the string decays to zero exponentially. It is also shown that the string displacement is bounded when a bounded distributed force is applied to it transversally. Furthermore, a few open problems regarding the stability and stabilization of strings with the Kelvin-Voigt damping are stated.