Stabilisation of Timoshenko beam system with a tip payload under the unknown boundary external disturbances

Abstract

This paper is concerned with the boundary stabilisation of a Timoshenko beam with a tip payload under the boundary external disturbances. Nonlinear feedback control laws are designed to reduce the effects of the external disturbances. Since the controlled system is nonlinear, the well posedness of the nonlinear closed-loop system is investigated using the theory of nonlinear maximal monotone operators and the variational principle. In addition, we show the exponential stability of the nonlinear controlled system using the Lyapunov direct method. In the end, the numerical simulations are displayed to illustrate the effectiveness of the proposed boundary controls.

Keywords:

• Timoshenko beam
• feedback control
• nonlinear monotone operators
• exponential stability

Acknowledgements

The authors would like to express their gratitude to the editors and the anonymous reviewers whose valuable comments and suggestions were very helpful to the improvement of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research is supported by the Natural Science Foundation of China[grant number 61174080].