Control of a riser through the dynamic of the vessel

Abstract

In this paper, we prove an exponential decay result for the energy associated to a flexible marine riser with vessel dynamics. By applying a control at the top boundary of the riser we shall attenuate its vibration in a fast manner. The method is based on the multiplier technique. The riser is modeled as a viscoelastic beam with a (slightly perturbed) standard relaxation kernel.

Keywords:

• exponential stabilization
• viscoelastic material
• relaxation function
• boundary control
• multiplier technique

AMS Subject Classifications:

• 35L20
• 93D15
• 93D20

Acknowledgements

The third author would like to thank King Fahd University of Petroleum and minerals for its continuous financial support.

Notes

No potential conflict of interest was reported by the authors.