Stabilization for a cable with tip mass under boundary input disturbance

Abstract

The stabilization problem for a cable with tip mass subject to boundary input disturbance is concerned in this paper. First, a nonlinear feedback controller is designed using sliding mode control method to reject the disturbance. Second, observation blind point which leads to zero output is found in this system. Third, the existence of the solution is obtained based on the solvability of a class of variational equations. Finally, by the LaSalle's Invariance Principle-like together with the observation blind point theory, we show the closed loop system converges asymptotically to zero.

Keywords:

• Cable with tip mass
• nonlinear controllers
• boundary disturbance
• asymptotic behavior

AMS Subject Classifications:

• 93D15
• 93C20
• 35B35
• 35P10

Acknowledgements

The authors would like to thank the referees for their useful and helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [NSFC-61903005, 61503276, 61773277].