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Nonlinear Dynamics

, Volume 95, Issue 2, pp 1395–1413 | Cite as

Dynamic modeling and vibration control of a three-dimensional flexible string with variable length and spatiotemporally varying parameters subject to input constraints

  • Xueyan Xing
  • Jinkun LiuEmail author
  • Zhijie Liu
Original Paper
  • 155 Downloads

Abstract

In this paper, a three-dimensional dynamic model is developed for a flexible string system with variable length as well as spatiotemporally varying parameters. The dynamic system model is described by coupled partial differential equations and ordinary differential equations. On the basis of the established model, a boundary control method is proposed via backstepping technology and Nussbaum functions to eliminate the vibration of the three-dimensional string with input constraints and disturbances. Deformations of the three-dimensional string system can be verified to converge to small neighborhoods of zero under the proposed control. Input constraints can also be guaranteed by applying smooth hyperbolic tangent function. Simulation results present that the vibration suppression of the flexible string can be achieved and input constraints can be ensured with the proposed control scheme.

Keywords

Three-dimensional flexible string Variable length Dynamic modeling Vibration control Input constraints Nussbaum function 

Notes

Acknowledgements

This work was supported by the Research Fund for the National Natural Science Foundation of China [Grant Number 61873296].

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Automation Science and Electrical EngineeringBeihang UniversityBeijingPeople’s Republic of China

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