Nonlinear Dynamics

, Volume 92, Issue 2, pp 531–541 | Cite as

Boundary control of an Euler–Bernoulli beam with input and output restrictions

  • Zhijie Liu
  • Jinkun Liu
  • Wei He
Original Paper


In this study, boundary control is considered for an Euler–Bernoulli beam subject to bounded input, bounded output, and external disturbances. Through utilizing the backstepping technology, a boundary control scheme is designed based on the original partial differential equations to regulate the vibration of the beam. An auxiliary system based on a smooth hyperbolic function is designed to handle the impact of the restricted input. And a barrier Lyapunov function is adopted to eliminate the impact of output restriction. It is proved that the input and output restrictions are circumvented simultaneously. Simulations are demonstrated for illustration.


Euler–Bernoulli beam Input and output restrictions Distributed parameter system Boundary control 



This work was supported by the National Natural Science Foundation of China [grant number 61374048] and the Excellence Foundation of BUAA for PhD Students [grant number 2017020].


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Copyright information

© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Automation Science and Electrical EngineeringBeihang UniversityBeijingChina
  2. 2.School of Automation and Electrical EngineeringUniversity of Science and Technology BeijingBeijingChina

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