Sliding mode vibration control of an Euler–Bernoulli beam with unknown external disturbances

• Published in: Nonlinear dynamics Vol. 110; no. 2; pp. 1393 - 1404
• Main Authors: Wang, Zhan, Wu, Wei, Görges, Daniel, Lou, Xuyang
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.10.2022; Springer Nature B.V
• Subjects: Automotive Engineering; Boundary control; Classical Mechanics; Closed loop systems; Control; Controllers; Design; Disturbances; Dynamical Systems; Engineering; Euler-Bernoulli beams; Liapunov functions; Mathematical models; Mechanical Engineering; Ordinary differential equations; Original Paper; Partial differential equations; Robustness (mathematics); Sliding mode control; Vibration; Vibration control; Boundary control; Euler–Bernoulli beam; Distributed parameter system; Sliding mode control
• ISSN: 0924-090X; 1573-269X
• DOI: 10.1007/s11071-021-06921-2

This paper addresses the stabilization problem of an Euler–Bernoulli beam system subject to an unknown time-varying distributed load and boundary disturbance. Based on Lagrangian–Hamiltonian mechanics, the model of the beam system is derived as a partial differential equation. Based on Lyapunov functions, a sliding surface is designed, on which the system exhibits exponential bounded stability and robustness against the external disturbances. A sliding mode controller which only uses boundary information is further proposed to drive the system to reach the sliding surface in finite time. Numerical simulations are shown to illustrate the validity of the proposed boundary control.