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

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.