Two Approaches to Stabilization for Euler-Bernoulli Beam Equation with Boundary Moment Control and Disturbance

In this paper, we consider boundary stabilization for a one-dimensional Euler-Bernoulli equation with boundary moment control and disturbance. The active disturbance rejection control (ADRC) and sliding mode control (SMC) approaches are adopted in investigation. By the ADRC approach, an extended state observer with time varying gain is designed to estimate the disturbance. It is shown that the closed-loop system is asymptotically stable after canceling the disturbance in the feedback loop. In the second part, the SMC is applied to reject the disturbance. The well-posedness of the closedloop system via SMC is proven and the monotonicity of the “reaching condition” is presented without differentiation for the sliding mode function which may not always exist for the weak solution. The numerical experiments are presented to illustrate the convergence and the peaking value reduction caused by the constant high gain in literature. The control energy is compared numerically for two approaches.