Two approaches to the stabilization of Euler-Bernoulli beam equation with control matched disturbance

The boundary feedback stabilization of a one-dimensional Euler-Bernoulli beam equation with the external disturbance flowing to the control end by the active disturbance rejection control (ADRC) and sliding mode control (SMC) are concerned. By the ADRC approach, the disturbance is estimated and canceled in real time. It is shown that the external disturbance can be attenuated in the sense that the resulting closed-loop system tends to any arbitrary given vicinity of zero as the time goes to infinity. In the second part, we use the SMC to reject the disturbance by removing the condition in ADRC that the derivative of the disturbance is supposed to be bounded. The existence and uniqueness of the solution for the closed-loop via SMC are proved, and the monotonicity of the “reaching condition” is presented. The numerical simulations validate the effectiveness of both methods.