Anti-disturbance control for a nonlinear flexible beam with velocity disturbance at the boundary (Q6103048)

The paper considers the boundary anti-disturbance problem for a nonlinear flexible beam system described by a PDE with general output disturbance at the boundary. It is assumed that the signal \(z_{\mathrm{out}}(t) = (z(L, t), z_t (L,t) + d(t))\), where \(d\) is unknown disturbance, has been measured by sensors. The authors present the boundary control such that the system is stabilized under certain assumptions about the disturbance. The active disturbance rejection control approach was adopted to design an extended state observer including the boundary controller and the disturbance estimator. Existence and uniqueness of the solution to the closed-loop system are studied using the Galerkin approximation. The asymptotic stability of the control system is justified by means of a suitable Lyapunov function. At last, finite element numerical modeling is performed to demonstrate control efficiency.