Robust Output Tracking for an Euler-Bernoulli Beam with Boundary Displacement Error Measurement Only

The motivation of the present paper comes from a recent paper [SIAM J.Control Optim., 57(2019), 1890-1928] where by the adaptive control method, an output tracking problem for an Euler-Bernoulli equation was considered. Although the paper used both boundary displacement tracking error and its derivative, only the asymptotic convergence is achieved under a man-made condition which is not necessary. In this paper, however, we use only tracking error to asymptotically achieve robust output tracking by the internal model principle. Our method is much more straightforward: design an observer based error feedback control for specially chosen frozen coefficients of the disturbances and show that the closed-loop system is robust to all possible disturbances. The paper gives a first PDE example for which only asymptotic stability is pursued in output tracking by the internal model principle. The numerical simulations validate the proposed feedback control.