Robust output feedback Control for an Euler-Bernoulli Beam Equation

In this paper, we address a two output tracking problem under the guidance of the internal model principle for an Euler-Bernoulli beam equation, which is motivated from a recent paper [SIAM J. Control Optim., 57 (2019), 1890-1928] where an adaptive control approach was used to estimate in real time all coefficients of the external harmonic disturbance. Compared with the aforementioned paper, we improve the results significantly from several aspects: a) both position and velocity are regulated simultaneously instead of a single position; b) the convergence is uniformly exponentially instead of asymptotically; c) the control contains essentially the internal model and is therefore conditionally robust; d) a manmade condition has been removed with a necessary assumption only. Our approach is systematic and straightforward in dealing with other PDEs with the same kind.