  We study output tracking and disturbance rejection for an Euler-Bernoulli
beam with Kelvin-Voigt damping. The system has distributed control and
pointwise observation. As our main result we design a finite-dimensional
low-order internal model based controller that is based on a spectral Galerkin
method and model reduction by Balanced Truncation. The performance of the
designed controller is demonstrated with numerical simulations and compared to
the performance of a low-gain internal model based controller.
