We consider an initial and boundary value problem modelling the vibrations of a Bernoulli-Euler beam with an attached piezoelectric actuator. We show that the Sobolev regularity of the solution is by 1/2 + epsilon higher than that one obtains by simply using the Sobolev regularity of the control term. The main results concern the dependence of the space of exactly controllable initial data on the location of the actuator. Our approach is based on the Hilbert uniqueness method introduced by Lions [Controlabilite exacte des systemes distribues, Masson, Paris, 1988] combined with some results from the theory of diophantine approximation.