In this paper, the problem of damping the impact induced vibrations of a circular ring is studied. Finite dimensional models of the structure are derived, based on the use of the eigenfunctions of the vibrating structure. The impacts are modelled by using the Valentine variables method in order to take into account the presence of the inequality constraint. The controllability of the finite-dimensional approximate models of the systems by means of the available control inputs is studied. Finally, the performance of a derivative control law is investigated.