The robust trajectory tracking problem is stated and solved for a thin planar sandwich structure, consisting of two piezoelectric films, mounted on an elastic support. The proposed controller asymptotically stabilises the structure, and guarantees for the generalised co-ordinates, which are introduced to approximately describe the shape of the structure, an arbitrarily bounded steady-state tracking error. The considered reference trajectories are derivable functions of time, ,with time derivatives bounded in norm from the first up to the third order. Analytic knowledge of the dynamic model of the structure is not necessary for the design of the controller, which is robust with respect to variations of the geometrical and physical parameters of the structure, and provides the steady-state gravity force rejection.