Starting from constitutive equations of a piezoelectric material, we built a Koiter shell model coupled with a piezoelectric actuator. After a mechanical interpretation of the effect of the actuator we prove a result of existence and uniqueness of the coupled model. We then discuss controllability results of Galerkin approximations of the model. The numerical tests carried out show the effectiveness of different control algorithms such as the projected Riccati algorithm. This efficiency depends strongly on the position and the shape of the actuator. We then study an algorithm for shape optimization based on the minimization of a criterion. The latter depends on the geometry of the actuator. The gradient of this criterion is calculated using domain derivation techniques.