Vibration damping of a cantilever plate is achieved by using a piezoelectric element simultaneously as passive single-mode device and active broad-band actuator. Control strategies are designed on the basis of a modal model of the coupled electro-mechanical structure. This model is obtained by using a suitable finite-element formulation together with a modal analysis. A purely passive single-mode control composed of an optimally tuned external RL shunt circuit and a purely active control based on classical LQG techniques are compared to a semi-active control obtained by tuning the external shunt circuit on the second vibration mode of the structure and using a LQG controller designed on the only first-mode model.