The global analytical modeling of a clamped plate equipped with piezoelectric sensor and actuator is developed. The vibrations of the plate are damped with a Linear Quadratic (LQ) control which exceeds the maximum voltage delivered by the piezoelectric actuator supplier, leading to a saturated imput. To deal with this problem of saturation, a sliding mode control is designed and the stability of the controlled system is examined via a Lyapunov approach.