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A predictive control method to perform the active damping of a flexible structure is here presented. The studied structure is a clamped-free beam equipped with collocated piezoelectric actuator/sensor. Piezoelectric transducers advantages lie in their compactness and reliability, making them commonly used in aeronautic applications, context in which our study fits. Theirs collocated placement allow the use of well-known control strategies with guaranteed stability. First an analytical model of this equipped beam is given, using the Hamilton's principle and the Rayleigh-Ritz method. After a review of the experimental setup (and notably of the piezoelectric transducers), two control laws are described. The chosen one, generalized predictive control (GPC), is compared to a typical control law in the domain of flexible structures, the positive position feedback, one of the control law mentioned above. Major befits of GPC lie in its robustness in front of model uncertainties and others disturbances. The results given come from experiments on the structure which performed by a DSP. GPC appears to suit for the considered study's context (i.e. damping of the first vibration mode). Some improvements may be reached. Among them, a more complex structure with more than a single mode to damp, and more uncertainties may be considered.