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The accuracy and resolution of metrological devices (coordinate measuring machines -CMM-, interferometers, etc.) are greatly affected by their robustness to external vibrations. This is especially important in the case of micrometric and nanometric microscopes, such as atomic force microscopes (AFM). In such cases, active vibration control strategies are frequently used, requiring actuators capable of fast and accurate responses. Piezoelectric actuators meet these requirements but they suffer from two major drawbacks, hysteresis, and rate dependence, which must be taken into consideration in the design of the control strategy. The present work proposes a novel active vibration control strategy using piezoelectric actuators for metrological devices affected by low external loads. The control strategy combines a classical sky-hook feedback with a feedforward control. The effect of hysteresis is minimized by compensating the senstivity variations of the actuator in oscillatory movements. For the design of the feedforward law, the present work demonstrates that a stack piezoelectric actuator working as a damper admits a mathematical description fulfilling differential flatness. It also proposes a formulation of the active vibration damping problem in terms of a trajectory tracking command perfectly fitted to the flatness-based control law. This strategy obtains damping improvements in the entire frequency range of operation without the instability problems derived from high feedback gains.