Active vibration damper for attenuating an oscillation of a vibratory structure, in particular a crane, having - a sensor which can be mounted on the vibratory structure, said sensor being designed to detect a movement component of the structure movement relative to a reference system, and to generate a corresponding sensor signal, - a rotary motor which can be mounted on the vibratory structure and which has a motor encoder, - a carriage which can be linearly driven by way of the motor and which moves a damping mass (m Damping) coupled to the vibratory structure, - a transmission mechanism arranged between the motor and the carriage, which converts the rotary movement of the motor into a linear movement of the carriage with a predetermined mechanical advantage, and - a controlling unit, the measured variable input of which is connected to the sensor and the manipulated variable output of which is connected to the motor, the controlling unit being arranged such that on the basis of the sensor signal generated by the sensor a controlling signal is generated for the motor, with which the motor can be controlled such that the carriage and therefore the damping mass (m Damping) execute a movement relative to a vibratory structure to compensate for the oscillation of the vibratory system, the controlling unit having a position estimator which is designed such that on the basis of the sensor signal, which is preferably an acceleration signal (a), it generates a position signal (x) representing the actual position of the vibratory structure, said position signal (x) being scaled with a weighting factor d/m and converted into an angular velocity control signal, taking into account the mechanical advantage of the transmission mechanism, the angular velocity control signal being fed to a velocity controller of the controlling unit as a setpoint variable, characterised in that the controlling unit is set up such that an actual angular velocity (ω Mot) of the motor detected indirectly via the motor encoder is fed to the velocity controller with a negative sign as an actual variable and in that the controlling unit is designed such that on the basis of the sensor signal a velocity signal (v) is generated, which is scaled with a damping factor d, is converted, taking into account the mechanical advantage of the transmission mechanism, and is applied to the controlling signal generated by the velocity controller. - a sensor which can be mounted on the vibratory structure, said sensor being designed to detect a movement component of the structure movement relative to a reference system, and to generate a corresponding sensor signal, - a rotary motor which can be mounted on the vibratory structure and which has a motor encoder, - a carriage which can be linearly driven by way of the motor and which moves a damping mass (m Damping) coupled to the vibratory structure, - a transmission mechanism arranged between the motor and the carriage, which converts the rotary movement of the motor into a linear movement of the carriage with a predetermined mechanical advantage, and - a controlling unit, the measured variable input of which is connected to the sensor and the manipulated variable output of which is connected to the motor, the controlling unit being arranged such that on the basis of the sensor signal generated by the sensor a controlling signal is generated for the motor, with which the motor can be controlled such that the carriage and therefore the damping mass (m Damping) execute a movement relative to a vibratory structure to compensate for the oscillation of the vibratory system, the controlling unit having a position estimator which is designed such that on the basis of the sensor signal, which is preferably an acceleration signal (a), it generates a position signal (x) representing the actual position of the vibratory structure, said position signal (x) being scaled with a weighting factor d/m and converted into an angular velocity control signal, taking into account the mechanical advantage of the transmission mechanism, the angular velocity control signal being fed to a velocity controller of the controlling unit as a setpoint variable, characterised in that the controlling unit is set up such that an actual angular velocity (ω Mot) of the motor detected indirectly via the motor encoder is fed to the velocity controller with a negative sign as an actual variable and in that the controlling unit is designed such that on the basis of the sensor signal a velocity signal (v) is generated, which is scaled with a damping factor d, is converted, taking into account the mechanical advantage of the transmission mechanism, and is applied to the controlling signal generated by the velocity controller.