A machine tool includes a machine control unit to output control signals to drives for machine elements. A tool which machines a workpiece is thereby moved relative to the workpiece in a position-controlled manner. Arranged in a first region of one machine element is an active vibration damper to damp vibration in a second region of the machine elements as the workpiece is machined by the tool. In order to detect the vibration, a first sensor is arranged in the first region of the machine element and a second sensor is arranged on another machine element or in a different region of the one machine element. Actual values detected by the first and second sensors and corresponding target values are supplied to a dual controller which determines on the basis of these values, a resulting manipulated variable for the active vibration damper and actuates the active vibration damper accordingly.