Machine tool, - wherein the machine tool has a plurality of machine elements, - wherein the machine elements can be moved relative to one another via drives of the machine tool, - wherein the machine tool has a machine control unit which identifies control signals for the drives and outputs them to the drives in order to move the machine elements of the machine tool relative to one another in a position-controlled manner, such that a tool which machines a workpiece is moved relative to the workpiece in a position-controlled manner, - wherein at least one active vibration damper is arranged in a first region of one of the machine elements in order to damp a vibration occurring during the machining of the workpiece by the tool in a second region of said machine element, - wherein a first sensor is arranged in order to detect the vibration to be damped at least in the first region of said machine element and a second sensor is arranged on another machine element or in another region of said machine element, in particular in the second region of said machine element, - wherein a first actual value detected by means of the first sensor and a second actual value detected by means of the second sensor as well as a first and a second target value (I1*, I2*) are supplied to a dual controller, - wherein the dual controller identifies a resulting manipulated variable (F*) for the active vibration damper on the basis of the detected first and the detected second actual value (I1, I2) and of the first and the second target value (I1*, I2*) and correspondingly activates the active vibration damper, characterised in that - the dual controller comprises a first controller to which the first target value (I1*) and the first detected actual value are supplied and which identifies a first connection variable therefrom, and - wherein the dual controller comprises a second controller to which the second target value (I2*) and the second detected actual value as well as the first connection variable are supplied and which identifies the resulting manipulated variable (F*) therefrom, - that the dual controller has a pilot-control block to which the first target value (I1*) and the first detected actual value are supplied and which identifies a second connection variable therefrom, and that the dual controller connects the second connection variable to the provisional manipulated variable (F'*) and in this way identifies the resulting manipulated variable (F*). - wherein the machine tool has a plurality of machine elements, - wherein the machine elements can be moved relative to one another via drives of the machine tool, - wherein the machine tool has a machine control unit which identifies control signals for the drives and outputs them to the drives in order to move the machine elements of the machine tool relative to one another in a position-controlled manner, such that a tool which machines a workpiece is moved relative to the workpiece in a position-controlled manner, - wherein at least one active vibration damper is arranged in a first region of one of the machine elements in order to damp a vibration occurring during the machining of the workpiece by the tool in a second region of said machine element, - wherein a first sensor is arranged in order to detect the vibration to be damped at least in the first region of said machine element and a second sensor is arranged on another machine element or in another region of said machine element, in particular in the second region of said machine element, - wherein a first actual value detected by means of the first sensor and a second actual value detected by means of the second sensor as well as a first and a second target value (I1*, I2*) are supplied to a dual controller, - wherein the dual controller identifies a resulting manipulated variable (F*) for the active vibration damper on the basis of the detected first and the detected second actual value (I1, I2) and of the first and the second target value (I1*, I2*) and correspondingly activates the active vibration damper, characterised in that - the dual controller comprises a first controller to which the first target value (I1*) and the first detected actual value are supplied and which identifies a first connection variable therefrom, and - wherein the dual controller comprises a second controller to which the second target value (I2*) and the second detected actual value as well as the first connection variable are supplied and which identifies the resulting manipulated variable (F*) therefrom, - that the dual controller has a pilot-control block to which the first target value (I1*) and the first detected actual value are supplied and which identifies a second connection variable therefrom, and that the dual controller connects the second connection variable to the provisional manipulated variable (F'*) and in this way identifies the resulting manipulated variable (F*).