Vibration damping in a machine tool having multiple vibration detection

A machine tool, comprising:

• a plurality of machine elements;
• a plurality of drives operably connected to the machine elements in one-to-one correspondence for moving the machine elements relative to one another;
• a machine control unit configured to identify control signals for the drives and to output the control signals to the drives in order to move the machine elements 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;
• an active vibration damper arranged in a first region of one of the machine elements in order to damp a vibration occurring during machining of the workpiece by the tool in a second region of the one of the machine elements;
• a first sensor arranged in the first region of the one of the machine elements to detect the vibration to be damped in the second region of the one of the machine elements;
• a second sensor arranged on another one of the machine elements or in another region of the one of the machine elements;
• and
• a dual controller receiving a first actual value detected by the first sensor, a second actual value detected by the second sensor, and first and second target values, said dual controller configured to identify a resulting manipulated variable for the active vibration damper based on the detected first and second actual values and the first and second target values and to correspondingly activate the active vibration damper, said dual controller comprising a first controller to which the first target value and the first detected actual value are supplied and which identifies a first connection variable from the first target value and the first detected actual value, and a second controller to which the second target value, the second detected actual value, and the first connection variable are supplied and which identifies a resulting manipulated variable from the second target value, the second detected actual value, and the first connection variable.