Abstract: A control device of a machine tool includes a position controller and a model of a position-controlled axis. The position controller receives a position setpoint value, a corresponding actual position value and a compensation value; determines therefrom a resulting value; determines based on the resulting value an actuating signal; and outputs the actuating signal to the position-controlled axis. The position and/or the orientation of the tool relative to the workpiece are adjusted based on the actuating signal. A sequence of successive control errors is stored, in a storage device and read out sequentially in accordance with a sequence of the position setpoint values and supplied to the model. The model determines from the read-out control error a respective compensation value which is then supplied to the position controller, while simulating the mechanically dynamic behavior of the position-controlled axis.