Abstract: In a method for controlling a positioning device, the positioning device has a stator and mover, the mover being movable relative to the stator; a position sensor configured to generate a position signal indicative of a position of the mover relative to the stator; a controller configured to receive the position signal, compare it to a setpoint signal to obtain an error signal, and generate a mover control signal on the basis of a signal component of the position signal, the controller having a variable gain. The positioning device, including the position sensor and the controller, defines a control loop. For error signals having a magnitude in a predefined range, the gain is selectively set to a value higher than a value for error signals having a magnitude outside the range.

Abstract: A stage system for a lithographic apparatus includes a stage, an over-determined number of actuators to act on the stage, at least two sensors to measure a position dependent parameter of the stage and to provide a respective sensor signal. The at least two sensors are arranged to measure the respective position dependent parameters in a same degree of freedom. A controller is provided to provide a controller output signal to at least one of the actuators in response to a setpoint and the position dependent parameter as measured by at least one of the sensors. A further controller is provided with the position dependent parameters measured by the sensors. The further controller is configured to determine a difference between the position dependent parameters from the sensors and to provide a further controller output signal to at least one of the actuators in response to the determined difference.

Abstract: In a lithographic apparatus, a feedforward transfer function of a control system, is determined by: a) iteratively learning a feedforward output signal of the control system by iterative learning control for a given setpoint signal; b) determining a relation between the learned feedforward output signal and the setpoint signal; and c) applying the relation as the feedforward transfer function of the control system. A learned feedforward, which has been learned for one or more specific setpoint signals only, can be adapted to provide a setpoint signal dependent feedforward output signal. The learned feedforward can be made more robust against setpoint variations.