Abstract: A stage system includes a movable stage, at least two encoder heads each constructed to provide an encoder signal representative of a position of the movable stage with respect to an encoder target structure, and a controller to control a position of the stage. The controller is provided with the encoder signals of each of the encoder heads. The controller is arranged to apply a weighting function to the encoder signals and to derive a position of the stage from the weighted encoder signals.

Abstract: A controller for a positioning device is constructed and arranged to receive a position signal indicative of a position of the positioning device, compare the position signal to a set-point signal indicative of a desired position of the positioning device to obtain an error signal, selectively modify the error signal based on the amplitude and the frequency content of the error signal to obtain a modified error signal, generate a control signal for controlling the positioning device on the basis of the modified error signal. The controller may be applied to control a positioning device in a lithographic apparatus.

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: 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.

Abstract: An optical disc drive apparatus (1) comprises: a read/write element (34) to be positioned with respect to the disc (2), and a detector (35) for generating a read signal (SR); actuator means (50) for controlling the positioning of said read/write element. A control circuit (90) receives said read signal and generates an actuator control signal (SCR), the control circuit having at least one variable gain (?). Said control circuit, actuator means, read/write element, and detector define a control loop (100) having a critical frequency (cocp). A non-linear state estimator (350) is used to selectively set said gain (?) to a first value for signal components having a frequency in a predefined range corresponding to said critical frequency (COCP) and to a second value for signal components having a frequency outside said range, said first value being lower than said second value.