Abstract: A method of determining a desired relative position between a first object of a lithographic apparatus and a second object of the lithographic apparatus. Generating a measurement signal representing a position of the first object relative to the second object, at an initial relative position. Determining a gradient associated with the initial relative position, based on the measurement signal. Determining a position set point based on the gradient and wherein the position set point comprises a three-dimensional dither signal. Controlling the position of the first object relative to the second object to a further relative position, based on the position set point.

Abstract: A method of determining a desired relative position between a first object of a lithographic apparatus and a second object of the lithographic apparatus. Generating a measurement signal representing a position of the first object relative to the second object, at an initial relative position. Determining a gradient associated with the initial relative position, based on the measurement signal. Determining a position set point based on the gradient and wherein the position set point comprises a three-dimensional dither signal. Controlling the position of the first object relative to the second object to a further relative position, based on the position set point.

Abstract: An object positioning system includes an object; a measurement system to measure the position of the object, wherein each sensor of the measurement system has an associated measurement area on the object and wherein a location of at least one measurement area on the object is dependent on the position of the object; an actuator system to position the object; a control system configured to drive the actuator system, wherein the control system includes an observer with a dynamic model of the object to estimate an internal dynamic behavior of the object, wherein the dynamic model includes the dependency of the location of at least one measurement area on the position of the object, and wherein the control system is configured to drive the actuator system in dependency of an output of the observer.

Abstract: An object positioning system including a movable object, an actuator system and a control system. The moveable object is moveable relative to a reference. The actuator system is configured to apply a force to the object at a force application location on the object in order to move the moveable object relative to the reference. The control system is configured to position a point of interest of the object relative to the reference. The control system is configured to drive the actuator system based on a parameter representing a spatial relationship between the force application location and the point of interest. The parameter is dependent on a further parameter representing a position of the object relative to the reference.

Abstract: A lithographic apparatus includes a driven object having compliant dynamics; a plurality of actuators configured to act on the driven object, wherein the plurality of actuators are over-determined in an actuator degree of freedom; a control system including a transformation matrix configured to generate controller output signals for each of the plurality of actuators in response to a setpoint, wherein the transformation matrix is configured such that the controller output signals do not excite the compliant dynamics of the driven object in at least one degree of freedom.

Abstract: An object positioning system including a movable object, an actuator system and a control system. The moveable object is moveable relative to a reference. The actuator system is configured to apply a force to the object at a force application location on the object in order to move the moveable object relative to the reference. The control system is configured to position a point of interest of the object relative to the reference. The control system is configured to drive the actuator system based on a parameter representing a spatial relationship between the force application location and the point of interest. The parameter is dependent on a further parameter representing a position of the object relative to the reference.

Abstract: An object positioning system includes an object; a measurement system to measure the position of the object, wherein each sensor of the measurement system has an associated measurement area on the object and wherein a location of at least one measurement area on the object is dependent on the position of the object; an actuator system to position the object; a control system configured to drive the actuator system, wherein the control system includes an observer with a dynamic model of the object to estimate an internal dynamic behavior of the object, wherein the dynamic model includes the dependency of the location of at least one measurement area on the position of the object, and wherein the control system is configured to drive the actuator system in dependency of an output of the observer.

Abstract: A lithographic apparatus includes a driven object having compliant dynamics; a plurality of actuators configured to act on the driven object, wherein the plurality of actuators are over-determined in an actuator degree of freedom; a control system including a transformation matrix configured to generate controller output signals for each of the plurality of actuators in response to a setpoint, wherein the transformation matrix is configured such that the controller output signals do not excite the compliant dynamics of the driven object in at least one degree of freedom.

Abstract: A lithographic apparatus includes an illumination system configured to condition a radiation beam, a support constructed to support a patterning device, the patterning device being capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam, a substrate table constructed to hold a substrate, a projection system configured to project the patterned radiation beam onto a target portion of the substrate, a chuck configured to hold and position an object, for example, the patterning device onto the support or the substrate onto the substrate table, the chuck including a base and a constraining layer. A damping layer including a viscoelastic material is provided between the base and the constraining layer.

Abstract: A controller is provided that controls an actuator system having a plurality of actuators arranged to act on an object. The controller uses a gain balancing matrix to convert a first control signal, representing a set of forces desired to be provided to the center of gravity of the object into a second control signal, representing an equivalent set of forces to be provided by the plurality of actuators. The system is further configured such that a first gain balancing matrix is used at a first frequency band and a second gain balancing matrix is used at a second frequency band.

Abstract: A servo control system to control a position of an object supported by a movable support includes a first measurement system to measure a position of the movable support, a comparative device to provide an error signal based on the comparison between a measured movable support position and a desired movable support position, a controller unit to provide a control signal based on the error signal, and an actuator configured to actuate the movable support based on the control signal. The servo control system further includes a slip compensation device to compensate a slip between the object and the movable support, the slip compensation device including a second measurement system to measure an object position with respect to the movable support, and an addition device to add a slip compensation signal to the measured movable support position or the error signal based on the measured object position.

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 is provided that controls an actuator system having a plurality of actuators arranged to act on an object. The controller uses a gain balancing matrix to convert a first control signal, representing a set of forces desired to be provided to the centre of gravity of the object into a second control signal, representing an equivalent set of forces to be provided by the plurality of actuators. The system is further configured such that a first gain balancing matrix is used at a first frequency band and a second gain balancing matrix is used at a second frequency band.

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: 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: A lithographic apparatus includes a movable part and a controller to control a position quantity of the movable part. The controller includes a first controller transfer function and a second controller transfer function. A selector selects the first controller transfer function or the second controller transfer function depending on a state of the movable part. The first controller transfer function may be chosen in a substantially stationary state of the movable part, while in a substantially non-stationary state of the movable part, the second controller transfer function may be chosen.

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 lithographic apparatus includes an illumination system configured to condition a radiation beam, a support constructed to support a patterning device, the patterning device being capable of imparting the radiation beam with a pattern in its cross-section to form a patterned radiation beam, a substrate table constructed to hold a substrate, a projection system configured to project the patterned radiation beam onto a target portion of the substrate, a chuck configured to hold and position an object, for example, the patterning device onto the support or the substrate onto the substrate table, the chuck including a base and a constraining layer. A damping layer including a viscoelastic material is provided between the base and the constraining layer.

Abstract: A lithographic apparatus includes a movable object and a control system to control the position of the movable object. The control system includes a position measurement system configured to measure the position of the movable object, a comparative unit configured to generate a servo error signal by subtracting a position signal representative of an actual position of the movable object from a reference signal, a control unit configured to generate a first control signal based on the servo error signal, a feed-forward unit configured to generate a feed-forward signal based on the reference signal, an addition unit configured to generate a second control signal by adding the first control signal and the feed-forward signal, and an actuator unit configured to actuate the movable object. A gain of the feed-forward unit is dependent on the position of the movable object.

Abstract: A servo control system to control a position of an object supported by a movable support includes a first measurement system to measure a position of the movable support, a comparative device to provide an error signal based on the comparison between a measured movable support position and a desired movable support position, a controller unit to provide a control signal based on the error signal, and an actuator configured to actuate the movable support based on the control signal. The servo control system further includes a slip compensation device to compensate a slip between the object and the movable support, the slip compensation device including a second measurement system to measure an object position with respect to the movable support, and an addition device to add a slip compensation signal to the measured movable support position or the error signal based on the measured object position.