Abstract:
A lithographic apparatus including: an 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 sequence of setpoints, wherein the transformation matrix is configured such that the controller output signals do not excite the compliant dynamics of the object in at least one degree of freedom.
Abstract:
The invention provides a method of determining a desired relative position between a first object of a lithographic apparatus and a second object of the lithographic apparatus, the method comprising: a. generating a measurement signal representing a position of the first object relative to the second object, at an initial relative position; b. determining a gradient associated with the initial relative position, based on the measurement signal; c. determining a position set point based on the gradient; d. 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 (P); a measurement system (MS) for measuring the position (APOS) of the object; an actuator system (AS) for positioning the object; a control system (CU, OBS) configured to drive the actuator system, wherein each sensor of the measurement system has an associated measurement area on the object, wherein a location of at least one measurement area on the object is dependent on the position of the object, wherein the control system (CU, OBS) comprises an observer (OBS) with a dynamic model of the object to estimate an internal dynamic behavior (IDB) 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 (CU, OBS) is configured to drive the actuator system (AS) in dependency of an output (IDB) of the observer (OBS) as well.
Abstract:
A lithographic apparatus including: an 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 sequence of setpoints, wherein the transformation matrix is configured such that the controller output signals do not excite the compliant dynamics of the object in at least one degree of freedom.
Abstract:
The invention provides a method to generate an acceleration setpoint profile for a movable object, wherein the method comprises: providing a time domain acceleration curve with finite acceleration time length, providing a time domain jerk curve with finite jerk time length, calculating a time domain convolution of the time domain acceleration curve and the time domain jerk curve to generate the acceleration setpoint profile, wherein the time domain jerk curve has a zero value at a start and an end of the finite jerk time length, and wherein an amplitude profile of the time domain jerk curve, when Fourier transformed into frequency domain, has an amplitude that decreases for higher frequencies with at least 60 dB per decade.