Lithographic apparatus, substrate support system, device manufacturing method and control program

A substrate support system comprising

• a substrate table having compliant dynamics:
• a plurality of actuators configured to act on the substrate table, wherein the plurality of actuators are over-determined in an actuator degree of freedom;
• a control system comprising 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 substrate table in at least one degree of freedom.

A lithographic apparatus comprising:

• a driven object having compliant dynamics;
• a plurality of actuators configured to act on the driven object;
• a plurality of sensors each configured to provide a sensor signal indicative of a position or displacement of the driven object, wherein the plurality of sensors are over-determined in a sensor degree of freedom;
• a transformation matrix configured to transform the sensor signals so as to not observe the effects of the compliant dynamics of the driven object in at least one degree of freedom, and a control system configured to generate controller output signals for each of the plurality of actuators in response to a setpoint and the transformed sensor signals.

A device manufacturing method using a lithographic apparatus, the method comprising:

• supporting a substrate on a substrate table having compliant dynamics and a plurality of actuators configured to act on the substrate table:
• using a plurality of sensors to generate respective sensor signals that are indicative of a position of at least one of the substrate and the substrate table,
• wherein the plurality of sensors are over-determined in a sensor degree of freedom;
• projecting a patterned beam onto the substrate to expose it to the respective pattern whilst positioning the substrate table;
• and
• applying a transformation matrix to the sensor signals to generate transformed sensor signals, the transformation matrix being configured such that the transformed sensor signals do not observe the compliant dynamics of the substrate table in at least one degree of freedom.

A lithographic apparatus comprising:

• an object having compliant dynamics;
• a plurality of actuators configured to act on the object, wherein the plurality of actuators are over-determined in an actuator degree of freedom;
• a controller comprising 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 object in at least one degree of freedom.