Lithographic motion control system and method
First Claim
1. A lithographic apparatus, comprising:
- a control system that controls a parameter of the lithographic apparatus, said control system comprising;
an actuator configured to adjust said parameter, said actuator having an actuator transfer function that comprises a stable inverse part and a remainder comprising a potentially unstable inverse part;
a feed-forward path comprising a feed-forward controller having a feed-forward controller transfer function, said feed-forward controller transfer function comprising a first part and a second part, said feed-forward controller transfer function first part comprising an inverse of said actuator transfer function stable inverse part;
a feed-back loop comprising a feed-back controller, said actuator, and a difference determinator having a difference determinator setpoint input and a difference determinator feed-back input, said difference determinator configured to determine a difference between respective signals at the difference determinator setpoint input and the difference determinator feed-back input; and
a setpoint path from the setpoint input to the difference determinator setpoint input, said setpoint path comprising a setpoint delay function, wherein said feed-forward transfer function second part is configured such that a difference in delay between the setpoint delay function and said feed-forward transfer function second part is equal to a delay of said potentially instable remainder of the actuator transfer function.
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Abstract
A lithographic apparatus comprising a control system, such as a motion control system, is presented. The control system includes an actuator for effecting a movement of a moveable part and a feed-forward path from a setpoint input of the control system to the actuator. The control system further includes a feed-back loop, a feed-forward transfer function of the feed-forward path having a feed-forward transfer function part which is an inverse of a part of the actuator transfer function having a stable inverse, the actuator transfer function including a part having a stable inverse and a remainder potentially having an unstable inverse. The setpoint path includes a setpoint delay function, and the feed-forward transfer function further includes a second feed-forward transfer function part. A difference in delay between the setpoint delay function and the second feed-forward transfer function part is equal to a delay of the potentially unstable remainder of the actuator transfer function. Further, a method is described to find an optimal feed-forward controller directly on the basis of measured data.
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Citations
9 Claims
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1. A lithographic apparatus, comprising:
a control system that controls a parameter of the lithographic apparatus, said control system comprising;
an actuator configured to adjust said parameter, said actuator having an actuator transfer function that comprises a stable inverse part and a remainder comprising a potentially unstable inverse part;
a feed-forward path comprising a feed-forward controller having a feed-forward controller transfer function, said feed-forward controller transfer function comprising a first part and a second part, said feed-forward controller transfer function first part comprising an inverse of said actuator transfer function stable inverse part;
a feed-back loop comprising a feed-back controller, said actuator, and a difference determinator having a difference determinator setpoint input and a difference determinator feed-back input, said difference determinator configured to determine a difference between respective signals at the difference determinator setpoint input and the difference determinator feed-back input; and
a setpoint path from the setpoint input to the difference determinator setpoint input, said setpoint path comprising a setpoint delay function, wherein said feed-forward transfer function second part is configured such that a difference in delay between the setpoint delay function and said feed-forward transfer function second part is equal to a delay of said potentially instable remainder of the actuator transfer function. - View Dependent Claims (2, 3, 4, 5)
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6. A method for controlling a parameter of a lithographic apparatus in response to a setpoint signal, said method comprising:
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providing an actuator configured to adjust said parameter, said actuator having an actuator transfer function that comprises a stable inverse part and a remainder comprising a potentially unstable inverse part;
deriving a feed-forward signal from the setpoint signal via a feed-forward path, said feed-forward path comprising a feed-forward controller having a feed-forward controller transfer function, said feed-forward controller transfer function comprising a first part and a second part, said feed-forward controller transfer function first part comprising an inverse of said actuator transfer function stable inverse part;
supplying said feed-forward signal to said actuator;
providing a feed-back loop comprising a feed-back controller, said actuator, and a difference determinator having a difference determinator setpoint input and a difference determinator feed-back input;
determining a difference between respective signals at said difference determinator setpoint input and said difference determinator feed-back input;
supplying said setpoint signal, via a setpoint path, from said setpoint input to said difference determinator setpoint input;
delaying said setpoint signal in said setpoint path by a setpoint path delay function; and
delaying said feed-forward signal in said feed-forward path by said feed-forward transfer function second part, wherein said feed-forward transfer function second part is configured such that a difference in delay between said setpoint delay function and said feed-forward transfer function second part is equal to a delay of said potentially instable remainder of the actuator transfer function.
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7. A control system for controlling a parameter, comprising:
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an actuator configured to adjust said parameter, said actuator having an actuator transfer function that comprises a stable inverse part and a remainder comprising a potentially unstable inverse part;
a feed-forward path comprising a feed-forward controller having a feed-forward controller transfer function, said feed-forward controller transfer function comprising a first part and a second part, said feed-forward controller transfer function first part comprising an inverse of said actuator transfer function stable inverse part;
a feed-back loop comprising a feed-back controller, said actuator, and a difference determinator having a difference determinator setpoint input and a difference determinator feed-back input, said difference determinator configured to determine a difference between respective signals at the difference determinator setpoint input and the difference determinator feed-back input; and
a setpoint path from the setpoint input to the difference determinator setpoint input, said setpoint path comprising a setpoint delay function, wherein said feed-forward transfer function second part is configured such that a difference in delay between the setpoint delay function and said feed-forward transfer function second part is equal to a delay of said potentially unstable remainder of the actuator transfer function.
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8. A method for dimensioning a transfer function of a feed-forward path in a control system comprising a feed-forward and a feed-back loop, said method comprising:
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providing a time dependent setpoint signal;
measuring a control error of said feed-back loop over time and in response to said setpoint signal;
filtering said setpoint signal based on characteristics of said feed-back loop;
defining a cost function comprising a difference between the measured control error and a product of said feed-forward transfer function and said setpoint signal; and
optimizing parameters of said feed-forward transfer function by applying an optimization algorithm directed to minimizing the cost function with respect to said measured setpoint signal and the measured control error. - View Dependent Claims (9)
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Specification