Lithographic motion control system and method

• US 20050267609A1
• Filed: 05/25/2004
• Published: 12/01/2005
• Est. Priority Date: 05/25/2004
• Status: Active Grant

• Current Assignee: ASML Netherlands BV (ASML Holding NV)
• Original Assignee: ASML Netherlands BV (ASML Holding NV)
• Inventors: Maria Van Den Biggelaar, Petrus Marinus Christianus, Van Donkelaar, Edwin Teunis
• Granted Patent: US 7,289,858 B2
• Time in Patent Office: Days
• US Class Current: 700/45
• CPC Class Codes: G05B 13/042 in which a parameter or coefficient is automatically adjusted to optimise the performance
• CPC Class Codes: G05B 21/02 electric

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.

Claims

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.

2. The lithographic apparatus of claim 1, wherein the setpoint delay function comprises an integer multiple of a sample time of the control system.

3. The lithographic apparatus of claim 2, wherein said feed-forward transfer function second part comprises said actuator transfer function potentially unstable inverse part which has been modified so that it contains a zero mirrored in a unity circle in a z-domain.

4. The lithographic apparatus of claim 1, wherein said setpoint delay function comprises said actuator transfer function potentially unstable inverse part and said feed-forward transfer function second part comprises a zero delay.

5. The lithographic apparatus of claim 1, wherein said feed-forward path and said setpoint path each comprise a further delay equal to at least one sample time of the control system to make the control system causal.

6. A method for controlling a parameter of a lithographic apparatus in response to a setpoint signal, said method comprising:

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.

7. A control system for controlling a parameter, 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 unstable remainder of the actuator transfer function.

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:

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.

9. The method of claim 8, wherein said optimization algorithm comprises an ARX optimization model.