Gain Balancing Matrix Controller for Lithographic Apparatus Resonance
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Solution Overview
Problem
Lithographic apparatus control systems face positioning errors due to resonant frequencies of the object, which can lead to stability issues and unacceptably large position errors, especially when deformation affects measurement accuracy.
Innovation Solution
A controller system using gain balancing matrices to convert control signals for an actuator system, with different matrices applied in different frequency bands to manage resonant frequencies and maintain system stability, ensuring accurate positioning.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If the bandwidth of the control system is lowered to avoid stability problems induced by resonant frequencies, then system stability is improved, but positioning accuracy deteriorates with unacceptably large position errors
Solution Approach 1:
The patent applies parameter changes by using frequency-dependent gain balancing matrices that adapt the control parameters based on the frequency band of the control signal. Different matrices are selected based on the frequency content of the signal, allowing the system to optimize performance for different frequency ranges rather than using a fixed parameter set throughout the entire bandwidth.
Solution Approach 2:
The control system implements dynamics by making the gain balancing matrix dynamic rather than static. The system automatically switches between different gain balancing matrices based on the frequency band of the control signal, enabling the controller to adapt its behavior in real-time to maintain stability at low frequencies while preserving accuracy at high frequencies.
2Measurement precision
If position measurements are taken at multiple locations on the object to determine rotation, then measurement precision is improved, but positioning accuracy deteriorates due to deformation-induced erroneous determination
Solution Approach 1:
The patent addresses this contradiction by changing the control parameters dynamically based on frequency. The gain balancing matrices are specifically designed to account for the relationship between multiple position measurements and the resulting rotation calculations, adjusting the weighting and combination of measurements based on the frequency band to minimize deformation-induced errors while maintaining measurement precision.
Data Source
AI summary
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.