Interpolating Control for Precision Positioning affected by pre-sliding Friction
Bibliographic record
Abstract
For wafer inspection, an X-Y stage is used to position the wafer under a probe, such as X-ray or similar, with an accuracy of tens of nano-meters or less. The point-to-point movement typically consists of three phases: “move” when the position is controlled to follow a so-called S-curve, “settle” when the position is made to enter the convergence window, and “idle” when residual vibrations are damped and the position reaches the set-point with required accuracy. The “move” and “settle” plants are characterized by double-integrator dynamics with viscous and Coulomb friction, and the “idle” plant by pre-sliding friction dynamics that can be modeled as one or more mass-spring-damper systems. Taking into account high-frequency parasitic resonances and anti-resonances, non-linearities, and uncertainties, it is in general difficult, or impossible, to design one linear regulator for all three phases. Hence, one regulator is generally applied for “move” and “settle”, and another one for the ”idle” phase. The problem of switching between the regulators, preferably in a bump-less way in order not to evoke the parasitic resonances, has been treated in an ad-hoc manner in the literature and in industrial practice. Here, we suggest bump-less transfer between the regulators based on interpolating control, using a recent, simple friction model that includes pre-sliding.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".