Model predictive control of Czochralski crystal growth process
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Bibliographic record
Abstract
This paper presents a model predictive control (MPC) formulation for the Czochralski (CZ) crystal growth which is given by the discrete finite-dimensional system representation of a class of parabolic partial differential equations (PDEs) with time-varying features. The motivation behind this work is to address the problem of stabilizing, infinite horizon, linear quadratic regulator synthesis for PDEs with time-dependent parameters which affect the dynamics of the underlying system and appear in the state-space representation. The modal decomposition of the PDE facilitates its approximation by a finite-dimensional linear state-space system. A receding horizon regulator is proposed which incorporates the time-dependence of the PDE parameters and numerical simulations are carried out which demonstrate the optimal stabilization of the process under state and input constraints.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it