Periodic Tracking Control Using Gain-Scheduled Fourier Series-Based Internal Models
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Bibliographic record
Abstract
Abstract This paper presents a gain-scheduled controller composed of a number of positive real controllers that contain internal models of reference command signals. Using the internal model principle as inspiration, and the Passivity Theorem to assure input-output closed-loop stability, the proposed controller is designed to realize tracking while maintaining input-output stability of the closed-loop system. The gain-scheduled nature of the internal models allows for a number of internal models to be simultaneously implemented. In particular, by expressing a periodic reference command as a Fourier series, the first few Fourier modes can be included as internal models in the controllers to be gain-scheduled, which reduces steady-state tracking error. An example involving tracking the outlet temperature of a heat exchanger is presented, where the first nine Fourier modes of the reference signal are used as internal models to reduce tracking error.
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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 | 0.001 |
| 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