Approximate Pole Placement with Dominance for Continuous Delay Systems by PID Controllers
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Bibliographic record
Abstract
Abstract It is well known that a continuous‐time feedback system with time delay has infinite spectrum and it is not possible to assign such infinite spectrum with a finite‐dimensional controller. In such a case, only the partial pole placement may be feasible and hopefully some of the assigned poles are dominant. But there is no easy way to guarantee dominance of the desired poles. In this paper, an analytical PID design method is proposed for continuous‐time delay systems to achieve approximate pole placement with dominance. Its idea is to bypass continuous infinite spectrum problem by converting a delay process to a rational discrete model and getting back continuous PID controller from its discrete form designed for the model with pole placement. Simulation results are included to illustrate the effectiveness of this method.
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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 | 0.001 | 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