On the design, robustness, implementation and use of quasi-linear feedback compensators
Bibliographic record
Abstract
A quasi-linear feedback compensator is one in which its poles depend in an appropriate way on its gain. The reason for introducing this new concept was the desire to remove the limitation to performance imposed by a plant with more than one pole in excess of its zeros. In this article it is shown that this objective is realized for plants with zeros in the left half of the complex plane. The consequences are surprising. In time domain it is possible to track arbitrarily fast a class of reference inputs despite a large class of disturbances and uncertainty in plant parameters. The response is non-oscillatory for high enough compensator gains, which is explained by the automatic adaptation of the closed loop poles to stability and stability margins for such gains. And in frequency domain the phase margin tends to 90° while the gain margin and crossover frequency become unlimited. Technically the design procedure of quasi-linear compensators presented here is based on our theoretical result concerning the asymptotic behaviour of the roots of certain polynomials in a complex variable which depend also on a large positive parameter. We also show how to implement such quasi-linear compensators in practical feedback control schemes, and their use at lower gains which is the case of most industrial applications.
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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 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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".