Implementation of stabilizing control laws - How many controller blocks are neede for a universally good implementation?
Bibliographic record
Abstract
In this article we investigated three questions. The first question deals with the existence of a universally good implementation of the control law u = Crr - Cyy. This question is answered in the literature, where it is shown that there does exist a universally good three-block implementation. We then turned to the second question, asking whether there exists a universally good implementation that has fewer than three controller blocks. We considered a broad collection of one- and two-block implementations and determined that none of them are good implementations. Consequently, none of the implementations that we considered are universally good. The final question asks whether, for a given plant and control law u = Crr - Cyy, there necessarily exists a good implementation that has fewer than three blocks. Again, based on the example (9)-(12), we conjecture that the answer is no. The overall conclusion of the article is therefore a conjecture, namely, that it is not only sufficient, but sometimes necessary, to use three controller blocks in a good implementation of u = Crr - Cyy
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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 | 0.006 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
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".