Performance limitations of the servomechanism problem when the number of tracking/disturbance poles increases
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Bibliographic record
Abstract
In this paper, we study the cheap control problem and determine what some of the inherent system limitations are in achieving high performance for LTI systems. In particular, we observe that a fundamental difficulty in designing a high performance controller for a system may occur, which is related to the infinite transmission zero structure of the system. A continuous measure, called the Toughness Index, is introduced to characterize such limitations. We then apply these results to the robust servomechanism problem (RSP), and show that the Toughness Index of the RSP becomes worst as the number of tracking/disturbance poles to be tracked/regulated increases. This implies that high performance control in the RSP cannot be obtained for a large number of tracking/disturbance poles, even for minimum phase systems.
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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