Integrator Leakage for Limit Cycle Suppression in Servo Mechanisms With Stiction
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Bibliographic record
Abstract
This paper reports quantitative answers to two questions regarding the limit cycle behavior arising from the servo mechanisms with stiction under the positional PID (Proportional-Integral-Derivative) control. The first question is, how large the magnitude of the limit cycle is for a given value of stiction force. The second one is how we should modify the PID controller to avoid this limit cycle with minimal degradation in the serve performance. The main approach is based on understanding key algebraic properties of the state trajectory. As a result, a simple bisection algorithm has been devised to compute the exact magnitude of the periodic solution for a given value of stiction. A direct extension of this algorithm enables us to find the minimum value of the integrator leakage to avoid the limit cycle. A numerical example demonstrates the main results.
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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