Integrator Leakage for Limit Cycle Suppression in Servo Mechanisms With Stiction
Bibliographic record
Abstract
It is well known that the positional proportional-integral-derivative (PID) control of a servo mechanism with stiction always leads to a limit cycle. Related to this fact, two basic questions have still remained unanswered. The first question is, if the limit cycle occurs, how large it becomes for a given value of stiction force. The second question, which is of more practical importance, is how we should modify the PID controller to avoid this limit cycle with minimal sacrifice of the servo performance. This paper presents a rigorous analysis to provide particular answers to these two questions, which turn out to be closely related to each other. More specifically, it is shown that, by exploiting algebraic properties of the state trajectory, a simple bisection algorithm can be devised to compute the exact magnitude of the periodic solution for a given value of stiction. Through the geometric analysis of the impact map, this result is then used to find the minimum value of the integrator leakage to avoid the limit cycle. The work in this paper will be useful as a specific reference in designing servo mechanisms with stiction free from limit cycle.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.000 |
| 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".