FURTHER RESULTS ON THE ZEROS OF A SLEWING RIGID-FLEXIBLE BEAM
Bibliographic record
Abstract
There is much research on the poles of the transfer function (between the beam-end displacement and base torque) of slewing single-flexible beams. However, there is no comprehensive report on their zeros. The study on the zeros is of great importance, especially from the controller design perspective, because some of these zeros are in the right-hand-side (RHS) of the domain S in the Laplace transform. These RHS zeros limit the control bandwidth; deteriorate the trade-off between the robustness and the desirable control performance. They also create challenges in the beam-end trajectory-tracking. It is for these reasons that a comprehensive study on the zeros is of valuable significance which for the first time is reported in this paper. It is shown here that the physical parameters of the slewing flexible beam fall into three categories with respect to the locations of the zeros. In the first category, an increase (or decrease) in values of physical parameters move the zeros further from (or closer to) the imaginary axis. The second category is composed of physical parameters where an increase (or decrease) in their values move the zeros closer to (or further from) the imaginary axis. The third category includes the physical parameters where the locations of the zeros are independent of their values.
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How this classification was reachedexpand
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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".