Modeling and Stabilizability of Voltage-Actuated Piezoelectric Beams with Magnetic Effects
Bibliographic record
Abstract
Models for piezoelectric beams and structures with piezoelectric patches generally ignore magnetic effects. This is because the magnetic energy has a relatively small effect on the overall dynamics. Piezoelectric beam models are known to be exactly observable and can be exponentially stabilized in the energy space by using a mechanical feedback controller. In this paper, a variational approach is used to derive a model for a piezoelectric beam that includes magnetic effects. It is proved that the partial differential equation model is well-posed. Magnetic effects have a strong effect on the stabilizability of the control system. For almost all system parameters the piezoelectric beam can be strongly stabilized, but it is not exponentially stabilizable in the energy space. Strong stabilization is achieved using only electrical feedback. Furthermore, using the same electrical feedback, an exponentially stable closed-loop system can be obtained for a set of system parameters of zero Lebesgue measure. These results are compared to those of a beam without magnetic effects.
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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 | 0.000 | 0.001 |
| 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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".