Nonlinear output control in hysteretic, saturating materials
Bibliographic record
Abstract
The problem of determining the drive waveform that produces a desired output from a hysteretic, saturating material is considered both theoretically and experimentally. The specific problem of interest is the production of a high-amplitude, but monofrequency, sinusoidal polarization response. (The techniques presented could also be used to control other physical variables, such as the strain, if desired.) Two sample materials were considered, one of which is characterized by relatively low hysteresis (tan δ≈0.03) and tested using mechanical prestresses of 20.7 MPa (3 kpsi) and 41.4 MPa (6 kpsi), and the other of which is characterized by relatively high hysteresis (tan δ≈0.11), and tested without a prestress. Both samples were fabricated from the electrostrictive material lead magnesium niobate (PMN), although a magnetostrictive material (such as Terfenol-D) could have been tested instead. The samples were subjected to a bias voltage and prestress in order to simulate conditions that might arise in a full transducer. By analytically inverting a theory of hysteresis [J. C. Piquette and S. E. Forsythe, J. Acoust. Soc. Am. 106, 3317–3327 (1999) and J. Acoust Soc. Am. 106, 3328–3334 (1999)], the required (predistorted) drive waveform was determined. Both semi-major and minor hysteresis loops, in both polarization and strain, were measured and the parameters of the theory determined by least-squares fitting. The measurements were obtained under quasi-static conditions, with drive frequencies at or below 10 Hz. The observed fits of theory to data are of high quality. The theory was then inverted analytically to determine the drive required to produce the desired monofrequency polarization response, having a peak polarization value approximately equal to that achieved using a biased sinusoid of AC amplitude equal to the bias. The total harmonic distortion (THD) in the output polarization resulting from the inverting drive, computed using 10 harmonics, was experimentally observed to be about an order of magnitude less than that resulting from a biased sinusoid in all cases. It is shown that the hysteresis loop arising when using the distortion-reducing drive is of smaller area than that obtained when driving with a sinusoid to achieve the same polarization amplitude. Thus, the distortion-reducing drive results in a smaller loss per cycle than is obtained with a sinusoidal drive.
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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 | 0.000 | 0.000 |
| Research integrity | 0.000 | 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".