Adaptive Estimation of Threshold Parameters for a Prandtl-Ishlinskii Hysteresis Operator
Bibliographic record
Abstract
The Prandtl-Ishlinskii (PI) operator has been used widely in the modeling and inverse compensation of hysteresis nonlinearity in actuators made of smart materials, such as piezoelectric and magnetostrictive materials. A PI operator consists of weighted superposition of play operators, each of which is characterized by a threshold (also known as radius) parameter that determines the width of the corresponding hysteresis loop. While much work has been reported in identifying the weight parameters for the play operators, the threshold parameters have typically been assigned a priori in an arbitrary fashion. In this paper, for the first time, an adaptive algorithm is proposed for estimating online the unknown thresholds of a PI operator. The key challenge is that the output of the PI operator depends on the play thresholds in a complex, nonlinear, and time-varying manner. To address this challenge, the proposed algorithm utilizes the instantaneous slope of the input-output graph of the PI operator to infer the operating regime of each play, based on which a modified estimation error function is derived that is proportional to the error of threshold parameters. It is further shown, under a mild condition on the input, the regressor vector is persistently exciting and a gradient algorithm (with parameter projection) results in parameter convergence. The approach is illustrated in detail with a two-play PI operator, along with the results for the general case of n-play operators. Simulation results are presented to demonstrate the effectiveness of the proposed approach.
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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 | 0.001 | 0.003 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".