Quadratic controller for a chaotic micro-resonator
Bibliographic record
Abstract
A model for a chaotic micro-oscillator is developed by adding a new control system to an electrostatic actuator consisting of two electrodes: the substrate and a cantilever beam on top. The electrostatic actuator itself has a single stable equilibrium over a range of voltage, whereas adding the controller, which has a quadratic function, creates a voltage range for bistability. The bi-stability represents a two well potential field that is used here to create chaos. The model of the beam actuator is a mathematical model of a continuous system with identified parameters from the experiments. The equations of motion are then descretized using the first mode shape of the beam and solved numerically to find the steady state oscillation. The range of the AC frequency and voltage excitation for sustained chaos creation is investigated through bifurcation diagrams which reveal two well chaos, periodic orbits and multiple periods. It is discovered that the proposed new controller has some important advantages over a previously introduced controller for creation of chaos. First, it has a simpler function making its implementation easier. Second, it has a larger bi-stability voltage range starting from zero that doubles the operating range for chaotic oscillation and decreases the actuation voltage by eleven times. At last but not least, the controller offers chaos in a three times wider AC voltage range than that of the previous controller.
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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 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".