A stability analysis of a decentralized adaptive feedback active control system of sinusoidal sound in free space
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Bibliographic record
Abstract
In some cases, the implementation of active control of sound in free space requires a large number of secondary sources and error sensors. In terms of control hardware, this may translate into considerable processing power requirement. A practical method to decrease processing power is to decentralize the control; that is, implement many single-input, single-output independent controllers operating simultaneously instead of a large multiple-input, multiple-output system. The main drawback of decentralized control is the risk of global instability. The purpose of this paper is to derive conditions under which globally stable control system behavior can be obtained in the case of adaptive feedback decentralized control for a sinusoidal disturbance. The main objective is to give practical conditions derived from the small gain theorem and the Nyquist criterion for the stability of the control system. These conditions only take into account the geometrical arrangement of the secondary sources and error sensors. This analysis involves a new parameter beta called "performance index," which is associated with both the convergence of the individual controllers and the global stability of the system. Simulation and experimental results are shown to illustrate the effectiveness of the developed analytical tools.
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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) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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 it