Robust Control of a Vibrating Beam Using the Hybrid Passivity and Finite Gain Stability Theorem
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Bibliographic record
Abstract
Our motivation is robust control of systems which are nominally passive, but experience a passivity violation. In particular, we consider the robust control of a two dimensional flexible beam equipped with a double-gimbaled control moment gyro used for actuation. First we present definitions related to the hybrid passivity and finite gain stability theorem. Calculation of the passivity and finite gain parameters (in a LTI, MIMO context) used to ensure the stability of two hybrid systems within a negative feedback loop is presented. After developing the plant dynamics it is shown that the plant in nominally passive, but including the gimbal motor dynamics induces a passivity violation. Using a numerical optimization strategy and guided by the hybrid passivity and finite gain stability theorem, controllers which are guaranteed to robustly stabilize the closed-loop are optimally found. The controller parameterization, optimization objective function, and optimization constraints are discussed.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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