Analysis and Simulation of Optimal Vibration Attenuation for Underactuated Mechanical Systems
Bibliographic record
Abstract
This paper deals with active optimal vibration attenuation of elastic structures modeled by finite elements. The system’s equations are linear with potentially large numbers of degrees of freedom, whereas the minimized performance index isquadratic. Theproblem isformulated inmodal space so thatthe dimension ofthe problem can belimitedtocontrollingsignificantmodesonly.Theirnumberisconsideredgreaterthanthenumberofindependent discrete actuators, making the system underactuated. The constraints resulting from underactuation are representedbythematrixofconstraints thatcouplesthe modalcontrols. Thismatrix, whichplaysanimportant role in predicting the systems controllability, is obtained by adding a set of dummy actuators. Themodal variables are in turn coupled via second-order nonholonomic constraints, which are satisfied with the help of time-dependent Lagrange multipliers. The optimality equations for the problem are derived in a compact form and solved by applying symbolic differential operators. The procedure, which applies standard finite element and mathematical software, renders the optimal actuation forces and the response of all controlled modes, or any selected degrees of freedom, for the entire control process. Two simulation examples are presented to illustrate the approach’s details and the use of controllability indicators derived from the matrix of constraints.
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How this classification was reachedexpand
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) | 0.000 | 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".