Direct Optimal Vibration Control of a Piezoelastic Plate
Bibliographic record
Abstract
An optimal control method for distributed parameter systems is developed and applied to active vibration control of a plate. Piezoelectric material is used as an actuator. The structural dynamics are modeled using the space—time assumed mode expansion technique (a Rayleigh—Ritz method applied to both time and space variables). In particular, the generalized coordinates (both mechanical and electrical) and all generalized forces are described in terms of expansion functions. Using Hamilton's law of varying action along with the space—time assumed mode expansion results in algebraic equations of motion. These are then used as the constraint equations in the optimal controller design. Using space—time expansion, the usual variational optimal control problem is transformed into an equivalent algebraic problem. Optimal solutions are then obtained in a closed form and the solution is global within the time period considered. The solution procedure does not lead to a Riccati equation as is the case in the conventional optimal control solutions. The direct optimal control problem of a vibrating plate is illustrated through simulations where a parametric study is undertaken to check the controller performance. This study shows that the developed optimal control method is simple and the structure—control interaction is an inherent property of the method.
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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 | 0.001 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 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".