Comparison of linear-quadratic and controllability criteria for actuator placement on a beam
Bibliographic record
Abstract
For control of a distributed parameter system, the performance of the controlled system is known to be dependent on the placement of the control actuator, and thus actuator location can be viewed as an additional variable in the controller design. The most common criterion in the engineering literature is to maximize a measure of the controllability. However, as shown here, this approach yields predictions that depend on the order of the model used for the calculations. Furthermore, minimizing the linear-quadratic cost is a common objective in controller design. It is reasonable then to choose the actuator location, as well as the controller itself, to minimize the linear-quadratic cost. In this paper, the performance of a controlled beam with the actuator chosen using these different criteria is examined. The effect of different weights in the cost function on the optimal actuator location is also examined. The control signal is calculated for a number of a different cases. It appears that optimal location of the actuator can improve performance without a corresponding increase in control effort, although possible saturation of control signals may be a concern in some applications.
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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".