An evaluation of integer- and fractional-order controllers for small satellites
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Fractional calculus (FC) represents the generalization of the integer calculus, in which the order of the exponent, as well as the differential and integral operators are restricted to integer values. This paper focuses on the existing fractional derivatives commonly used, while highlighting the advantages and disadvantages of each one of them. Furthermore, a mathematical interpretation of the fractional derivative is presented. The superiority of FC and its relative merits are also addressed through a specific example related to control engineering. This example deals with the implementation of a proportional integral derivative (PID) controller, where the objective is to evaluate a fractional- and integer-order PID controllers for the purpose of correcting the error in a dynamic process based on specific performance measures (e.g., overshoots, undershoots, transient response, and steady-state error). The simulation results indicates that the fractional-order PID provides a significant improvements compared to the integer-order PID, as well as a more flexible structure to adapt optimally to the process at hand.
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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) | 0.000 | 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 it