System Elegant-frequency Characteristics, Wave-sign Diagrams and Stability Criterion
Bibliographic record
Abstract
Frequency domain method is a crucial technique for analyzing systems in classical control theory, relying primarily on logarithmic frequency characteristics. Characteristic curves generated in semi-logarithmic coordinate systems are typically displayed using a widely recognized chart known as a Bode diagram. However, creating a Bode diagram is an inconvenient process and results in abstract plots. Additionally, incomplete ranges of styles in basic links, along with varying expressions of open-loop frequency characteristics under different forms of feedback, create difficulties in understanding and challenges in application. This paper begins by classifying basic links in detail and constructing gain-phase frequency characteristics from logarithmic frequency characteristics. Then, a functional transformation is applied to plot characteristic curves in a Cartesian coordinate system of linear division, similar to those in a Bode diagram, by which gain-phase frequency characteristics are converted into elegant-frequency characteristics. This approach eliminates difficulties in plotting and understanding of a Bode diagram associated with using a semi-logarithmic coordinate system. On this basis, this paper proposes the concept of loop elegant-frequency characteristics, to solve the problems of misleading and inconvenient applications of open loop frequency characteristics. Elegant-frequency characteristics can facilitate efficient engineering applications, such as analysis, calculation and system correction, and enable the derivation of additional new features, such as wave-sign characteristics and stability criterion, which enhances the frequency domain method and advances the associated knowledge system.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.004 | 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".