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 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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".