Adaptive 2-DOF Control for Tracking Sinusoidal Signals With Unknown Frequency
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Bibliographic record
Abstract
Tracking sinusoidal signals with unknown and time-varying frequencies is essential in many adaptive control applications. This paper presents a real-time method for tracking sinusoidal reference signals with unknown frequencies within a narrow bandwidth. The reference signals may include multiple harmonics and a DC bias. The proposed approach integrates a sinusoidal internal model with a Two-Degree-of-Freedom control structure. Unlike traditional methods that rely on offline tuning, this technique updates the controller coefficients online. A high-pass filter with notch characteristics (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>f</i></sub>) is used to derive update equations for the Two-Degree-of-Freedom controller and the internal model parameters. These equations are obtained by matching the closed-loop transfer function of the algorithm to that of the desired filter (1 − <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i><sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><i>f</i></sub>). The method is evaluated in MATLAB/Simulink using a second-order plant as an example. Two test cases are presented: the first involves a reference signal with a frequency change and a DC bias, while the second includes two additional harmonics. The algorithm is also tested without coefficient updating for comparison. Results show that the proposed method can accurately track signals with unknown and changing frequencies. It keeps the tracking error very small and quickly adjusts to frequency changes, making it suitable for real-time control in dynamic systems.
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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 | 0.000 | 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 | 0.001 |
| 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