Nonlinear backstepping hierarchical control of shake table using high‐gain observer
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Bibliographic record
Abstract
Abstract Shake table testing is a common technique used to examine the responses of structures under dynamic loads. Shake table is often regulated using linear controller, such as proportional‐integral‐derivative (PID) controller. However, traditional PID control cannot consider inherent nonlinearities in the structural and control systems. In this paper, a series of novel backstepping control methods, which consider the nonlinearities in the structural and control systems, have been developed. In addition, high‐gain observers, which can provide highly accurate estimation of the shake table displacement, velocity and acceleration, are also developed. The proposed backstepping control methods and high‐gain observers are implemented in a hierarchical framework, where the high‐level backstepping controller generates the command signal for the low‐level controller to execute. A total of four hierarchical backstepping control methods, including the acceleration‐based backstepping hierarchical control (ABHC), the ABHC with high‐gain observer (ABHCO), the displacement‐based backstepping hierarchical control (DBHC) and the DBHC with high‐gain observer (DBHCO), have been implemented. Detailed parameter studies have been conducted to identify the optimized parameters for the proposed hierarchical backstepping control methods. The proposed control method is verified through a series of shake table tests. The experimental results show the ABHC, ABHCO, DBHC and DBHCO can all achieve high‐performance shake table control, especially with superior acceleration tracking over the traditional PID control. Overall, ABHCO achieves the best tracking performance for displacement, velocity and acceleration.
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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) | 0.001 | 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 | 0.001 |
| 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