Nonlinear backstepping hierarchical control of shake table using high‐gain observer
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.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 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 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".