A Discrete Optimal Control Method for a Flexible Cantilever Beam with Time Delay
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Time delay inevitably exists in active control systems. It may cause unsynchronized control forces that can not only degrade the performance of the control systems, but also induce instability of the dynamic systems. In this paper, an active vibration controller (with time delay) for a flexible cantilever beam is studied and a method for treating the time delay is proposed. The dynamic equation of the controlled mode with time delay is first presented using the independent modal space control, and is then discretized and transformed into a standard discrete form with no explicit time delay by augmenting the state variables. The continuous performance index is also transformed into a discrete form. Then, a discrete optimal control algorithm is designed based on the augmented state system. Since time delay effect is incorporated in the mathematical model of the dynamic system throughout the control design and no approximations and assumptions are made in the control algorithm derivation, system stability is guaranteed. Furthermore, the extraction of modal coordinate from actual physical measurements and the conversion to actual control force from modal one are presented. The feasibility and efficiency of the proposed control algorithm are demonstrated by numerical simulation studies, which indicate that the vibration of the beam may be suppressed significantly using the proposed control algorithm. Instability may occur if the time delay is neglected in control design.
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.
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 | 0.000 |
| 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