Some new notions in the stability investigations and design of controllers for nonlinear systems
Bibliographic record
Abstract
Design of an adaptive controller for complex dynamic systems is a big challenge faced by the researchers. In this paper, we introduce a novel concept of dynamic pole motion (DPM) for the design of an error-based adaptive controller (E-BAC). The purpose of this novel design approach is to make the system response reasonably fast with no overshoot, where the system may be timevarying and nonlinear with only partially known dynamics. The E-BAC is implanted in a system as a nonlinear controller with two dominant dynamic parameters, the dynamic position feedback and the dynamic velocity feedback. For illustrating the strength of this new approach, in this paper we give an example of a flexible robot with nonlinear dynamics. In the design of this feedback adaptive controller, parameters of the controller are designed as a function of the system error. The position feedback Kp(e, t) and the velocity feedback Kv(e, t) are continuously varying as a function of the system error e(t). In these feedback parameters, the position feedback Kp(e, t) controls the system bandwidth, thereby the rise time in step response, whereas the velocity feedback Kv(e, t) controls the damping ratio of the system thereby the overshoot in the step response. For large errors, Kp(e, t) is large which increases the bandwidth of the system thereby a smaller rise time. Whereas, for decreasing errors, Kp(e, t) is continuously decreased to a small value with decreasing bandwidth of the system. Similarly, but contrarily, Kv(e, t) is kept very small for large errors, and it is continuously increased to a large value for decreasing error. Hence, in the design of the proposed adaptive controller, the position feedback Kp(e, t) and the velocity feedback Kv(e, t) are formulated as functions of the system error, and this approach for formulating the adaptive controller yields a very fast response with no overshoot.
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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 | 0.003 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.002 |
| Bibliometrics | 0.002 | 0.001 |
| Science and technology studies | 0.001 | 0.005 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.003 | 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".