Design of Gain-Scheduled Strictly Positive Real Controllers Using Numerical Optimization for Flexible Robotic Systems
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Bibliographic record
Abstract
The design of gain-scheduled strictly positive real (SPR) controllers using numerical optimization is considered. Our motivation is robust, yet accurate motion control of flexible robotic systems via the passivity theorem. It is proven that a family of very strictly passive compensators scheduled via time- or state-dependent scheduling signals is also very strictly passive. Two optimization problems are posed; we first present a simple method to optimize the linear SPR controllers, which compose the gain-scheduled controller. Second, we formulate the optimization problem associated with the gain-scheduled controller itself. Restricting our investigation to time-dependent scheduling signals, the signals are parameterized, and the optimization objective function seeks to find the form of the scheduling signals, which minimizes a combination of the manipulator tip tracking error and the control effort. A numerical example employing a two-link flexible manipulator is used to demonstrate the effectiveness of the optimal gain-scheduling algorithm. The closed-loop system performance is improved, and it is shown that the optimal scheduling signals are not necessarily linear.
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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 | 0.003 | 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 | 0.000 |
| 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