Discrete Output Regulator Design for a Coupled ODE-PDE System
Bibliographic record
Abstract
This manuscript addresses the design of a discrete regulator for an unstable coupled ODE-PDE cascade system with a recycle stream. The proposed regulator design considers a state feedback gain control law with the input applied to the ODE system. The controller has to ensure the closed-loop system stability and proper output tracking of reference signals. The discrete nature of the design is achieved by application of structure preserving Cayley-Tustin discretization to the coupled system given by a first-order ODE and a first-order hyperbolic PDE without the use of any spatial approximation and/or model order reduction. For the stabilization, the backstepping methodology is applied to ensure the system is mapped to the desired stable target system. To achieve adequate tracking, an exosystem representation is assumed in the design and leads to the corresponding Sylvester equation. The corresponding relationship between the continuous and discrete setting is shown. Finally, the simulations show the performance of the designed regulator for proper stabilization and trajectory tracking.
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How this classification was reachedexpand
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 | 0.001 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".