Optimal LQ-Feedback Regulation of a Nonisothermal Plug Flow Reactor Model by Spectral Factorization
Bibliographic record
Abstract
The linear-quadratic (LQ) optimal temperature and reactant concentration regulation problem is studied for a partial differential equation model of a nonisothermal plug flow tubular reactor by using a nonlinear infinite dimensional Hilbert state space description. First the dynamical properties of the linearized model around a constant temperature equilibrium profile along the reactor are studied: it is shown that it is exponentially stable and (approximately) reachable. Next the general concept of LQ-feedback is introduced. It turns out that any LQ-feedback is optimal from the input-output viewpoint and stabilizing. For the plug flow reactor linearized model, a state LQ-feedback operator is computed via the solution of a matrix Riccati differential equation (MRDE) in the space variable. Thanks to the reachability property, the computed LQ-feedback is actually the optimal one. Then the latter is applied to the nonlinear model, and the resulting closed-loop system dynamical performances are analyzed. A criterion is given which guarantees that the constant temperature equilibrium profile is an asymptotically stable equilibrium of the closed-loop system. Moreover, under the same criterion, it is shown that the control law designed previously is optimal along the nonlinear closed-loop model with respect to some cost criterion. The results are illustrated by some numerical simulations.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".