Optimal control of axial dispersion tubular reactors with recycle: Addressing state‐delay through transport <scp>PDEs</scp>
Bibliographic record
Abstract
Abstract The optimal control of an axial tubular reactor with a recycle stream is addressed as a key type of setting for distributed parameter systems in chemical engineering. The intrinsic time delay from the recycle process, thus far overlooked in relevant literature, is modelled as a transport partial differential equation (PDE), resulting in a system of coupled parabolic and hyperbolic PDEs. Utilizing Danckwerts boundary conditions, the reactor is boundary‐controlled with the control input at the inlet. A continuous‐time optimal linear quadratic regulator is developed to stabilize the infinite‐dimensional system, employing a late lumping approach in order to preserve the properties of the original infinite dimensional system in controller design. The full‐state feedback regulator is designed by solving the Operator Riccati Equation (ORE), leveraging the system's Riesz‐spectral properties. To address practical limitations of full‐state feedback, a Luenberger observer is also proposed, enabling state reconstruction from boundary measurements. Numerical simulations are conducted to evaluate the proposed control strategies. The results demonstrate that the full‐state feedback regulator effectively stabilizes the system. A comparison is made between two configurations where different numbers of eigenmodes were selected to design the controller. The observer‐based regulator also stabilizes the system successfully using merely output measurements, effectively overcoming the challenge of limited state access.
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.
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 | 0.000 |
| 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 | 0.001 |
| 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".