Improved gain conditioning for linear model predictive control
Bibliographic record
Abstract
Industrial practitioners who develop linear model predictive control (MPC) applications want to prevent undesirable controller behaviour caused by ill-conditioned gain matrices and model mismatch. In this work, we propose improvements to an existing orthogonalization-based method for gain conditioning. In this offline algorithm, manipulated variables (MVs) are ranked based on their influences on the controlled variables (CVs), so that problematic MVs with correlated effects can be identified. A constrained linear least-squares optimization problem is then solved to adjust columns in the gain matrix that correspond to problematic MVs. Our goal is to update this optimization problem to prevent the optimizer from switching the signs of some gains. The updated algorithm also permits control practitioners to hold key gains constant if their estimated values are trusted. Finally, we extend the methodology to condition gain submatrices, which arise when CVs are removed from the MPC problem. An industrial fluidized catalytic cracking case study is used to test the proposed method. The conditioned gains lead to improved controller performance and less aggressive movement of MVs when there is a plant-model mismatch. • Ill-conditioned gain matrices with plant mismatch may cause poor MPC performance. • Problematic manipulated variables with correlated effects are identified. • Constrained linear optimization is used for gain conditioning. • Scenarios where controlled variables are removed from MPC are addressed. • Industrial fluid catalytic cracking case study is used to validate the method.
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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 | 0.002 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.002 |
| Insufficient payload (model declined to judge) | 0.006 | 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".