Robust batch‐to‐batch optimization in the presence of model‐plant mismatch and input uncertainty

• Published in: AIChE journal 2017-07, Vol.63 (7), p.2660-2670
• Main Authors: Hille, Rubin, Mandur, Jasdeep, Budman, Hector M.
• Format: Article
• Language: English
• Subjects: Batch culture; batch processes; Chaos theory; Chemical engineering; Convergence; Cost function; Estimates; Mathematical models; model‐plant mismatch; Motivation; Optimization; parameter selection; Parameter sensitivity; polynomial chaos expansion; Predictions; robust model‐based optimization; Robustness; Uncertainty
• ISSN: 0001-1541; 1547-5905
• DOI: 10.1002/aic.15645

In model‐based optimization in the presence of model‐plant mismatch, the set of model parameter estimates which satisfy an identification objective may not result in an accurate prediction of the gradients of the cost‐function and constraints. To ensure convergence to the optimum, the predicted gradients can be forced to match the measured gradients by adapting the model parameters. Since updating all available parameters is impractical due to estimability problems and overfitting, there is a motivation for adapting a subset of parameters for updating the predicted outputs and gradients. This article presents an approach to select a subset of parameters based on the sensitivities of the model outputs and of the cost function and constraint gradients. Furthermore, robustness to uncertainties in initial batch conditions is introduced using a robust formulation based on polynomial chaos expansions. The improvements in convergence to the process optimum and robustness are illustrated using a fed‐batch bioprocess. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2660–2670, 2017