Robust optimization of solid-liquid batch reactors under parameter uncertainty

Unknown parameters in batch process models can be estimated as uncertainties owing to model mismatch, measurement errors and even the absence of variable measurements. Applying a model-based dynamic optimization with the estimated parameter values is likely to violate path and end-point constraints. This work aims at developing a robust off-line optimization strategy to overcome model uncertainty and improve control feasibility. First, model parameter uncertainty is quantified by the likelihood confidence region from parameter estimation. A two-stage multi-scenario approach is performed to enhance robustness of optimal solutions by adding worst-case scenarios to the optimal control problem. Detailed formulations of two stages for batch process optimal control under multiple scenarios and feasibility evaluation over the uncertainty space are introduced. Additionally, to avoid local solutions at the feasibility stage, we develop a multi-start approach to solve nonlinear programming problems starting from extreme points on the hyper-elliptical confidence region. This robust optimization approach is applied to case studies of industrial solid-liquid batch reactors. The results indicate the proposed approach is able to enhance robustness of optimal control and prevent hard constraint violations within a few iterations. (C) 2019 Elsevier Ltd. All rights reserved.