Toward Robust Optimal Control of Chromatographic Separation Processes With Controlled Flow Reversal

ABSTRACT Column liquid chromatography is an important technique applied in the production of biopharmaceuticals, specifically for the separation of biological macromolecules such as proteins. When setting up process conditions, it is crucial that the purity of the product is sufficiently high, even in the presence of perturbations in the process conditions, e.g., altered buffer salt concentrations. Our goal is to employ a model‐based approach for robust process optimization where we aim to safeguard the purity level of the product against uncertainties in the model parameters. Furthermore, we include the possibility of reversing the flow direction as an additional time‐dependent control degree of freedom, as a flow reversal is often performed in practice to achieve better separation. We present a strategy where a flow reversal is incorporated effectively in a mathematical model for column chromatography, eventually leading to the challenging class of mixed‐integer optimal control problems constrained by advection‐diffusion‐reaction‐type partial differential equations. Furthermore, we examine a sampling‐based strategy toward robustly optimal switching control applied to chromatographic separation processes. By means of a computational study, we discuss the quality of the presented approach and how reversing the flow direction may play a role in terms of the quality of the solutions.