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Processes 2015, 3(3), 568-606; doi:10.3390/pr3030568

Methods and Tools for Robust Optimal Control of Batch Chromatographic Separation Processes

1
Department of Chemical Engineering, Lund University, P.O. Box 124, SE-221 00 Lund, Sweden
2
Centre for Mathematical Sciences, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
3
Modelon AB, Ideon Science Park, SE-223 70 Lund, Sweden
4
Department of Automatic Control, Lund University, P.O. Box 118, SE-221 00 Lund, Sweden
*
Author to whom correspondence should be addressed.
Academic Editor: Carl D. Laird
Received: 13 May 2015 / Accepted: 7 July 2015 / Published: 16 July 2015
(This article belongs to the Special Issue Algorithms and Applications in Dynamic Optimization)
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Abstract

This contribution concerns the development of generic methods and tools for robust optimal control of high-pressure liquid chromatographic separation processes. The proposed methodology exploits a deterministic robust formulation, that employs a linearization of the uncertainty set, based on Lyapunov differential equations to generate optimal elution trajectories in the presence of uncertainty. Computational tractability is obtained by casting the robust counterpart problem in the framework of bilevel optimal control where the upper level concerns forward simulation of the Lyapunov differential equation, and the nominal open-loop optimal control problem augmented with the robustified target component purity inequality constraint margin is considered in the lower level. The lower-level open-loop optimal control problem, constrained by spatially discretized partial differential equations, is transcribed into a finite dimensional nonlinear program using direct collocation, which is then solved by a primal-dual interior point method. The advantages of the robustification strategy are highlighted through the solution of a challenging ternary complex mixture separation problem for a hydrophobic interaction chromatography system. The study shows that penalizing the changes in the zero-order hold control gives optimal solutions with low sensitivity to uncertainty. A key result is that the robustified general elution trajectories outperformed the conventional linear trajectories both in terms of recovery yield and robustness. View Full-Text
Keywords: batch chromatography; uncertainty; robust optimal control; PDE-constrained dynamic optimization; collocation; nonlinear programming; algorithmic differentiation; modelica batch chromatography; uncertainty; robust optimal control; PDE-constrained dynamic optimization; collocation; nonlinear programming; algorithmic differentiation; modelica
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Holmqvist, A.; Andersson, C.; Magnusson, F.; Åkesson, J. Methods and Tools for Robust Optimal Control of Batch Chromatographic Separation Processes. Processes 2015, 3, 568-606.

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