Open-loop optimal control of batch chromatographic separation processes using direct collocation

Holmqvist, Anders; Magnusson, Fredrik

doi:10.1016/j.jprocont.2016.08.002

Cited by 22 publications

(9 citation statements)

References 71 publications

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“…This is especially computationally beneficial when considering large-scale dynamic optimization used e.g. to obtain discretized multi-level elution trajectories for high productivity and high yield batch chromatographic processes (Holmqvist and Magnusson (2016); Sellberg et al (2017)) or for global downstream optimization (Huuk et al (2014); Baumann et al (2015); Pirrung et al (2017)). It is also computationally advantageous when considering closed loop non-linear model predictive control (MPC) applications including state-estimation.…”

Section: Paper Objectivesmentioning

confidence: 99%

A stabilized nodal spectral solver for liquid chromatography models

Meyer

Huusom

Abildskov

2019

Computers & Chemical Engineering

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Section: Paper Objectivesmentioning

confidence: 99%

A stabilized nodal spectral solver for liquid chromatography models

Meyer

Huusom

Abildskov

2019

Computers & Chemical Engineering

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“…The current state-of-the-art methodology for optimization of HPLC separations has been limited to linear [17,18], concave/convex [19] and step elution trajectories [20]. A novel open-loop optimal control strategy for simultaneous optimization of general elution trajectories and target component fractionating decisions was recently developed by Holmqvist and Magnusson [21], Holmqvist et al [22]. The present investigation is a direct continuation of these studies and the overall objective is to extend the open-loop optimal control strategy with a robust worst-case formulation and benchmark the robustness of general elution trajectories, with respect to target component purity, with that of the conventional linear trajectories.…”

Section: Solvent Composition Trajectory Elution Strategiesmentioning

confidence: 99%

“…[21]. The scope for this work and the proper specification of the methods and tools were conceived in discussions between all authors.…”

Section: Acknowledgmentsmentioning

confidence: 99%

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

et al. 2015

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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.

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“…High order methods that aim to obtain a desired resolution using the smallest number of degrees of freedom (DOFs) possible have been developed during the last decades. The introduction of such methods in the field of chromatography is important since they have the potential to significantly reduce the required computational effort when solving large-scale [13,14], dynamic [15] or large parameter estimation [16,17] optimization problems which are gaining increasing practical importance due to the allowance of fast and cheap process development.…”

Section: Introductionmentioning

confidence: 99%