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

Anders Holmqvist, Christian Andersson, Fredrik Magnusson, Johan Åkesson

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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.
Original languageEnglish
Pages (from-to)568-606
Number of pages38
Issue number3
Publication statusPublished - 2015

Bibliographical note

The information about affiliations in this record was updated in December 2015.
The record was previously connected to the following departments: Numerical Analysis (011015004), Chemical Engineering (011001014), Department of Automatic Control (011017000)

Subject classification (UKÄ)

  • Chemical Process Engineering


  • Nonlinear programming
  • Collocation
  • PDE-constrained dynamic optimization
  • Robust optimal control
  • Batch chromatography
  • Uncertainty
  • Modelica
  • Algorithmic differentiation


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