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

Research output: Contribution to journalArticle

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.

Details

Authors
  • Anders Holmqvist
  • Christian Andersson
  • Fredrik Magnusson
  • Johan Åkesson
Organisations
External organisations
  • Modelon AB
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Chemical Process Engineering

Keywords

  • Nonlinear programming, Collocation, PDE-constrained dynamic optimization, Robust optimal control, Batch chromatography, Uncertainty, Modelica, Algorithmic differentiation
Original languageEnglish
Pages (from-to)568-606
Number of pages38
JournalProcesses
Volume3
Issue number3
StatePublished - 2015
Publication categoryResearch
Peer-reviewedYes

Bibliographic 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)

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Related projects

Fredrik Magnusson, Johan Åkesson, Anders Holmqvist, Karl Berntorp & Christian Andersson

2012/02/012017/02/01

Project: ResearchIndividual research project

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