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

Holmqvist, Anders LU ; Andersson, Christian LU ; Magnusson, Fredrik LU and Åkesson, Johan (2015) In Processes 3(3). p.568-606
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... (More)
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. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Nonlinear programming, Collocation, PDE-constrained dynamic optimization, Robust optimal control, Batch chromatography, Uncertainty, Modelica, Algorithmic differentiation
in
Processes
volume
3
issue
3
pages
38 pages
publisher
MDPI AG
external identifiers
  • wos:000363981100005
ISSN
2227-9717
DOI
10.3390/pr3030568
project
LCCC
collocation
language
English
LU publication?
yes
id
32686b2a-f453-4dda-a3f1-1b95f275d4c5 (old id 7752353)
date added to LUP
2015-08-03 08:58:53
date last changed
2016-08-19 15:22:52
@article{32686b2a-f453-4dda-a3f1-1b95f275d4c5,
  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.},
  author       = {Holmqvist, Anders and Andersson, Christian and Magnusson, Fredrik and Åkesson, Johan},
  issn         = {2227-9717},
  keyword      = {Nonlinear programming,Collocation,PDE-constrained dynamic optimization,Robust optimal control,Batch chromatography,Uncertainty,Modelica,Algorithmic differentiation},
  language     = {eng},
  number       = {3},
  pages        = {568--606},
  publisher    = {MDPI AG},
  series       = {Processes},
  title        = {Methods and Tools for Robust Optimal Control of Batch Chromatographic Separation Processes},
  url          = {http://dx.doi.org/10.3390/pr3030568},
  volume       = {3},
  year         = {2015},
}