Methods and Tools for Robust Optimal Control of Batch Chromatographic Separation Processes
(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)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/7752353
- author
- Holmqvist, Anders LU ; Andersson, Christian LU ; Magnusson, Fredrik LU and Åkesson, Johan
- organization
- publishing date
- 2015
- 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
- scopus:84984616805
- ISSN
- 2227-9717
- DOI
- 10.3390/pr3030568
- project
- Numerical and Symbolic Algorithms for Dynamic Optimization
- LCCC
- language
- English
- LU publication?
- yes
- additional info
- 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)
- id
- 32686b2a-f453-4dda-a3f1-1b95f275d4c5 (old id 7752353)
- date added to LUP
- 2016-04-01 14:22:41
- date last changed
- 2023-10-15 17:07:29
@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}}, keywords = {{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 = {{https://lup.lub.lu.se/search/files/3939433/8229347.pdf}}, doi = {{10.3390/pr3030568}}, volume = {{3}}, year = {{2015}}, }