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.
Highlights
Isolation of a high-purity target component from a multicomponent mixture is of significant importance in the pharmaceutical and biochemical industries [1]
The United States Food and Drug Administration (US FDA) has published a series of new guidelines to promote flexibility for innovation while appropriately managing variability in the process performance attributes for continual improvement via process analytical technology (PAT) and quality-by-design (QbD) principles [4,5]
JModelica.org [73] is an open-source platform for simulation and optimization of models described in either the Modelica [74] or Optimica language [75] or as Functional Mock-up Units (FMUs) following the Functional Mock-up Interface (FMI) [76]
Summary
Isolation of a high-purity target component from a multicomponent mixture is of significant importance in the pharmaceutical and biochemical industries [1]. The United States Food and Drug Administration (US FDA) has published a series of new guidelines to promote flexibility for innovation while appropriately managing variability in the process performance attributes for continual improvement via process analytical technology (PAT) and quality-by-design (QbD) principles [4,5]. QbD promotes improved process understanding during process and product development and building quality in the design instead of testing for quality. This can be achieved via correlative, causal, or mechanistic knowledge and at the highest level via first principle models. PAT has been gaining a lot of momentum in the biopharmaceutical community due to the potential for continuous real time quality assurance resulting in improved operational control and compliance [6]
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