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

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.

Robust Multi-Objective Optimization of Chromatographic Rare Earth Element Separation

“…The robust optimization method in this study is similar to the methods presented in [29] [33]. The main difference is that the model responses of the introduced disturbances in this study are obtained stochastically, instead of alternatively utilizing a deterministic approach through linearization of the uncertainty set.…”

“…This implies that a process disturbance, however slight, can cause a batch failure in terms of not meeting the purity constraint [26] [29]. In order to account for such disturbances it is necessary to formulate a robust counterpart problem, which in this study will be accomplished by introducing a back-off term to the purity inequality constraint in Equation (10e).…”

A Modular Framework for the Modelling and Optimization of Advanced Chromatographic Processes

“…For this reason, the Simulator can simulate a ProcessModel for a fixed number of cycles, or continue simulating until the corresponding module in Figure 1 confirms that cyclic Stationarity is reached. Different criteria can be specified such as the maximum deviation of the concentration profiles or the peak areas of consecutive cycles [28]. The simulation terminates if the corresponding difference is smaller than a specified value.…”

High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments

“…We list below only a few examples over the past year (since 2015). Recent applications of WENO schemes can be found in the simulations of astrophysics and geophysics [55,83,137,140,162,172,215,223], atmospheric and climate science [70,181,225], batch chromatographic separation [101], biomolecular solvation [286], bubble clusters in fluids [222], combustion [11,15,24,164,214,268], detonation waves [92,114,145,233], elastic-plastic solids [173], flame structure [261], granular gas [3], hypersonic flows [109], infectious disease models [209], laser welding [174], magnetohydrodynamics [20,166], mathematical finance for solving the Black-Scholes equation [90], multiphase and multispecies flows [13,91,108,110,159,160,239], networks and blood flows [168], ocean waves [28,125], oil storage process [196], rarefi...…”