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Predictive control of crystal size distribution in protein crystallization

Published on Jul 1, 2005in Nanotechnology3.399
· DOI :10.1088/0957-4484/16/7/034
Dan Shi6
Estimated H-index: 6
(UCLA: University of California, Los Angeles),
Prashant Mhaskar31
Estimated H-index: 31
(UCLA: University of California, Los Angeles)
+ 1 AuthorsPanagiotis D. Christofides62
Estimated H-index: 62
(UCLA: University of California, Los Angeles)
Abstract
This work focuses on the modelling, simulation and control of a batch protein crystallization process that is used to produce the crystals of tetragonal hen egg-white (HEW) lysozyme. First, a model is presented that describes the formation of protein crystals via nucleation and growth. Existing experimental data are used to develop empirical models of the nucleation and growth mechanisms of the tetragonal HEW lysozyme crystal. The developed growth and nucleation rate expressions are used within a population balance model to simulate the batch crystallization process. Then, model reduction techniques are used to derive a reduced-order moments model for the purpose of controller design. Online measurements of the solute concentration and reactor temperature are assumed to be available, and a Luenberger-type observer is used to estimate the moments of the crystal size distribution based on the available measurements. A predictive controller, which uses the available state estimates, is designed to achieve the objective of maximizing the volume-averaged crystal size while respecting constraints on the manipulated input variables (which reflect physical limitations of control actuators) and on the process state variables (which reflect performance considerations). Simulation results demonstrate that the proposed predictive controller is able to increase the volume-averaged crystal size by 30% and 8.5% compared to constant temperature control (CTC) and constant supersaturation control (CSC) strategies, respectively, while reducing the number of fine crystals produced. Furthermore, a comparison of the crystal size distributions (CSDs) indicates that the product achieved by the proposed predictive control strategy has larger total volume and lower polydispersity compared to the CTC and CSC strategies. Finally, the robustness of the proposed method (achieved due to the presence of feedback) with respect to plant-model mismatch is demonstrated. The proposed method is demonstrated to successfully achieve the task of maximizing the volume-averaged crystal size in the presence of plant-model mismatch, and is found to be robust in comparison to open-loop optimal control strategies.
  • References (58)
  • Citations (84)
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#2Nael H. El-Farra (UCLA: University of California, Los Angeles)H-Index: 34
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In this work, we consider nonlinear systems with input constraints and uncertain variables, and develop a robust hybrid predictive control structure that provides a safety net for the implementation of any model predictive control (MPC) formulation, designed with or without taking uncertainty into account. The key idea is to use a Lyapunov-based bounded robust controller, for which an explicit characterization of the region of robust closed-loop stability can be obtained, to provide a stability ...
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We have shown previously that large high-quality single protein crystals can be grown by varying temperature in a predetermined fashion such that the solution supersaturation and the rate of crystal growth are maintained at a constant value in batch crystallization systems. Here we have adapted the constant supersaturation control (CSC) methodology to isothermal crystal growth. In this version of the CSC protocol, dynamic control is provided by changing precipitant concentration through a dialys...
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#1Nikos V. Mantzaris (Rice University)H-Index: 13
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The operation of chemical processes often requires respecting constraints on manipulated inputs and process states. Input constraints typically reflect limits on the capacity of control actuators, such as valves or pumps, whereas state constraints represent desirable ranges of operation for process variables, such as temperatures or concentrations. Constraints, however, limit the set of initial conditions, starting from where a process can be stabilized at a possibly open-loop unstable steady st...
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A hybrid control structure that unites bounded control with model predictive control (MPC) is proposed for the constrained stabilization of nonlinear systems. The structure consists of: (1) a finite-horizon model predictive controller, which can be linear or nonlinear, and with or without stability constraints, (2) a family of bounded nonlinear controllers for which the regions of constrained closed-loop stability are explicitly characterized and (3) a high-level supervisor that orchestrates swi...
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In this work, a hybrid control scheme, uniting bounded control with model predictive control (MPC), is proposed for the stabilization of linear time-invariant systems with input constraints. The scheme is predicated upon the idea of switching between a model predictive controller, that minimizes a given performance objective subject to constraints, and a bounded controller, for which the region of constrained closed-loop stability is explicitly characterized. Switching laws, implemented by a log...
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Solubility and growth rate of orthorhombic lysozyme (from hen egg-white) crystals were measured at 0.1 and 100 MPa. A growth or dissolution rate of a given concentration was measured, and the solubility was determined as the concentration at which the crystal did not grow or dissolve. The solubility decreased with increasing pressure at 30, 35 and 40 °C. This means that the supersaturation, σ (= lnC/C e, C: protein concentration, C e: solubility), increases; hence, the crystallization is enhance...
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