Journal
COMPUTERS & CHEMICAL ENGINEERING
Volume 33, Issue 10, Pages 1685-1691Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.compchemeng.2009.04.012
Keywords
Crystallization control; Batch nonlinear model predictive control; Robust optimal control; Population balance model; Distribution shaping control; Quadrature method of moments; Method of characteristics
Funding
- Engineering and Physical Sciences Research Council [EP/E022294/1] Funding Source: researchfish
- EPSRC [EP/E022294/1] Funding Source: UKRI
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The paper presents a novel control approach for crystallization processes, which can be used for designing the shape of the crystal size distribution to robustly achieve desired product properties. The approach is based on a robust optimal control scheme, which takes parametric uncertainties into account to provide decreased batch-to-batch variability of the shape of the crystal size distribution. Both open-loop and closed-loop robust control schemes are evaluated. The open-loop approach is based on a robust end-point nonlinear model predictive control (NMPC) scheme which is implemented in a hierarchical structure. On the lower level a supersaturation control approach is used that drives the system in the phase diagram according to a concentration versus temperature trajectory. On the higher level a robust model-based optimization algorithm adapts the setpoint of the supersaturation controller to counteract the effects of changing operating conditions. The process is modelled using the population balance equation (PBE), which is solved using a novel efficient approach that combines the quadrature method of moment (QMOM) and method of characteristics (MOC). The proposed robust model based control approach is corroborated for the case of various desired shapes of the target distribution. (C) 2009 Elsevier Ltd. All rights reserved.
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