Model predictive control for semi-batch reactive crystallization process

Abstract

Reactive crystallization or precipitation is widely used for the production or purification of valuable substances such as catalysts, ceramics, pigments, cosmetics and pharmaceuticals. In the crystallization process, the size distribution of crystals can affect subsequent operations such as filtration, drying and storage. Normally, the objective of the crystallization process is to achieve a specified the average crystal size. This research presents the implementation of a dynamic optimization strategy in a semi-batch reactive crystallization process to determine an optimal operating concentration policy maximizing an average crystals size subject to a product quality constraint, i.e., the requirement of coefficient of variation. Instead of assuming the perfect tracking of the optimal concentration profile, a nonlinear model predictive control (MPC) is applied to track the obtained optimal concentration policy. As feedback information of states at each time step is required in the MPC algorithm, an extended Kalman filter (EKF) is incorporated to provide the estimate of non-measurable states and uncertain kinetic model parameters in the MPC algorithm. Simulation results demonstrate that the average crystal size is increased by 30% compared with the constant feed rate control strategy. The robustness of the semi-batch reactive crystallizer control is improved by the MPC control integrated with the EKF.