A method for handling batch-to-batch parametric drift using moving horizon estimation: Application to run-to-run MPC of batch crystallization

In this work, we develop a run-to-run (R2R) model parameter estimation scheme based on moving horizon estimation (MHE) concepts for the modeling of batch-to-batch process model parameter variation using a polynomial regression scheme in a moving horizon fashion. Subsequently, the batch process model parameters computed via the proposed R2R model parameter estimation scheme are used in a model predictive controller (MPC) within each batch to compute a set of optimal jacket temperatures for the production of crystals with a desired shape distribution in a batch crystallization process. The ability of the proposed method to suppress the inherent variation in the solubility caused by batch-to-batch parametric drift and handle the noise in post batch measurements is demonstrated by applying the proposed parameter estimation and control method to a kinetic Monte Carlo (kMC) simulation model of a batch crystallization process used to produce hen-egg-white (HEW) lysozyme crystals. Furthermore, the performance of the proposed R2R model parameter estimation scheme is evaluated with respect to different orders of polynomials and different moving horizon lengths in order to calculate the best parameter estimates. The average crystal shape distribution of crystals produced from the closed loop simulation of the batch crystallizer under the MPC with the proposed R2R model parameter estimation scheme is much closer to a desired set point value compared to those of the double exponentially weighted moving average based MPC (dEWMA-based MPC) and that of MPC based on the nominal process model. (C) 2015 Elsevier Ltd. All rights reserved.