(663b) Detection and Isolation of Batch-to-Batch Parametric Drift in Protein Crystallization

Modeling and control of batch crystallization is of significant interest to pharmaceutical industry because the bioavailability of drugs highly depends on the size and shape distributions of their active pharmaceutical ingredients. Within this context, the dominant dynamic behavior of the evolution of key crystallization variables is modeled through a process model, which is used for the design of an in-batch model predictive controller (MPC) to regulate the average crystal size and shape distributions obtained at the end of the batch process. However, due to unknown batch-to-batch parametric drifts, the process model employed for in-batch control and estimation purposes may significantly deviate from the actual process behavior. More specifically, small batch-to-batch changes in the pH level, buffer concentration, or impurity concentration in the feedstock container may significantly alter the quality (e.g., size and shape) of the crystal products [1]. There are previous contributions that have considered run-to-run (R2R) control schemes that deal with batch-to-batch parametric drifts in a variety of batch processes [2-5].

In the present work, in order to further refine the R2R approach by relaxing the requirement of the post-batch measurements over multiple batch runs, we focus on the design of parametric drift detection and isolation (PDDI) scheme for the detection and isolation of the parametric drift. Using this scheme, it becomes easier to precisely calculate the magnitude of the process drift because parametric drift candidates are narrowed down from the set of all possible drift candidates.  The proposed PDDI scheme uses in-batch (protein solute concentration and crystallizer temperature) and post-batch measurements (crystal product attributes) and consists of two parts: preparatory stage before batch-to-batch operation and post-batch stage during batch-to-batch operation. The goal of the preparatory stage is to compute the threshold values and signatures for each parametric drift using simulations and batch process common cause variance described by noise. During the batch-to-batch operation, the proposed PDDI system monitors closed-loop process residuals, which are computed by taking the difference between the time profiles of the states obtained through in-batch and post-batch measurements, from the time profiles of the states obtained from the drift-free simulation with noise. Then, we compare the residuals with signatures obtained in the preparatory stage for each parametric drift for isolation of a parametric drift. The PDDI system estimates the magnitude of the parametric drift via a multi-variable optimization problem and updates the parameters of the batch process model used in the in-batch MPC system to compute a set of jacket temperatures for the production of crystals with a desired shape distribution in the next batch. The performance of the MPC with the proposed PDDI scheme is demonstrated by applying it to a multiscale simulation of a batch protein crystallization process with parametric drifts.

[1] Cacioppo E, Pusey ML. The solubility of the tetragonal form of hen egg white lysozyme from pH 4.0 to 5.4. J. of Crystal Growth. 1991;114:286-292.

[2] Campbell WJ, Firth SK, Toprac AJ, Edgar TF. A comparison of run-to-run control algorithms. In Proceedings of the American Control Conference, Anchorage, AK, 2002:2150-2155.

[3] Wang Y, Gao F, Doyle FJ. Survey on iterative learning control, repetitive control, and run-to-run control. J. of Process Control. 2009;19:1589-1600.

[4] Kwon JS, Nayhouse M, Orkoulas G, Ni D, Christofides PD. Run-to-Run-based model predictive control of protein crystal shape in batch crystallization. Ind. & Eng. Chem. Res. 2015;54:4293-4302.

[5] Kwon JS, Nayhouse M, Orkoulas G, Ni D, Christofides PD. A method for handling batch-to-batch parametric drift using moving horizon estimation: application to run-to-run MPC of batch crystallization. Chem. Eng. Sci. 2015;127:210-219.