(17g) A Hybrid Model Based Model Predictive Control Strategy for Particle Processes

Control of particle processes is a challenging task due to their complex and multivariable kinetics. The outcome of these processes, including crystallization, flocculation and emulsification, must comply with a given set of quality attributes related to particle properties. In an industrial setting, failure to comply with these quality attributes typically results in either reprocessing or even disposal of the product. Advanced control strategies, such as model predictive control is one way to tackle these issues optimally. However, they require the development of predictive process model whose cost may be out of proportion to the price of the product. It is therefore likely that more advanced control strategies are to be actively deselected in the development of new processes.

In the past two decades, hybrid modelling approaches have emerged that may reduce the cost of model development [1, 2, 3]. This is achieved by using a machine-learning approach to estimate particle phenomena kinetics, which are typically the most difficult and thereby the most expensive to determine. The data-driven kinetic model is combined with first principles models, such as mass and population balances, resulting in model predictions that are only physically and chemically feasible. Recently, Nielsen et al. [4] have presented a hybrid modelling framework for particle processes, using a deep neural network to estimate particle phenomena kinetics, that allows for real-time training of the hybrid model using data from an on-line/at-line particle analysis sensor.

In this work, a model predictive control (MPC) strategy is presented for particle processes, utilizing a non-linear hybrid particle model. The hybrid model is generated using the modelling framework by Nielsen et al. [4], which is capable of modelling various particle phenomena using time-series data from an on-line/at-line particle analysis sensor and a flexible number of other on-line/at-line/in-line/soft-sensors. The hybrid model is continuously trained during process operation in the current strategy, while in parallel being used for finding the optimal control actions by solving a multi-objective non-linear MPC problem. This forms an adaptive control strategy that can be continuously refined during process operation. The MPC problem is solved using a differential evolution optimizer (rand/1/bin) by Storn and Price [5]. This is done to reduce the risk of converging to local minima, which inherently will be present when using heavily parametric machine learning models as a deep neural network used in the modelling framework.

The performance of the hybrid model based MPC strategy is presented through both a theoretical and an experimental case study of a batch cooling crystallization of lactose. The controlled variables are here the final mean crystal size and reactor temperature, with the manipulated variable being the heating and cooling profile during a fixed batch duration. Hence, the MPC problem is a shrinking horizon problem, where end-of-batch simulations are carried out for each particle analysis measurement with a sampling frequency of 10 minutes. The nucleation and crystal growth kinetics are here estimated using a deep neural network with on-line measured solute concentration, in-line reactor temperature and on-line measured particle size distribution as inputs. This model is combined with a solute mass balance and a medium-resolution discretized population balance model, producing predictions of the future particle size distribution.

Through the two case studies, it is demonstrated how the presented model predictive control strategy can be successfully employed with only limited prior process knowledge and data, and thereby potentially reducing the cost of introducing model predictive control in new particle processes. Furthermore, it is shown how the model predictive control strategy can adapt to drifting particle processes dynamics by continuously training the hybrid model in parallel with solving the MPC problem.

[1] V. Galvanauskas, P. Georgieva, S. F. D. Azevedo, Dynamic optimisation of industrial sugar crystallizationprocess based on a hybrid (mechanistic+ann) model (2006). doi:10.1.1.124.7855.

[2] Y. Meng, S. Yu, J. Zhang, J. Qin, Z. Dong, G. Lu, H. Pang, Hybrid modeling based on mechanistic and data-driven approaches for cane sugar crystallization, J. Food Eng. 257 (2019) 44-55. doi:10.1016/j.jfoodeng.2019.03.026.

[3] P. K. Akkisetty, U. Lee, G. V. Reklaitis, V. Venkatasubramanian, Population balance model-based hybrid neural network for a pharmaceutical milling process, J. Pharm. Innov. 5 (2010) 161-168. doi:10.1007/s12247-010-9090-2.

[4] R. F. Nielsen, N. Nazemzadeh, L. W. Sillesen, M. P. Andersson, K. V. Gernaey, S. S. Mansouri, Hybrid machine learning assisted modelling framework for particle processes, Submitted to Comput. Chem. Eng. (2020)

[5] R. Storn, K. Price, Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces, J. Glob. Optim., 11, 341 359, 1997.