Development of a recurrent neural networks-based NMPC for controlling the concentration of a crystallization process

Abstract

Crystallization is a separation and purification process relevant to industrial sectors, such as pharmaceuticals. The maximum possible recovery of solute amount is one of its goals, and the temperature profile is crucial to achieve this. In this work, neural networks-based models were developed to predict the solute concentration of a batch crystallization process and used as internal model in a nonlinear model predictive controller. Three different neural network architectures were considered: the multilayer perceptron (MLP) network, the echo state network (ESN), and the long short-term memory (LSTM). The dataset used for training and testing applied a co-teaching learning algorithm, which uses simulated and experimental data from the batch crystallization of the potassium sulfate (K2SO4). The three network structures were trained to predict the solute concentration one step ahead, using the current temperature and concentration values as feed, and the predictive performances were evaluated for larger prediction horizons. A nonlinear model predictive controller (NMPC) based on the ESN, the most efficient neural network design, was successfully applied to the batch crystallization process to maintain the solute concentration on its desired trajectories by manipulating the operating temperature. The controller's behavior was studied for three different set-points of concentration and supersaturation, varying the initial concentration. The performance of the proposed NMPC was compared to a controller based on a more traditional approach, using the MLP network as internal model.

Keywords

• Crystallization
• Neural networks
• Echo state network
• LSTM
• NMPC