Data-Driven Modeling and Control of Batch and Continuous Processes using Subspace Methods

Abstract

This thesis focuses on subspace based data-driven modeling and control techniques for batch and continuous processes. Motivated by the increasing amount of process data, data-driven modeling approaches have become more popular. These approaches are better in comparison to first-principles models due to their ability to capture true process dynamics. However, data-driven models rely solely on mathematical correlations and are subject to overfitting. As such, applying first-principles based constraints to the subspace model can lead to better predictions and subsequently better control. This thesis demonstrates that the addition of process gain constraints leads to a more accurate constrained model. In addition, this thesis also shows that using the constrained model in a model predictive control (MPC) algorithm allows the system to reach desired setpoints faster. The novel MPC algorithm described in this thesis is specially designed as a quadratic program to include a feedthrough matrix. This is traditionally ignored in industry however this thesis portrays that its inclusion leads to more accurate process control. Given the importance of accurate process data during model identification, the missing data problem is another area that needs improvement. There are two main scenarios with missing data: infrequent sampling/ sensor errors and quality variables. In the infrequent sampling case, data points are missing in set intervals and so correlating between different batches is not possible as the data is missing in the same place everywhere. The quality variable case is different in that quality measurements require additional expensive test making them unavailable for over 90\% of the observations at the regular sampling frequency. This thesis presents a novel subspace approach using partial least squares and principal component analysis to identify a subspace model. This algorithm is used to solve each case of missing data in both simulation (polymethyl methacrylate) and industrial (bioreactor) processes with improved performance.