System identification and trajectory tracking control of batch processes using Latent Variable Models

This thesis considers the problem of model identification and trajectory tracking control in batch processes. From the point of view of a control engineer, finite duration of the process, not operating around the equilibrium point, and time-varying operating conditions with nonlinear behavior are amongst the most significant differences between batch and continuous processes. The major contribution of this thesis is to develop an alternative to Nonlinear Model Predictive Control (NMPC) by incorporating Latent Variable Models (LVMs) in the course of an MPC algorithm (called LV-MPC).;Furthermore, different latent variable modeling alternatives for modeling of batch processes are investigated from the view point of their application in the course of LV-MPC. Two modeling alternatives previously proposed in the literature are incorporated in the course of the LV-MPC methodology: Batch-Wise Unfolding (BWU), and Observation-Wise with Time-lag Unfolding (OWTU). The BWU modeling approach addresses the nonlinearity and time varying properties of the batch process. However, it needs a large number of batch runs in the training dataset. The OWTU approach leads to a Linear Time Invariant (LTI) modeling of the process which captures the average process dynamics. However, it needs only 1-3 batch runs for building the process model which makes this approach attractive for practical situations. In addition, a new modeling approach is proposed in this study which tries to capture the major benefits of both BWU and OWTU while avoiding the drawbacks of each one. It is called the Regularized Batch-Wise Unfolding (RBWU) modeling approach. This modeling approach has the capability of modeling the nonlinearity and time-varying properties almost as accurately as BWU and at the same time it leads to a smoother PCA model and needs fewer numbers of observations for building the model as compared to BWU. The performances of the three latent variable modeling approaches in the course of LV-MPC for trajectory tracking are illustrated using two simulated batch reactor case studies. Recommendations are then given on which modeling approach to use under different scenarios.;In the last stage of this research, various issues on the closed-loop identification of empirical latent variable models for model predictive control (MPC) of batch processes are investigated. It is shown that in most cases, it is possible to identify the batch process models only from historical batches without the need for external excitation of the closed-loop system by dither signal on top of the controller output. The maximum requirement would be to use extra batch runs with different set-point trajectories in the training dataset. The issue of model bias in closed-loop identification is investigated and the desirable controller characteristics to be used in the data generation step to minimize this bias in the latent variable models are discussed.;Two control formulations are developed in this study: Control in the latent variable space and control in the original variable space. The algorithms are based on multi-phase PCA models developed on batch data arrays. In both cases prediction of the future trajectories is accomplished using statistical latent variable missing data imputation methods. It is shown that the two control formulations are complementary to each other. The control in the latent space is the infinite horizon LV-MPC, while the control in the original variable space is the finite horizon LV-MPC. The proposed LV-MPCs can handle constraints. The methods are tested on two simulated batch reactor case studies.