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In this work, a parameter tuning problem of two-degrees-of-freedom model predictive control of industrial paper-making processes is explored to achieve satisfactory time-domain robust closed-loop performance in terms of worst-case overshoots and worst-case settling times, under user-specified parametric uncertainties. An efficient visualization method is first developed to characterize the set of time-domain closed-loop responses in the presence of parametric model–plant mismatch. On the basis of the visualization technique and the unmodality/monotonicity properties of the performance indices with respect to the tuning parameters, the feasibility of the tuning problem can be analyzed, and a three-step iterative line-search based automatic tuning algorithm is proposed to determine the controller parameters that meet the time-domain performance requirements robustly for the given parametric uncertainty specifications. The effectiveness of the algorithm is illustrated by applying the results to a process from stock to conditioned weight in an industrial paper machine and by comparing the performance of the algorithm with that of brutal search.

Deep learning models have been applied to industrial process fault detection because of their ability to approximate the complex nonlinear behavior. They have been proven to outperform the shallow neural network models. However, there are no good guidelines on how to build these deep models. Therefore, a good deep model is often constructed through a trial-and-error exercise. It is not easy to interpret the model because of features that do not have any physical interpretation. In addition, latent variables (or features) in a deep model are not independent. This causes features to overlap with each other, resulting in challenges in evaluating distributions of features and designing suitable monitoring indices. Finally, typical deep learning models in process monitoring are used in a deterministic manner and do not automatically provide confidence levels for each decision. In this paper, a variational autoencoder is utilized to develop a framework for monitoring uncertain nonlinear processes. The learned latent variables are guaranteed to be independent (or orthogonal) of each other under a specific optimization objective with constraints. The proposed method provides the density estimates of latent variables and residuals instead of point estimates. The density functions are used to design appropriate indices for monitoring. A simulation example and an industrial paper machine example are presented to validate the effectiveness of the proposed method.