A batch-to-batch optimization methodology for producing a desired molecular-weight distribution (MWD) using an approximate model is presented. The method uses fundamental polymer knowledge in order to simplify an otherwise complicated optimization problem and provide significant freedom in manipulated variable selection. A measurement of the MWD at the end of the batch is used to update manipulated variable trajectories for the next batch, thus iterating into a good operating policy. The optimization approach is then extended for use as an on-line control method. To achieve this, it was necessary to address the modeling of highly correlated measurement error typically observed in the MWD measurements. A multivariable statistical process control (MSPC) monitoring scheme is developed for deciding when a new batch optimization is required. The optimizer remains on, but dormant, while the desired MWD is being produced, and it re-optimizes the process quickly if the process changes and a poor quality polymer is produced. The combined MSPC/batch-to-batch optimizer is demonstrated on a simulated semi-batch polystyrene reactor.

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The problem of driving a batch process to a specified product quality using data-driven model predictive control (MPC) is described. To address the problem of unavailability of online quality measurements, an inferential quality model, which relates the process conditions over the entire batch duration to the final quality, is required. The accuracy of this type of quality model, however, is sensitive to the prediction of the future batch behavior until batch termination. In this work, we handle this "missing data" problem by integrating a previously developed data-driven modeling methodology, which combines multiple local linear models with an appropriate weighting function to describe nonlinearities, with the inferential model in a MPC framework. The key feature of this approach is that the causality and nonlinear relationships between the future inputs and outputs are accounted for in predicting the final quality and computing the manipulated input trajectory. The efficacy of the proposed predictive control design is illustrated via closed-loop simulations of a nylon-6,6 batch polymerization process with limited measurements.

Effective control of quality variables in high-dimensional processes is considered. Because of the high dimension of the output space, control of a subset of the quality variables is often practiced, to indirectly control the entire quality space. An example of this type of situation is the control of the full molecular weight distribution (MWD). Often, indirect control of the MWD, for example, by controlling an average of the distribution, is practiced instead. It is shown in this paper that, as a controller eliminates a disturbance in the controlled variables (for example, the weight-average chain length), it transfers and can possibly inflate the disturbance in the remaining quality variables (the full MWD). Therefore, while it may appear that good control is being achieved (the average is at its target), the polymer quality has, in fact, degraded. A simple analysis tool, called the disturbance inflation factor (DIF), is introduced to predict this effect. The DIF is used to predict which manipulated variable results in the best control of the full MWD while acting only on a single measured variable such as the weight-average chain length. It is further applied to evaluate if control of the full distribution may be improved by considering other controlled variables, such as the number-average chain length, or other manipulated variables, such as combinations of the existing manipulated variables. The ideas are illustrated on a simulated polystyrene reactor.