Quantification of model uncertainty and its impact on the optimization and state estimation of batch processes via Tendency modeling

Approximate process models for batch reactor can be developed via a grey-box modeling technique called Tendency modeling. Because these models are approximate models, the introduction of process-model mismatch may have a significant effect on the success of the optimization or state estimation of batch reactor processes.;After some modifications to the existing Tendency modeling algorithm, aimed at making the methodology more efficient and systematic, are presented, the effect of the process-model mismatch on the optimization is studied. The uncertainty of the Tendency model is represented by the uncertainty of the model parameters. By considering the sensitivity of the optimal control problem with respect to the uncertain model parameters, confidence limits can be placed on the optimal input policy as well as on the predicted performance of the process. The uncertainty of the optimal operating policy and the predicted performance can indicate whether the process will actually result in the performance predicted by the model.;If the uncertainty is too large, the process can be run under a sub-optimal policy that is at a fraction of the distance between the previous policy and the calculated optimal one, so that the uncertainty of the new policy is reduced to an acceptable level. Under these sub-optimal policies, the process is still led toward the optimum but the likelihood of the process resulting in a performance far different from the model's prediction is reduced. Two simulated examples and one experimental example are presented to illustrate these concepts.;In addition, the impact of the process-model mismatch on the state estimation of batch processes is examined. The use of Tendency models in Kalman filter algorithms is presented and a methodology to tune the model covariance matrix from knowledge of the parametric uncertainty of the Tendency model is proposed. Two simulated examples are presented.