Optimizing autocatalysis with uncertainty by derivative‐free estimators

Abstract

SummaryA derivative‐free estimator was introduced to alleviate the drawbacks of the conventional Kalman filter when performing nonlinear analyses under different circumstances. In this work, the scaled Unscented Kalman Filter, Divided Difference Kalman filter, and Cubature Kalman filter (CKF) were selected to investigate the effectiveness of these filters in predicting the states of a complex semi‐batch reaction between propionic anhydride and 2‐butanol. The estimator's performance was evaluated under four different case studies, that is, under normal condition, under poor estimator initialization, under disturbances, and under parameter uncertainty. Results from the study show that CKF was the best option for an online dynamic optimization because of its highest degree of accuracy and stability under the normal and noisy conditions. Under normal condition, CKF yielded the lowest root mean square error of 0.61 × 10−2. Under uncertain initial condition, disturbance and parameter uncertainty, the lowest error of 1.83 × 10−2, 1.04 × 10−2, and 0.81 × 10−2 were obtained, respectively.