Accurate state estimation in the Van der Vusse reaction

This paper discusses the state estimation task in the Van der Vusse reaction, which is a classical benchmark in a number of control studies in chemistry. Recently, it was shown that the extended Kalman filter is not able to estimate accurately the concentrations in this reaction on the basis of temperature measurements, only. Here, we demonstrate that modern state estimation methods, such as the continuous-discrete unscented and cubature Kalman filters and the accurate continuous-discrete extended Kalman filter, can calculate the off-set free concentration estimates of the stochastic Van der Vusse example with disturbance in the feed concentration by means of only temperature measurements. These nonlinear filters are also compared in the accuracy of state estimation in this challenging test problem to expose that all the mentioned state estimators work well and can be used for concentration estimation in chemistry research and industrial implementation. However, the accurate continuous-discrete extended Kalman filter is more flexible and robust. It treats successfully (i.e. without any manual tuning) the stochastic Van der Vusse reaction scenario for various disturbances in the feed concentration and for different control times.