Performance Evaluation of Bayesian State Estimators for Nonlinear DAE Systems Using a Moderately High Dimensional Reactive Distillation Column Model

Abstract

Abstract If it is desired to control a reactive distillation (RD) system at an unstable operating point, then use of a reliable nonlinear state estimator becomes an essential step in the controller synthesis. This work aims at carrying out a comparative evaluation of the performances of two recently developed nonlinear Bayesian estimators for systems modelled as DAEs, namely extended Kalman filter (EKF) and unscented Kalman filter (UKF) (Mandela et al., 2010). Efficacies of DAE-EKF and DAE-UKF have been evaluated by simulating state estimation problems associated with a benchmark ideal RD column (Olanrewaju and Al-Arfaj, 2006). When compared on the basis of sum squared estimation errors, the DAE-UKF was found to outperform the DAE-EKF. However, contrary to the claims in the state estimation literature regarding the computational efficiency of UKF vis a vis EKF, the average computation time needed for the DAE-EKF computations was found to be significantly less (by factor of 50) than the average computation time needed for the DAE-UKF computations. Moreover, the performance of DAE-EKF was found to improve if the top and the bottom concentration measurements are included in the estimation problem along with temperature measurements on alternate trays. Thus, DAE-EKF was found to be better suited for development of an observer based control scheme.