(693g) Batch Polymerisation State and Parameter Estimation – a Bayesian Adaptive Ekf

Two estimation methods, the extended Kalman filter (EKF) and a Bayesian estimation framework are studied and contrasted through application to a benchmark batch solution polymerization reactor. A Bayesian estimation framework is proposed for the tracking of time-varying parameters and incorporated into a Bayesian parameter adaptive EKF for joint state and parameter estimation. The Bayesian approach is a statistical procedure that allows the systematic incorporation of prior knowledge about the model and model parameters, the appropriate weighting of experimental data, and the use of probabilistic models for the modelling of sources of experimental error. An alternative to the EKF through the introduction of a Bayesian estimation framework is proposed for the tracking of time-varying parameters and estimation of the process states. The Bayesian method is a statistical procedure that allows the systematic incorporation and proper weighting of experimental data, prior knowledge of model and parameters and probabilistic models of sources of experimental error. The interplay of these elements determines the best model parameter estimates. Furthermore, because of its probabilistic structure, the method also characterises uncertainty of the estimates in a natural way. In the study, the well known extended Kalman filter (EKF) is used as the base-line case for estimating the states and time varying model parameters. Despite the large number of papers discussing the control of polymer properties using an EKF, few tackle the major issues of robust parameter updating (e.g. Gagnon and MacGregor, 1991; Kozub and MacGregor, 1992; Crowley and Choi, 1997, 1998). MacGregor and co-workers (1991, 1992) analysed the parameter updating issues and emphasised the need to update as many parameters as possible in order to include all potential process changes that can affect the process. The understanding that the estimation algorithm may fail in the presence of systematic errors such as unmodelled disturbances, modelling errors or time-varying parameters has also been highlighted by Scali, et al. (1997). Systematic errors such as the presence of impurities, reactor fouling and errors in the knowledge of the kinetic constants are the main cause of plant-model mismatch in chemical process and particularly in polymerisation reactors. Parameter adaptation is one of the most powerful properties of the estimator to deal with model mismatch. The state vector can be augmented with those parameters whose values are poorly known and time-varying parameters are treated as state variables and estimated along with the process states. The background to the proposed approach is shaped by the need to satisfy complex property requirements for the final polymer and simultaneously achieve the greatest economic potential during the batch operation where most mechanical and rheological properties of the polymer products are directly or indirectly linked with the molecular structural properties of polymer chains (e.g., molecular weight distribution, MWD, copolymer composition distribution - CCD, chain sequence length distribution - CSD, etc.), which are difficult (sometimes impossible) to measure on-line. In practice, the operation of polymerisation reactors is influenced by both process disturbances and model parameter variations due to the inherent process-model mismatch or the changing operating conditions of the process. Unless the time-varying model parameter values and subsequently the optimal control trajectory are updated regularly during the batch operation, the control strategy fails to meet the product quality specifications and the operating requirements (Ruppen et al. 1997).