(757d) Covariance Estimation of a Laboratory Emulsion Polymerization System: Comparison Between ALS and Direct Optimization Methods

Emulsion polymerization processes have called the attention of the process systems engineering community for the last decades. In particular, several techniques, including process modeling, control, optimization, and state estimation, have been successfully applied to these processes with the goal of obtaining the desired final polymer specification. Specifically, the implementation of online state estimation is necessary to monitor and control the particle diameter, the distribution of the molecular weights, among other properties. For this purpose, stochastic state estimators are able to provide an accurate solution if the correct set of covariance matrices is obtained to define their statistics. A number of techniques for covariance estimation are available in the literature, such as direct optimization^[1], autocovariance least-squares (ALS)^[2,3], among others. This presentation will focus on the application of the direction optimization and ALS techniques to determine the noise covariances for state estimation of a laboratory emulsion polymerization system.

In previous contributions^[4,5], a direct optimization method was employed to obtain the covariance matrices for monitoring batch polymerization processes using recursive state estimators, such as the extended Kalman filter (EKF) and the unscented Kalman filter (UKF). Moreover, the ALS technique was successfully implemented to define the statistics of a moving horizon estimator (MHE) for the analysis of semicontinuous polymerization processes^[6]. The estimation results obtained for both cases were in complete agreement with experimental data for all the analyzed reaction systems. Thus, both covariance estimation techniques provided adequate sets of covariance matrices (Q and R) for monitoring such reaction systems.

The objective of this presentation is to analyze the implementation of the above covariance estimation techniques for a laboratory emulsion polymerization reaction system. Four reactions were carried out using vinyl acetate, with isoperibolic and isothermal operation modes. Also, the jacket flow rate was keep constant during operation and samples were taken out in order to evaluate the conversion by gravimetry for further validation. Typically, for such systems, covariance and state estimation techniques are applied using only simulated data. Also, a comparison between different covariance estimation techniques has not yet been carried out. We perform this comparison here between the direct optimization and the ALS methods using the same scenario, including the number of process and measurement noises as well as the experimental data sets. These obtained covariance matrices are then employed to define the statistics of several state estimators, including EKF, UKF and MHE, and their estimation performances are compared using the validation data. Preliminary results indicate that the ALS technique combined with MHE performs satisfactorily given the accuracy of the prediction of the conversion obtained by gravimetry. Finally, the comparison carried out in this work will provide covariance and state estimation guidelines for these reaction systems facilitating their improvement and industrial implementation.

1.        D. I. Wilson, M. Agarwal, Computers & Chemical Engineering, 1998, 22, 1653.

2.        F. V Lima, J. B. Rawlings, AIChE Journal, 2011, 57, 996.

3.        F. V. Lima, M. R. Rajamani, T. A. Soderstrom, J. B. Rawlings, IEEE Trans. Ctl. Sys. Tech, 2012, in press.

4.        F. D. Rincón, M. Esposito, G. A. C. Le Roux, C. Sayer, P. H. H. de Araújo, AIChE Annual Meeting, 2011.

5.        F. D. Rincón, M. Esposito, P. H. H. de Araújo, C. Sayer, G. A. C. Le Roux, Macromolecular Reaction Engineering,  2012, 7, 24.

6.        F. D. Rincón, M. Esposito, P. H. H. de Araújo, C. Sayer, F. V. Lima, G. A. C. Le Roux, AIChE Annual Meeting,        2012.