(486p) Comparative Study of New On-Line State Estimation Techniques Applied to Polymer Processes

The quality of information in a chemical plant affects significantly the results of optimization and control tasks, which has a notorious impact on product specifications achievement and production costs. In order to improve the overall process performance, Dynamic Real Time Optimization (DRTO) closed loops have begun to be implemented. DRTO loops comprise state estimation, dynamic optimization and control tasks[1].

Transient states are very important in polymer process operation, and hence DRTO can significantly improve the process performance. However, different types of problems are usually encountered when trying to implement this strategy. This work will focus on the state estimation task. One of the problems facing state estimation is the high nonlinearity of these systems. Another problem is that several important variables, which are related to end-use polymer properties, cannot be measured on-line or can only be measured at low sampling frequencies and with significant delays[2]. Therefore, an appropriate approach for state estimation is required.

The Extended Kalman Filter (EKF) is the classic technique employed in state estimation. However, under some situations this technique may present problems, particularly in the case of high nonlinear systems such as polymer processes. For instance, it can become unstable (ill-conditioned problems); the filter gain can become infinite if noise-free measurements are present; the filter may diverge or provide biased estimates when some of the disturbances are non-stationary or in presence of modeling errors.

A relatively new method known as the Unscented Kalman Filter (UKF) has been developed for nonlinear processes. In this method, the statistical properties of the estimates are computed without resorting to linearization of the nonlinear equations[3]. Based on the UKF formulation, different variants with potential applications in chemical process have been recently proposed. However, reported applications mostly involve simple processes represented by small models. A thorough analysis of the performance of these techniques when applied to more complex systems such as those found in polymer engineering is still required.

In this work, we compare the performance of three different on-line state estimation schemes based on the UKF when applied to a complex polymerization process: the basic UKF, the Unscented Recursive Nonlinear Dynamic Data Reconciliation (URNDDR) and the Reformulated Constrained Unscented Kalman Filter (RCUKF). The first approach is the classical UKF. In this method the probability density function of the states is approximated by a sample of points which are propagated using the nonlinear model, and the state and covariance matrix are computed using the corresponding sample statistics. The second strategy incorporates to the classical UKF the ability to handle algebraic constraints and bounds, without sacrificing the essential recursive nature of the estimation procedure[4]. In the last method, the correction step of the algorithm is reformulated and different constraint candidate sets may be considered within the UKF approach[5].

The selected case study consists of a continuous copolymerization process. The copolymer is produced in a reactor with a recycle loop. The comonomers methyl methacrylate and vinyl acetate are continuously added together with azobisiso-butyronitrile (initiator), benzene (solvent) and acetaldehyde (chain transfer agent). The monomer stream may also contain inhibitors such as m-dinitrobenzene. These feed streams are combined with the recycle stream and flow to the reactor. Polymer, solvent, unreacted monomers, initiator and chain transfer agent flow out of reactor to a separator, from which unreacted monomers and solvent continue on to purge point. After the purge they are stored in a recycle hold tank[6]. This system was represented by a first principles model consisting of a set of differential algebraic equations (DAE).

The computational load and the square root error are employed to evaluate the performance of the three approaches for their application in DRTO loops. Results show that the classical UKF is easier to implement and has better performance than EKF. The URNDDR ensures that state estimates satisfy bounds and other constraints and gives more accurate estimates at the expense of increasing the computational load. Regarding the last approach, its performance depends on the number of constraints and the optimization solution method.

References

[1] Kadam J.V. (2007), Integration of Economical Optimization and Control for Intentionally Transient Process Operation. Assessment and Future Directions of Nonlinear Model Predictive Control, 419-434.

[2] Richards, J.; Congalidis, J. P. (2006), Measurement and Control of Polimerization Reactors. Computers and Chemical Engineering, 30, 1447-1463.

[3] Julier, J.; Uhlmann J. K. (1997), A New Extension of the Kalman Filter to Nonlinear Systems. Proc. SPIE, 3068, 182.

[4] Vachhani, P.; Narasimhan, S.; Rengaswamy, R. (2006), Robust and Reliable Estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation. Journal of Process Control, 16, 1075-1086.

[5] Kolås, S.; Foss, B.A.; Schei, T.S. (2009), Constrained Nonlinear State Estimation based on the UKF Approach. Computers and Chemical Engineering, doi:10.1016 / j.cornpchemeng. 2009.01.012.

[6] Congalidis, J. P.; Richards, J. ; Ray, W. H. (1989), Feedforward and Feedback Control of a Solution Copolimerization Reactor. AIChE Journal, 35, 891-907.