State estimation for semi-batch polymerization reactors

Three approaches to nonlinear state estimation are evaluated for application to semi-batch polymerization problems. The semi-batch emulsion copolymerization of styrene/butadiene rubber (SBR) is used as a case study. The first approach considered for nonlinear state estimation is the extended Kalman filter. This approach is demonstrated to be useful and simple to apply, but can be slow to converge from state initialization errors due to the recursive nature of the algorithm. To improve convergence, the extended Kalman filter can be augmented with a second extended Kalman filter, or a recursive prediction error estimator, to provide improved estimates of the unknown initial states. The final approach considered is the use of a full on-line, nonlinear optimization procedure using all the data available at each time. The reiterative extended Kalman filter approach is shown to be best suited for semi-batch polymerization problems. The importance of incorporating nonstationary disturbance and/or model mismatch states to prevent bias in the state estimates is also demonstrated. Furthermore, it is shown that, by introducing sufficient well-chosen nonstationary stochastic states, the performance of the extended Kalman filter can be made robust to a wide range of unknown disturbances and model mismatch.