State Estimation with Delayed Measurements In Polymer Processes Using Unscented Transform Filters

Wednesday, October 19, 2011
Exhibit Hall B (Minneapolis Convention Center)
Ruben Galdeano, Mariano Asteasuain and Mabel C. Sanchez, Chemical Engineering, Planta Piloto de Ingeniería Química (UNS-CONICET), Bahía Blanca, Argentina

On-line state estimation is a key task in control and real-time optimization of polymer processes. Different techniques for nonlinear state estimation have been used for years in polymerization processes, such as state estimation via nonlinear observers, data reconciliation, moving horizon estimation, neural networks and fuzzy logic.[1-3] One of the most widespread approaches is the extended Kalman filter (EKF). However, this strategy may present problems in the case of highly nonlinear systems.[4] A relatively new method, known as the Unscented Kalman Filter (UKF), has been developed for this type of processes. It is based on the unscented transform technique, a mechanism for propagating the mean and covariance of a random variable through a nonlinear transformation.[5]

A particular characteristic of polymer processes is that several variables related to product quality can only be measured at low sampling rates and with significant time delays. In spite of its significance, few works related to state estimation in these processes refer to the use of delayed measurements and how they affect the quality of the estimate. Some methodologies have been developed for the optimal treatment of time delayed measurements in the framework of Kalman filters. A comprehensive reviews of these can be found in Gopalakrishnan et al.[5] In the case of the UKF, few works related to state estimation with delayed measurements applied different techniques.[6-7]

In this work, two approaches for the treatment of delayed measurements within the framework of the UKF are presented. One of them is based on a fusion strategy in which the filter algorithm is modified in order to account for the delayed measurements. The gain matrix is changed in such a way that the update of the state vector and covariance matrix can be done in a single step. The second one is based on a sample state augmentation, which consists in augmenting the states influenced by the delayed measurement when it arrives.

The proposed UKF algorithms were applied to the state estimation in a solution polymerization reactor.[8] The computational load and the square root error were employed to evaluate the performance. The results show that these two techniques ensure quality and stability of the estimation. Also, the proposed methodologies reduce the computation time adequately, making it an attractive alternative for on-line application.


[1] Tatiraju S, Soroush M, Ogunnaike BA. Multirate Nonlinear Estimation with Application to a Polynerization Reactor . AIChE J. 1999; 45, 769-780.

[2] Narasimhan S, Jordache C. Data Reconciliation  and Gross Error Detection: An Intelligent Use of Process Data, USA: Houston, Texas. Gulf Publishing Co; 2000.

[3] Romagnoli  JA, Sánchez MC. Data Processing and Reconciliation for Chemical Process Operations. USA: San Diego, California. Academic Press; 2000.

[4]Simon D. Optimal State Estimation: Kalman, H [infinity] and Nonlinear Approaches, USA:New Jersey: John Wiley & Sons, Inc; 2006.

[5] Gopalakrishnan  A, Kaisare  NS, Narasimhan  S. Incorporating Delayed and Infrequent Measurements in Extended Kalman Filter Based Nonlinear Estimation. Journal of Process Control. 2011;21:119-129

[6] Hermoso-Carazo A, Linares-Pérez J. Unscented filtering algorithm using two-step randomly delayed observations in nonlinear systems. Appl. Math. Model. 2009; 33:3705-3717.

[7] Galdeano R, Asteasuain M, Sanchez MC. Unscented Transformation-based filters. Performance Comparison Analysis for the State Estimation in Polymerization Processes with Delayed Measurements. Macromolecular Reaction Engineering. 2011; In Press

[8] Congalidis  JP,  Richards  J,  Ray  WH. Feedforward and Feedback Control of a Solution Copolimerization Reactor. AIChE Journal.1989; 35:891-907.

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