(188r) A Case Study on Semi-Batch Endpoint Control

The endpoint control problem appears in many chemical processes in which neither of the two starting reactants can remain at the end of the reaction. Having unreacted materials in the final product above some threshold may ruin the batch due to a number of reasons, including difficultly of separation and progression of side reactions after limiting reagent has vanished. Modeling the process is vital in determining how much of each reactant to add in the presence of disturbances, side reactions, and measurement uncertainties. In this talk, a comparison study is performed between four modeling techniques for endpoint control of a semi-batch process: parameter estimation, principal component regression, projection onto latent structures (also known as partial least squares), canonical correlation analysis, and subspace identification.

The case study considers a semi-batch process taken from a collaboration with Eastman Kodak (Rawlings, Jerome, Hamer, & Bruemmer, 1989) (Rawlings & Ekerdt, 2012, Section 9.3). A dihalogenated precursor is dehalogenated using an organic base to form the divinyl product, which is used in photographic film production. Historically, this process has been manually controlled by operators. The batch reactor is charged initially with some approximately known amount of the precursor. Then, a fixed amount of the base B is added to the batch that is sure not to overshoot the end point. A measurement is obtained to check how close the batch is to the specification. Then, a series of injections of B are performed slowly with measurements being taken after each until the target product specification is met. Batch times can be long and vary based on operator experience. Since the conventional method involves conservative trial and error, production is slow and operating costs are high. The primary objective is to automate control and speed up the addition of B to reduce batch times and to increase the profitability of the process. Model predictive control (MPC) is one such advanced control system that can provide these benefits. Since a system model is required for MPC, several modeling techniques are explored in this document.

Both regression-based models of the time-unfolded data and dynamic state-space models are considered. Projection onto latent structures (PLS) and canonical correlation analysis (CCA) are used to develop the regression-based models (Wold, 1966; Hotelling, 1936). Subspace identification and parameter estimation techniques are used for the dynamic state-space models. Subspace identification techniques have been extended to batch processes using (Corbett & Mhaskar, 2016). After validation of these models, the MPC problem is formulated. Using feedback with regression-based models in this context is discussed to ensure zero offset. Simulation results comparing the closed-loop performance of the resulting controllers are presented. We conclude with remarks on the effectiveness and ease of implementation for each modeling technique.

References
Corbett, B., & Mhaskar, P. (2016). Subspace identification for data-driven modeling and quality control of batch processes. AIChE J., 62(5), 1581–1601.
Hotelling, H. (1936). Relations between two sets of variates. Biometrika, 28(3-4), 321–377.
Rawlings, J. B., & Ekerdt, J. G. (2012). Chemical reactor analysis and design fundamentals (2nd ed.). Madison, WI: Nob Hill Publishing. (664 pages, ISBN 978-0-9759377-2-3)
Rawlings, J. B., Jerome, N. F., Hamer, J. W., & Bruemmer, T. M. (1989). End-point control in semi-batch chemical reactors. In Proceedings of the IFAC symposium on dynamics and control of chemical reactors, distillation columns, and batch processes (pp. 323–328).
Wold, H. (1966). Estimation of principal components and related models by iterative least squares. In P. R. Krishnaiah (Ed.), Multivariate analysis (pp. 391–420). Academic Press.