Model-based On-Line Optimization Framework for Semi-batch Polymerization Reactors

Until recently, computational complexities and lack of detailed, nonlinear dynamic models have stood as main obstacles to widespread industrial adoption of model-based on-line optimization for operation of batch and semi-batch reactors. With recent advances in both dynamic modeling techniques and nonlinear programming (NLP) solvers, it is conceivable now to use significantly-sized, nonlinear models directly for on-line state/parameter estimation and optimal control calculations. In this study, we propose a framework for doing this. In the proposed framework, nonlinear first principles dynamic model-based optimizations are performed at several time points throughout a batch run over a fixed horizon, in order to estimate the current state of the model and to refine the target batch time and input variables. Here we combine shrinking horizon nonlinear model predictive control (sh-NMPC) with expanding horizon least squares estimation (eh-LSE). This framework is tested on a large-scale anionic propylene oxide (PO) polymerization process, whose operation considers not only certain end-product specifications but also safety constraints. It is shown that the proposed method is not only computationally feasible (averaging less than 10 CPU seconds at each sampling time) but leads to excellent performance, satisfying the product specification target despite initialization errors and measurement noise.