Feedback control of polymer quality in semi-batch copolymerization reactors

Abstract

An on-line, nonlinear inferential feedback control strategy for semi-batch emulsion copolymerization reactors is proposed. The proposed strategy features a nonlinear estimator to infer copolymer properties from indirect noisy measurements taken from the process during operation, an on-line implementation of optimal open-loop operating policies for the control of copolymer properties and reactor conditions, and a feedback controller to correct for errors in the recomputed optimal trajectories. In this paper, simulated control of the properties of styrene/butadiene rubber (SBR) is considered. Using knowledge of the modelled chemical reaction mechanisms, a procedure is proposed for developing optimal operating policies based on establishing conditions for maintaining fixed instantaneous copolymer properties or reactor conditions. Well-known univariate approaches are extended to the multivariate case, and new policies are proposed. It is shown that a wide range of copolymer property specifications can be met through the applications of these operating policies. The open-loop feedforward control trajectories required in these policies are simple to compute and, therefore, can be continually recomputed on-line using the improved state estimates provided by the nonlinear state estimator. When the estimated instantaneous conditions or copolymer properties are not at their desired set points, feedback control corrections to the computed open-loop input trajectories are required to eliminate the error. A simple modification to the computation of any open-loop control policy is proposed to introduce feedback control. The modification leads to decoupled, linear first-order responses to estimated set point errors. In the simulation example, the nonlinear inferential feedback control strategy is shown to provide excellent control over copolymer properties, and is demonstrated to the robust to state initialization errors, disturbances and model mismatch. The simple and effective semi-batch control strategy offers a very useful alternative to computationally intensive on-line optimization procedures.