Online optimizing control of molecular weight properties in batch free-radical polymerization reactors

An online optimizing control scheme that ensures the satisfaction of the final polymer property specifications under the influence of time-varying model parameters and unknown initial conditions is developed for a batch polymerization reactor. The proposed control scheme combines a state/parameter estimator with an optimization step that calculates periodically the time optimal polymerization temperature based on the most recent information about the process. The state/parameter estimation step includes an extended Kalman filter for estimating the state variables and the time-varying termination rate constant of the model and a nonlinear optimization-based estimator for calculating the concentration of impurities at the start of the polymerization. The time optimal polymerization temperature that drives the process to the desired final polymer property specifications is determined using a dynamic programming technique based on the simultaneous discretization approach. A quadratic performance index is defined in terms of the squared differences between the achieved and desired values of final monomer conversion, number- and weight-average molecular weights, and the entire desired molecular weight distribution. The time optimal temperature policy is implemented, as a sequence of discrete set-point changes, by the regulatory control system of the reactor. The proposed control strategy manages to optimally satisfy the control objectives and keep the product quality indicators close to the desired levels in a least-squares sense by successfully alleviating the detrimental effects of process disturbances and model parameter variations.