Real Time Optimal Control and State Estimation in Semi-Batch Free-Radical Polymerization Reactors

State estimation is a powerful tool for calculating indirectly important on-line properties of products during polymerization reactions. In free-radical polymerization processes, the trajectory of number average molecular weight permits to define and control the ending characteristics of a polymer as well as its molecular weight distribution. The Automatic Continuous Online Monitoring of Polymerization reactions (ACOMP) provides online measurements of molecular weight average and monomer concentration during polymerization reactions. However, for estimating all other process variables characterizing the process behavior, it is required to implement real time state estimation for tracking their evolution while the reaction takes place.

In this study, a validated nonlinear dynamic process model is combined with an Extended Kalman Filter (EKF) and a non-linear controller. The EKF is employed to improve the accuracy of the measurements and full state estimation while the controller regulates the flow of monomer/initiator to follow an optimal trajectory. As it is known, the efficiency and stability of the EKF depends heavily on the proper tuning of its parameters. Therefore, in this work a novel approach for improving the performance and stability of the EKF is presented. The filter free parameters, which are the covariance matrix of the process, covariance matrix of the noise and error covariance of the initial states, are tuned by using a metaheuristic stochastic global optimization technique able to minimize high dimensional optimization problems.

The feasibility of the approach was validated using a fully automated pilot scale experimental unit running under DCS and connected to ACOMP for on-line state estimation and optimal control. The free-radical polymerization reactions for synthetizing poly-acrylamide using KPS as initiator was utilized as case study. Results illustrate excellent performance and robustness of the filter and controller for achieving the optimal trajectory. Furthermore, real-time molecular weight distribution is monitored using the EKF state estimation.