Nonlinear model predictive control of end-use properties in batch reactors under uncertainty

A reliable batch control strategy should be able to address the objectives of meeting the product quality specifications while operating in an optimal manner. The use of Nonlinear Model Predictive Control (NLMPC) with dynamic process model and static property model for the control of end-use properties is studied. The effect of uncertainty on the state estimation and control and the methodology to incorporate it is the main focus of this work. Two approaches to systematically estimate the process noise covariance matrix for Extended Kalman Filter using the information about model uncertainty are proposed. The proposed two methods calculate time-varying values of the process noise covariance on-line, which are used by the filter. The NLMPC of end-use properties is formulated to control them at a target region, which represents the desired product specifications. A technique using successive linear approximation of the target region is used to find the control moves. The approach to handle uncertainty in NLMPC is based on moving away from the boundaries of the end-use property target region to an appropriate point. This utilizes the joint confidence regions for the end-use properties that are determined online. The Nonlinear Model Predictive Controller problem under uncertainty is formulated as a semi-infinite programming problem. This problem is solved using outer-approximation algorithm and the features of the problem formulation are utilized to reduce the computational demands for the solution. The emulsion polymerization process for styrene is chosen as an example to study the effectiveness of the developed methodologies. The end-use product properties like tensile strength and melt index are controlled in the desired target regions using the manipulated variables, the addition of monomer and the addition of chain transfer agent as well as the flow rate of the coolant.