Optimization of diffusion-controlled free radical polymerizations in a distributed parameter system

This paper deals with open-loop optimal boundary control for free radical polymerizations of styrene in the casting process. The system is characterized by a set of parabolic partial differential equations, where the monomer conversion, initiator conversion, moments of dead polymers, and temperature (state variables) depend on both time and radial position in the reactor. The objective is to seek the optimal wall temperature that will minimize either reaction time or molecular weight distribution (MWD). A kinetic-diffusion model considering the gel effect and the glass effect is used. By using variational methods, the problems can be formulated via either "early discretization" or "late discretization" approach. The Min-H technique is applied to the problems formulated by the "early discretization" approach in obtaining optimal wall temperature profiles. For the system studied, it is found that variations of the optimal wall temperature profiles show great resemblance to those obtained for the corresponding lumped-parameter cases.