Dynamic optimization of batch free radical polymerization with conditional modeling formulation through the adaptive smoothing strategy

With the increase of conversion and viscosity, a batch free radical polymerization (FRP) may encounter complicated phenomena, including the gel, glass, and cage effects. These effects normally lead to a conditional modeling formulation described by a set of differential-algebraic equations (DAEs). Discontinuous gradient exists at model switches triggered by occurrence of the effects, which cause difficulty for dynamic optimization on the batch process. To deal with the discontinuity, interior-point smooth approximations are proposed to describe the model switches at the occurrence of the effects. An adaptive smoothing strategy, which can efficiently balance the efficiency of optimization and the accuracy of the approximated model, is proposed for the dynamic optimization. To show the effectiveness of this smoothing strategy, case studies for optimal operating profiles in a polymerization process of methyl methacrylate are conducted. Good computational performance is achieved with the proposed strategy. (C) 2018 Elsevier Ltd. All rights reserved.