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.

随着转化率和粘度的增加，间歇式自由基聚合（FRP）可能会遇到复杂的现象，包括凝胶，玻璃和笼效应。这些影响通常导致由一组微分代数方程（DAE）描述的条件建模公式。由效果发生触发的模型开关处存在不连续的梯度，这给批处理过程的动态优化带来了困难。为了处理不连续性，提出了内点平滑逼近来描述效应发生时的模型切换。针对动态优化问题，提出了一种可以有效平衡优化效率和近似模型精度的自适应平滑策略。为了展示这种平滑策略的有效性，进行了甲基丙烯酸甲酯聚合过程中最佳操作曲线的案例研究。所提出的策略实现了良好的计算性能。