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基于抛物线型偏微分方程(PDE)研究了直拉式单晶炉中生长界面的温度控制,将Galerkin法应用于PDE的处理,求解中使用空间映射对较复杂形状的空间区域进行简化,并用Karhunen-Loève(KL)分解法求取经验特征方程;针对非齐次边界条件,设计了一种高效的模型分解方法,基于优化模型引入最优控制方法实现了温度控制,验证了模型的有效性.
Based on the parabolic partial differential equation (PDE), the temperature control of growth interface in a Czochralski single crystal furnace was studied. The Galerkin method was applied to the treatment of PDE. In the solution, spatial maps were used to simplify the spatial regions with more complex shapes. Karhunen -Loève (KL) decomposition method is used to obtain the empirical characteristic equation. For the non-homogeneous boundary conditions, an efficient model decomposition method is designed. Based on the optimization model, the optimal control method is introduced to realize the temperature control, and the validity of the model is verified.