A new control structure with constant pulling speed for growing high-quality crystal in the Czochralski (CZ) method is presented in this brief. In this control structure, the pulling speed is not involved in the controlling of crystal diameter and only the temperature is used as the control quantity. Due to the time delay and the nonlinearity relationship are commonly involved between the temperature and crystal diameter, which make the diameter control difficult and complicated, a generalized predictive controller (GPC) based on the stacked sparse autoencoder (SSAE) is proposed under the new control structure. The time delay is obtained by using the correlation identification algorithm, the input order and output order are determined by the Lipchitz quotients algorithm, and the prediction model is trained by SSAE. Combining the SSAE with the nonlinear GPC algorithm, the control law of the temperature is calculated for diameter control. The simulation result verifies the correctness of the proposed control algorithm. The experimental result indicates that the new control structure with constant pulling speed is more conducive to growing high-quality crystal, avoiding the fluctuation of pulling speed. The proposed SSAE-based GPC algorithm can accurately track the reference diameter. The studies in this brief provide a feasible strategy for growing large size and high-quality crystal in the CZ method.

中文翻译：

---

基于堆叠稀疏自编码器的CZ-Si晶体生长过程中晶体直径的非线性广义预测控制

简要介绍了一种新的控制结构，该控制结构具有恒定的拉速，用于以Czochralski（CZ）方法生长高质量的晶体。在这种控制结构中，提拉速度不涉及晶体直径的控制，而仅将温度用作控制量。由于温度和晶体直径之间通常存在时间延迟和非线性关系，这使得直径控制变得困难和复杂，在这种新型控制下，提出了一种基于堆叠稀疏自编码器（SSAE）的广义预测控制器（GPC）。结构体。通过使用相关性识别算法获得时间延迟，通过Lipchitz商算法确定输入顺序和输出顺序，并通过SSAE训练预测模型。结合SSAE和非线性GPC算法，计算出温度控制规律，以进行直径控制。仿真结果验证了所提控制算法的正确性。实验结果表明，新型的恒定提拉速度控制结构更有利于高品质晶体的生长，避免了提拉速度的波动。所提出的基于SSAE的GPC算法可以准确跟踪参考直径。本简要研究为采用CZ方法生长大尺寸和高质量晶体提供了可行的策略。实验结果表明，新型的恒定提速控制结构更有利于高品质晶体的生长，避免了提速的波动。所提出的基于SSAE的GPC算法可以准确跟踪参考直径。本简要研究为采用CZ方法生长大尺寸和高质量晶体提供了可行的策略。实验结果表明，新型的恒定提速控制结构更有利于高品质晶体的生长，避免了提速的波动。所提出的基于SSAE的GPC算法可以准确跟踪参考直径。本简要研究为采用CZ方法生长大尺寸和高质量晶体提供了可行的策略。