The product quality of injection-molded plastic is closely related to the injection flow velocity of molten plastics. In this article, an optimal tracking control problem for the injection flow front position arising in the filling process in the injection molding machine (IMM) is considered, and an intelligent real-time optimal control method based on deep neural networks (DNNs) is developed for the online tracking of the flow front position to improve the efficient production process of the plastics. To this end, a highly nonlinear dynamic model describing the filling process is first proposed and then an optimal control problem is formulated. A high-fidelity numerical optimization approach known as the Gauss pseudospectral method is used to numerically obtain the optimal state-control solutions, which can then be saved as a huge training data set for the DNNs. The DNNs architecture is then developed and offline trained using the obtained data set to determine the best state–control relationship. As a consequence, the well-trained DNN may be utilized to produce the matching optimum feedback action on-board. Numerical studies are also carried out to verify the performance of our proposed approach.

中文翻译：

---

基于深度学习的注塑机流锋位置最优跟踪控制

注塑塑料的产品质量与熔融塑料的注射流速密切相关。本文针对注塑机 (IMM) 充填过程中出现的射流前沿位置优化跟踪控制问题，开发了一种基于深度神经网络 (DNN) 的智能实时优化控制方法用于流动前沿位置的在线跟踪，以提高塑料的高效生产过程。为此，首先提出描述填充过程的高度非线性动态模型，然后制定最优控制问题。一种称为高斯伪谱法的高保真数值优化方法用于在数值上获得最佳状态控制解决方案，然后可以将其保存为 DNN 的庞大训练数据集。然后开发 DNN 架构并使用获得的数据集进行离线训练以确定最佳状态-控制关系。因此，训练有素的 DNN 可用于在机上产生匹配的最佳反馈动作。还进行了数值研究以验证我们提出的方法的性能。