Injection molding is a pivotal industrial process renowned for its high production speed, efficiency, and automation. Controlling the motion speed of injection molding machines is a crucial factor that influences production processes, directly affecting product quality and efficiency. This paper aims to tackle the challenge of achieving optimal tracking control of injection speed in a standard class of injection molding machines (IMMs) characterized by nonlinear dynamics. To achieve this goal, we propose a learning-based model predictive control (LMPC) scheme that incorporates Gaussian process regression (GPR) to predict and model uncertainty in the injection molding process (IMP). Specifically, the scheme formulates a nonlinear tracking control problem for injection speed, utilizing a GPR-based learning residual model to capture uncertainty and provide accurate predictions. It learns the dynamics model and historical data of the IMM, automatically adjusting the injection speed according to target requirements for optimal production control. Additionally, the optimization problem is efficiently solved using a control-constrained differential dynamic programming approach. Finally, we conduct comprehensive numerical experiments to demonstrate the effectiveness and efficiency of the proposed LMPC scheme for controlling injection speed in IMP.

注塑成型是一个关键的工业过程，以其高生产速度、效率和自动化而闻名。控制注塑机的运动速度是影响生产过程的关键因素，直接影响产品的质量和效率。本文旨在解决在以非线性动力学为特征的标准类注塑机 (IMM) 中实现注射速度最佳跟踪控制的挑战。为了实现这一目标，我们提出了一种基于学习的模型预测控制（LMPC）方案，该方案结合高斯过程回归（GPR）来预测和建模注塑过程（IMP）中的不确定性。具体来说，该方案制定了注射速度的非线性跟踪控制问题，利用基于探地雷达的学习残差模型来捕获不确定性并提供准确的预测。它学习注塑机的动力学模型和历史数据，根据目标要求自动调整注射速度，以实现最佳生产控制。此外，使用控制约束微分动态规划方法可以有效地解决优化问题。最后，我们进行了全面的数值实验，以证明所提出的 LMPC 方案用于控制 IMP 注射速度的有效性和效率。