Deep drawing is a metalworking procedure aimed at getting a cold metal sheet plastically deformed in accordance with a pre-defined mould. Although this procedure is well-established in industry, it is still susceptible to several issues affecting the quality of the stamped metal products. In order to reduce defects of workpieces, process control approaches can be performed. Typically, process control employs simple proportional-integral-derivative (PID) regulators that steer the blank holder force (BHF) based on the error on the punch force. However, a single PID can only control single-input single-output systems and cannot handle constraints on the process variables. Differently from the state of the art, in this paper we propose a process control architecture based on Model Predictive Control (MPC), which considers a multi-variable system model. In particular, we represent the deep drawing process with a single-input multiple-output Hammerstein-Wiener model that relates the BHF with the draw-in of $n$ different critical points around the die. This allows the avoidance of workpiece defects that are due to the abnormal sliding of the metal sheet during the forming phase. The effectiveness of the proposed process controller is shown on a real case study in a digital twin framework, where the performance achieved by the MPC-based system is analyzed in detail and compared against the results obtained through an ad-hoc defined multiple PID-based control architecture. Note to Practitioners—This work is motivated by the emerging need for the effective implementation of the zero-defect manufacturing paradigm in the Industry 4.0 framework. Especially in the deep drawing process, various quality issues in stamped parts can lead to significant product waste and manufacturing inefficiencies. This turns into considerable economic losses for companies, particularly in the automotive sector, where deep drawing is one of the most used cold sheet metal forming techniques. In most applications, only sample inspections are performed on batches of finished-product, with subsequent losses of time and resources. For the sake of improving the workpiece quality, innovative strategies for real-time process control represent a viable and promising solution. In this context, the proposed MPC-based process control approach allows the correct shaping of the metal sheet that is getting deformed during the forming stroke, thanks to the draw-in monitoring at various locations around the die. The draw-in is indeed one of the most effective forming variables to control in order to provide a correct BHF during the forming stroke. A useful and easy-to-implement non-linear metal sheet deep drawing process model is provided by this paper to perform an innovative process control strategy. A comprehensive methodology is applied in detail to an automotive case study, ranging from process modeling (model identification and validation based on experimental data acquisition) to MPC implementation (controller tuning and testing and software-in-the-loop system validation). The presented method can be easily implemented on any real deep drawing press, providing the multivariable constrained process with a suitable control system able to make the stamped parts well formed.

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基于 MPC 的拉深过程控制：汽车行业 4.0 案例研究

拉深是一种金属加工程序，旨在使冷金属板根据预定义的模具发生塑性变形。尽管此程序在工业中已得到广泛认可，但它仍然容易受到影响冲压金属产品质量的几个问题的影响。为了减少工件的缺陷，可以执行过程控制方法。通常，过程控制采用简单的比例-积分-微分 (PID) 调节器，根据冲压力的误差来控制压边力 (BHF)。但是，单个 PID 只能控制单输入单输出系统，不能处理过程变量的约束。与现有技术不同的是，在本文中，我们提出了一种基于模型预测控制 (MPC) 的过程控制架构，该架构考虑了多变量系统模型。 $n$模具周围的不同临界点。这可以避免由于金属板在成型阶段的异常滑动而导致的工件缺陷。所提出的过程控制器的有效性在数字孪生框架中的真实案例研究中得到了展示，其中详细分析了基于 MPC 的系统实现的性能，并与通过自组织定义的多个基于 PID 的系统获得的结果进行了比较控制架构。从业者须知——这项工作的动机是对在工业 4.0 框架中有效实施零缺陷制造范式的新兴需求。尤其是在深拉过程中，冲压件的各种质量问题会导致严重的产品浪费和制造效率低下。这给公司带来了巨大的经济损失，特别是在汽车行业，其中深冲是最常用的冷金属板成型技术之一。在大多数应用中，只对成批的成品进行抽样检验，从而造成时间和资源的损失。为了提高工件质量，实时过程控制的创新策略代表了一种可行且有前途的解决方案。在这种情况下，所提议的基于 MPC 的过程控制方法允许在成型行程期间变形的金属板的正确成型，这要归功于在模具周围不同位置的拉入监控。为了在成型行程中提供正确的 BHF，拉入确实是要控制的最有效的成型变量之一。本文提供了一个有用且易于实现的非线性金属板拉深工艺模型，用于执行创新的工艺控制策略。一个全面的方法被详细应用于汽车案例研究，从过程建模（基于实验数据采集的模型识别和验证）到 MPC 实施（控制器调整和测试以及软件在环系统验证）。