MPC-Based Process Control of Deep Drawing: An Industry 4.0 Case Study in Automotive

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.