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

Abstract

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 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> 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. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —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.