## 2 State of the Art
### Die Bending
#### 2.1.2 Control Approaches  
There are numerous examples in the literature of how to compensate for springback during sheet metal bending. Numerical or experimental tests are usually carried out to investigate the springback for specific combinations of material, sheet thickness and bending radius. However, compensation usually refers to (iterative) design adjustments to the tool system in order to match the desired product geometry. References [11; 12] both propose approaches based on the displacement adjustment method. Here, the shape deviation is iteratively reduced based on the displacement of simulation nodes and can therefore be time consuming. Due to the higher flexibility of air bending, multiple approaches can be found in the literature for controlling the springback inline. One possible approach is incremental bending. Reference [13] presents press brake bending, where the punch stroke is divided into incremental steps, after which the workpiece is unloaded multiple times. From the multiple collected pairs of loaded and unloaded bending angles, the actual thickness and material properties of the workpiece are predicted based on an analytical model. This information is then used to predict the springback using the plane strain theory. Similarly, reference [14] uses a semi-analytical process simulation in combination with online measurements to compensate for springback during air bending. In order to compensate for the effects of fluctuating material properties on a bending angle, reference [15] uses force signals from an adjacent forming stage of a progressive die for material characterization. It has been demonstrated that a LASSO regression may serve to reduce the deviation by 24%. More recent studies focus on the use of artificial neural networks for springback prediction. Reference [16] shows an example where neural networks are trained with FEM simulations to predict springback. The predictions of the network align well and thus represent an inline-capable alternative to FEM. Reference [17] developed a tool path planning strategy based on RL and supervised learning. The efficacy of this approach is evaluated through a case study, which involves an FEM simulation of a rubber tool forming process. It has been demonstrated that a substantial reduction in geometry deviations can be achieved. Reference [18] presents a method for predicting springback in air bending of high-strength sheet metal using a neural network. The springback is predicted by the model based on process parameters like sheet thickness, punch radius and material coefficients. The model was then validated by numerical and experimental tests. Reference [19] develops a neural network control system along with a stepped binder force trajectory to control the springback in a steel channel forming process. In order to demonstrate the generalizability of the model, various configurations of material and lubrication conditions that had not been used for training were employed. Although significant improvements in accuracy were achieved, the study also highlights the need for more advanced sensing  
Figure 2: Stresses and bending angles in flexible die bending.  
technologies and the implementation of real-time closed-loop control to further enhance process stability and performance. Reference [20] addresses this issue by presenting an online springback compensation model for an air bending process. The study demonstrates that in-line control of the bending process can be achieved by integrating camera-based bending angle detection with neural networks and the press controller. The results show that the control strategy significantly improves the accuracy of the achieved bending angle.