The study for stability of closed-loop control system based on multiple-step incremental air-bending forming of sheet metal

To solve the springback problem for sheet metal forming, feedback control idea in automatic control theory is introduced to incremental air-bending forming process. The advanced control techniques are used to solve precision forming for workpiece of sheet metal. However, stability, accuracy, and rapidity of closed-loop control can directly affect system normal operation. Aiming to analyze the effect of stability on the quality of the formed workpiece, a closed-loop control system model for incremental air-bending forming is established. The transfer function and characteristic equation of the closed-loop system are solved through theory deduction and minor incremental linearization method. Both simulations with Matlab/Simulink and root locus results show that, as the overall gain is equal to one, the shape of formed part could converge to the target shape at the fastest rate. Finally, a semiellipse-shape workpiece is manufactured with the corrected mold obtained by the closed-loop forming method. The experimental results show that the closed-loop forming way is feasible and the means of correcting the mold parameters by iterative compensation of the stable closed-loop control system is effective. It can be taken as a new approach for sheet metal incremental air-bending forming and mold design.