# Research on Springback Compensation Method of Roll Forming Based on Improved Fuzzy PID Control
## 1 Introduction
Although the above-mentioned scholars have proposed corresponding control schemes and compensation methods for sheet springback, these are all for the advanced prediction of springback amounts and do not respond to the real-time changing springback amounts of sheets. Therefore, there still exists a certain degree of forming error, and there is a lack of high-precision control methods [18]. It is also difficult to guarantee the control accuracy during the circular rolling process. [PERSON] et al. [19] established a finite element model for the radial-axial rolling of super-large ring components integrated with a fuzzy control algorithm for ring center offset. They investigated the variation laws of the ring center offset under conventional control with the optimal speed-matching coefficient and adaptive fuzzy control. [PERSON] and [PERSON] [20] proposed a method for measuring the real-time dimensions of ring components during the rolling process to achieve real-time monitoring of the growth rate. They also established a design-driven control method for the growth rate of ring components (the ideal-state control method). Through a real-time error-feedback regulation strategy, small-scale errors caused by dynamic defects were eliminated, enabling the growth rate to precisely approach the target value. [PERSON] and [PERSON] [21] designed a fuzzy self-adaptive PID controller for a cold bending machine for profiles. Based on conventional PID control, this controller uses fuzzy logic to adjust PID parameters online according to the deviation and its rate of change, further improving the performance of the PID controller and enhancing the accuracy of the position control system. [PERSON] et al. [22] adopted a Siemens S7-200 SMART programmable logic controller (PLC) as the slave station controller. They used an acquisition module to collect the position data of magnetic grid rulers and encoders and a proximity switch for zero-point calibration. The improved system features good stability and easy operation, and the adjustment accuracy of the roll position can reach \(\pm 1\) mm with less time consumption, meeting the requirements for automatic adjustment of the roll position and improving the production efficiency of enterprises. Although the above-mentioned control systems have established corresponding control models, proposed new control methods, and improved control accuracy and anti-interference capabilities, etc., during the control process, they are still unable to respond promptly to the springback of metal sheets. The errors caused by springback during the sheet forming process are still difficult to reduce. To design a reliable and efficient control strategy suitable for circular roll forming, it is essential to simultaneously consider the influence of sheet springback during the circular rolling process and the control accuracy of the circular rolling process. In this paper, the gap between the working roll and the driven rolls is adjusted by means of sheet springback feedback, thereby achieving the control of sheet circular roll forming. The main contributions lie in the proposal of a kinematic model for circular rolling springback compensation and an improved fuzzy PID controller based on the CWP optimization algorithm. The proposed kinematic model for circular rolling springback compensation effectively reduces the circular roll forming error caused by sheet springback.