# Research on Springback Compensation Method of Roll Forming Based on Improved Fuzzy PID Control
## 3 Springback Compensation Control Algorithm
### Simulation Analysis of CWP  
To further verify the superiority of the springback compensation control strategy using the CWP optimization algorithm, under the same conditions, MATLAB/Simulink (Version R2021b) was employed to simulate the control effects of the circular roll forming process with and without the springback compensation control strategy, as well as with and without CWP optimization. To simulate the springback of the sheet metal during the circular rolling process, a springback interference quantity is added in the simulation. When the springback of the sheet metal is detected by the distance sensor, the controller adopting the springback compensation strategy will adjust the motor rotation angle to change the gap between the  
\begin{table} \begin{tabular}{c c} \hline \hline
**Parameter** & **Numerical Value** \\ \hline \(\omega_{\max}\) & 0.9 \\ \(\omega_{\min}\) & 0.2 \\ \(c_{1\max}\) & 2 \\ \(c_{1\min}\) & 1.3 \\ \(c_{2\max}\) & 1.7 \\ \(c_{2\min}\) & 0.6 \\ \(p_{\max}\) & 0.5 \\ \(p_{\min}\) & 0.1 \\ Population size & 20 \\ \(t_{\max}\) & 10 \\ \hline \hline \end{tabular}   
working roll and the driven roll, ultimately correcting the springback of the sheet metal. In contrast, the controller without the springback compensation strategy only adjusts the motor rotation angle based on the feedback from the encoder. The simulation results of the circular roll forming control are shown in Figure 10 (all three curves use the encoder as feedback). The curve without the springback compensation strategy fails to respond to the springback during the forming process and ultimately cannot reach the desired forming value. The curve that adopts the springback compensation and is controlled by the traditional fuzzy PID can eventually reach the expected value, yet the response during the control process is too slow, the overshoot is excessive, and the robustness is low, which is not conducive to actual production forming. The control strategy using springback compensation and the fuzzy PID controller optimized by CWP has higher control accuracy. It can not only ensure control precision but also maintain relatively stable operation during the control process, with a small overshoot and a fast response speed, meeting the requirements of the actual production process. The specific numerical values of various parameters for the three curves are presented in Table 5.  
The core of this research focuses on the construction of the system architecture and the verification of basic functions. For Figures 8 and 10, our main concern is the impact of springback interference on the performance of the controller. By simulating the springback phenomenon of sheet metal in actual production, we incorporate the key factor of springback interference into the model. Although some preliminary explorations have been conducted regarding measurement noise or control delays, they have not reached a stage where they can be comprehensively and systematically presented. Currently, our emphasis is on establishing a fundamental understanding of the controller's performance under idealized conditions. Figure 10: Simulation results of roll forming control. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Control Simulation** & **Rise Time, t/s** & **Peak Time, t/s** & **Overshoot, \(\delta\)/\%** & **Control Error, e/\%** \\ \hline Without CWP optimization & 0.5087 & 0.86 & 23.04 & 0.162 \\ After CWP optimization & 0.2139 & 0.31 & 0.99 & 0.004 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Control result parameter values. To validate the core functions of the proposed roll bending process control scheme, regarding the performance of the optimization algorithm, our primary objective is to demonstrate the effectiveness of the entire control system in achieving precise roll bending results. Our work mainly revolves around the roll bending results, and using the proposed method, we have significantly improved the forming quality in these results.