# Research on Springback Compensation Method of Roll Forming Based on Improved Fuzzy PID Control
## 1 Introduction  
Circular roll forming of metal sheets is extensively employed in industries such as aerospace, construction, automotive manufacturing, shipbuilding, and electronics [1, 2, 3, 4]. Plate-rolling machines play a pivotal role in the circular roll forming of metal sheets. Among them, three-roll plate-rolling machines are widely utilized in the industrial field. The precision of circular roll forming is subject to the influence of numerous factors. Notably, the continuous springback generated during the rolling process of metal sheets stands as the most substantial interfering factor [5, 6]. Regarding the circular roll forming of metal sheets, scholars from around the globe have carried out extensive research efforts. [PERSON] [7] conducted a study on the springback and stress distribution characteristics of 316 L austenitic stainless-steel sheets after JCOE bending and unloading. By implementing corresponding compensation for the pre-bending amount, the bending forming accuracy was enhanced. The model constructed by [PERSON] can provide a theoretical foundation for actual production. [PERSON] and [PERSON] [8] explored the ellipticity issue in three-roll bending and established a quantitative relationship between the reduction amount and the elastic area. [PERSON] and [PERSON] [9] proposed a continuous compound straightening process for three-roll bending of large-diameter longitudinal-seam welded pipes and developed experimental equipment. The feasibility of the new processwas experimentally verified. [PERSON] et al. [10], by means of a model prediction error classification model and a model prediction correction method considering error compensation, constructed a prediction-correction model for elongation after fracture considering error compensation. This model enabled the prediction accuracy of elongation after fracture within an absolute error range of \(\pm\)0.9% to reach 94.63%. [PERSON] et al. [11] developed an angle compensation method based on the UDT-type angle adjustment method. High-precision springback control was achieved through finite element analysis simulation, providing a new approach for effective springback control during the roll forming process of high-speed steel with complex cross-sections. [PERSON] et al. [12] proposed an experimental model for the roll forming process of a symmetric U-shaped cross-section of advanced high-strength steel (AHSS) material (DP600 type). The optimal values of process parameters for the minimum elastic longitudinal strain at each rolling station and the shear strain at the strip edge were calculated. This led to a reduction of 20-35% in the elastic longitudinal strain and 30-50% in the shear strain at all rolling stations, thereby improving the rolling quality. [PERSON] and [PERSON] et al. [13] took into account the mechanical problems in the three-roll bending forming process, established a mechanical model for the upper roll, and analyzed the method of using deflection compensation to improve the circular rolling quality. [PERSON] [14] considered the influence of bending force and residual stress in the asymmetric roll bending forming process, established theoretical models for predicting bending force and residual stress, and analyzed the causes of residual stress. [PERSON] et al. [15] established a hybrid numerical analysis method to study the influence of bending force and bending radius on the displacement of the upper roll. [PERSON] and [PERSON] [16] considered the influence of the non-linear elastic modulus on the springback prediction of high-strength steel roll forming. Through experiments and simulations, it was demonstrated that the variable elastic modulus model is more accurate than the constant elastic modulus model in predicting springback problems. [PERSON] and [PERSON] [17] studied the surface wear depth of pipes and explored the influence of forming process parameters on wear.