# System Design and Experimental Study of a Four-Roll Bending Machine
## 4 Control System Design
### Control Process  
Based on the working principle and control requirements of the four-roll bending machine, its control process can be designed as a multi-feedback semi-closed-loop control system. Combined with a symmetric layout, it enables automated processing of plate bending and forming.  
Manual Operation and Feedback: In manual mode, the HMI sends a single instruction to the motion controller for single-step control. Upon receiving the instruction, the motion controller executes the corresponding operation and sends feedback information identical to the instruction code back to the HMI. After receiving the feedback, the HMI confirms that the instruction has been successfully sent and executed.  
Automatic Batch Instruction Execution: For complex bending tasks, a large number of control instructions can be pre-stored in an execution file. The motion controller reads and executes the instruction sequence in this file, thereby completing batch operation execution to realize an automated bending process. The control process of the four-roll bending machine is described below, as illustrated in Figure 14.  
Figure 13: Overall Architecture of the Four-Roll Bending Machine Control System.  
Upon program initiation, the system first checks whether initialization and reset are completed and verifies if all rollers are at the home position. If not, manual homing is required. After homing confirmation, the profile is placed, and the system enters automatic bending mode with the preset radius R input. The system automatically calculates the side roller displacement Y based on its built-in mathematical model. The motion controller outputs a digital signal, which the servo driver converts into a pulse + direction signal to drive the lower roller servo cylinder, pushing the lower roller upward to clamp the profile. Simultaneously, the left roller servo cylinder pushes the left roller upward to the centering position, triggering the drive roller action command. The stepper motor drives the drive  
Figure 14: Control Flow Chart.  
roller to rotate clockwise until the left end face of the profile contacts the left roller end face, completing centering and transitioning to the pre-bending phase. During pre-bending, the left roller servo cylinder retracts the left roller to its initial position, and the drive roller rotates counterclockwise to retract the profile. Subsequently, the right roller servo cylinder drives the right roller upward by displacement Y, and the stepper motor drives the drive roller to rotate clockwise until it reaches the left end of the left roller end face, completing pre-bending. The process then enters the bending stage: the right roller servo cylinder retracts the right roller to its initial position, while the left roller servo cylinder pushes the left roller upward by displacement Y, and the drive roller rotates clockwise until the profile is fully bent. After bending completion, the left and lower rollers return to their initial positions for unloading. Manual bending operation is largely consistent with automatic mode but requires manual input of the preset side roller displacement Y, with each operational step needing manual button confirmation by the operator. The drive roller rotation speed is set via HMI voltage adjustment.  
This study adopts the post-springback radius-lateral roller displacement relationship model proposed by [PERSON] et al. (2018) as the mathematical description of the roll bending process, where the model expression can be formulated as:  
\[Y=11230\times{R_{f}}^{-0.7039}+21.7. \tag{22}\]  
where \(Y\) represents the lateral roller displacement and \(R_{f}\) represents the roll bending radius.