Research on fuzzy proportional–integral–derivative (PID) control of bolt tightening torque based on particle swarm optimization (PSO)

Abstract. Bolt connections are common in industrial and manufacturing applications; however, improper torque tightening can lead to issues such as over-tightening or under-tightening, which negatively affect connection quality and lifespan. To enhance the precision of bolt tightening, this paper introduces a particle swarm optimization (PSO) algorithm to optimize a fuzzy proportional–integral–derivative (FPID) controller. Effective methods for adjusting the parameters of the PSO and FPID control systems are also explored to improve the control performance while ensuring stability and reliability under complex load conditions. Simulations were conducted using MATLAB Simulink to compare the tightening speeds of the PSO-optimized FPID controller, the PSO-optimized PID controller, the traditional FPID controller, and the PID controller. Results indicate that the PSO-optimized FPID controller significantly improves the response speed, reduces overshoot, and enhances the system's adaptability and robustness. In experiments targeting a torque of 12 N m, the average deviation is 0.108 N m, achieving a control accuracy of 0.9 %. These findings validate the effectiveness of the proposed control system and demonstrate a marked improvement in the precision of bolt tightening. Overall, this research highlights the potential of integrating PSO into FPID control to enhance the bolt connection quality and reliability, addressing a critical aspect of industrial fastening.