IMPA-optimized fuzzy FOPID tension control for transformer insulation winding under periodic disturbances

Periodic tension fluctuations induced by a non-circular mandrel remain a major challenge in transformer rectangular-coil insulation winding. This study proposes a fuzzy fractional-order PID (FOPID) control method optimized by an improved marine predators algorithm (IMPA). Dynamic and geometric periodic-disturbance models of the winding system are established. IMPA, incorporating the Safe Experimentation Dynamics Algorithm (SEDA), is used to tune the baseline FOPID parameters offline, while fuzzy logic adjusts the controller gains online. Simulation results show that the proposed method reduces peak error and periodic fluctuations under different tension and speed step conditions; compared with conventional PID, the maximum reduction in peak tension error is approximately 42%. Experiments further show that, over the tested operating conditions, the maximum static error rate and fluctuation rate are 2.495% and 23.273%, respectively. These results demonstrate the effectiveness and practical feasibility of the proposed method for stable tension regulation during rectangular-coil transformer insulation winding in practical manufacturing applications.