Periodic adaptive learning operation control method for maglev trains using multi-harmonic estimation

A model reference periodic adaptive learning control method based on multi-harmonic resistance estimation (MH-MRAC-PALC) was proposed according to the periodic operation characteristics of maglev trains on fixed routes to improve the operation control position and speed tracking accuracy of maglev trains. The designed composite controller consists of three parts: feedback control, feedforward control, and the multi-harmonic resistance estimation compensator. Meanwhile, based on Lyapunov stability theory, the parameter update rate of the estimation compensator was designed. By integrating real-time data of the current cycle and historical cycle operation information, online estimation and dynamic compensation of the operating resistance were achieved with the MH-MRAC-PALC controller. Based on the maglev test line, numerical simulation was conducted, and comparative analysis between the designed controller, conventional PID controller and MH-MRAC controller was carried out. The simulation results show that after 20 cycles of learning, the position tracking performance of the MH-MRAC-PALC controller is significantly improved, its root mean square error (RMSE) is reduced from 0.076 4 m in the first cycle to 0.006 9 m, and the maximum error is reduced from 0.254 8 to 0.027 4 m. Additionally, the speed tracking RMSE is reduced from 0.035 6 m·s^-1 to 0.002 9 m·s^-1, and the maximum error is reduced from 0.104 7 to 0.012 2 m·s^-1. In comparison, the position and speed RMSEs of the PID controller are 0.633 6 m and 0.076 3 m·s^-1, respectively, and those of the MH-MRAC controller are 0.085 3 m and 0.040 1 m·s^-1, respectively. After 20 operation cycles of learning, the MH-MRAC-PALC controller can accurately estimate the multi-harmonic resistance. In complex working conditions with unknown resistance and slope disturbance, the controller exhibits stronger anti-interference ability and higher tracking accuracy. Compared with traditional PID control and MRAC control, the MH-MRAC-PALC control method achieves accurate resistance estimation, reduces the position and speed tracking errors, and significantly improves the operation control performance of maglev trains through the periodic learning mechanism.