Performance Analysis of Backstepping Control Technique for Magnetically Levitating Train System in the Presence of Time Varying Load

Abstract

Magnetically levitating trains (maglev) are becoming a popular research topic these days since they are a fast mode of public transportation that is environment friendly and requires little maintenance. Because of the maglev train system is a highly nonlinear and unstable system, its efficacy is dependent on a well-designed tracking controller to stabilize the train and follow the desired reference signal. This research work focuses on the performance analysis of a backstepping controller (BSC), which is used for the tracking control of the maglev train with time varying load change and external disturbance. The proposed BSC controller parameters are obtained by minimizing the IAEU using the particle swarm optimization (PSO) algorithm. The LQR controller incorporating with an integral action is also designed for comparison purpose. MATLAB software is used to verify both controllers’ tracking performance using different types of reference signals, as well as their performance robustness under the effects of mass change and external disturbance force. The obtained simulation results demonstrate that the backstepping control method outperforms the LQR by reducing peak time by 68% and 30.8%, settling time by 28.8% and 27.7%, rise time by 26% and 26.7%, and IAEU by 26.1% and 25.3%, for upward and downward reference signals, respectively. Similarly, the BSC maintains improved tracking performance by lowering the IAEU value for both multiple step and sinusoidal signals. The performance robustness of both controllers is tested using load variations of up to 40% mass change, time varying load changes, and external disturbance force. In the 40% load change, the proposed control method gives 0.652sec, 0.129sec, 0.193sec, and 0.183 of peak time, rise time, settling time, and IAEU, which are small in comparison to the LQR, respectively. In the external disturbance force rejection test, the BSC settles at 0.193sec with 0.196 IAEU value despite the fact that the overshoot (0.11%) is slightly higher than the LQR controller. For the tracking performance robustness against both time-varying load changes and external disturbance force, the BSC provides 18.993%, 0.124sec, 12.129sec, and 0.317 of overshoot, rise time, settling time, and IAEU, which are all small compared to the LQR. Generally, the simulation results showed that the proposed BSC outperformed the LQR controller in terms of both tracking performance and robustness against load variation and external disturbance force.