Optimal Backstepping and Feedback Linearization Controllers Design for Tracking Control of Magnetic Levitation System: A Comparative Study - Al-Ani, Fatin R.; Lutfy, Omar F.; Al-Khazraji, Huthaifa (Universitas Muhammadiyah Yogyakarta, 2024)
In this paper, the stabilization and trajectory tracking of the magnetic levitation (Maglev) system using optimal nonlinear controllers are considered. Firstly, the overall structure and physical principle represented by the nonlinear differential equations of the Maglev system are established. Then, two nonlinear controllers, including backstepping control (BSC) and feedback linearization (FL), are proposed to force the position of the ball in the Maglev system to track a desired trajectory. In terms of designing the control law of the BSC, the Lyapunov function is utilized to guarantee an exponential convergence of the tracking error to zero. For developing the control law of the FL, an equivalent transformation to convert the nonlinear system into a linear form is used, and then, the state feedback controller (SFC) method is utilized to track the ball to the desired position. In order to obtain a higher accuracy in motion control of the ball, the gains’ selection for the controllers to reach the desired response is achieved using the swarm bipolar algorithm (SBA) based on the integral time absolute error (ITAE) cost function. Computer simulations are conducted to evaluate the performance of the proposed methodology, and the results prove that the proposed control strategy is effective not only in stabilizing the ball but also in rejecting the disturbance present in the system. However, the BSC exhibits better performance than that of the FL-SFC in terms of reducing the ITAE index and improving the transit response even when the external disturbance is applied. The numerical results show that the settling time reduced to 0.2 seconds compared to 1.2 seconds for FL-SFC. Moreover, the ITAE index is reduced to 0.0164 compared to 0.2827 seconds for FL-SFC. In the context of external disturbance, the findings demonstrate that BSC reduced the recovery time to 0.05 seconds compared to 0.65 seconds for FL-SFC.