Optimal Synergetic and Feedback Linearization Controllers Design for Magnetic Levitation Systems: A Comparative Study

In this paper, the stabilization and trajectory tracking of the magnetic levitation (Maglev) system using optimal nonlinear controllers are investigated. Firstly, the overall structure and physical principle represented by the nonlinear differential equations of the Maglev system are established. Then, two nonlinear controllers, namely synergetic control (SC) and feedback linearization based state feedback controller (FL-SFC), are proposed to force the ball's position using the voltage control input in the Maglev system to track a desired trajectory. For the SC design, the Lyapunov function is employed to guarantee an exponential convergence of the tracking error to zero. In the FL-SFC approach, an equivalent transformation is used to convert the nonlinear system into a linear form, and then the state feedback controller (SFC) method is utilized to track the ball to the desired position. The swarm bipolar algorithm (SBA) based on the integral time absolute error (ITAE) cost function is employed to determine the gains of the controllers to achieve the desired response. Computer simulations are conducted to evaluate the performance of the proposed methodology. The results indicate that in normal conditions, the SC controller is more effective than the FL-SFC controller in controlling the Maglev system. Both controllers achieve zero maximum overshoot and zero steady-state error, but SC responds faster, with a settling time of 0.35 seconds compared to FL-SFC's 1.2 seconds. This highlights SC's superior dynamic performance in speed and accuracy. Additionally, when the Maglev system experiences external disturbances, SC shows better resilience, recovering in just 0.1 seconds, while FL-SFC takes 0.65 seconds. The SC exhibits better performance than that of the FL-SFC in terms of reducing the ITAE index and improving the transient response, even when external disturbances are applied.