Non-linear robust control of a voltage-controlled magnetic levitation system with a feedback linearization approach

The magnetic levitation system's control problem is of considerable scientific interest because the system is open-loop unstable and highly non-linear, and the system's parameters are uncertain. In this paper, the system is formulated by a third-order non-linear differential equation. Based on this third-order non-linear system, the system is first linearized by applying the feedback linearization method. Then, the controller is designed based on a global sliding mode technique, which is able to stabilize a linearized system. Experimental results show that, compared with the classic proportional-integral- derivative (PID) controller, the proposed controller provides excellent transient response performance and the system is robust against the non-linear parameter perturbation. Further experiments show that the sampling period is an important parameter to the system robustness. The reason is explained theoretically, and the analysis shows that in the practical global sliding mode control (GSMC) system the smaller the sampling period is, the more robust the controller will be.