Robust Position Control of a Levitating Ball via a Backstepping Controller

Abstract

In this paper, a combination of a robust backstepping controller and an integral action for a magnetic levitation system is presented. The mathematical model of the magnetic levitation system containing uncertainties and high-order nonlinear terms has quite a complex structure. The principal aim of this study is to drive the ball position to the desired reference in the presence of a complex structure, parametric uncertainties, and time-varying disturbances. The designed nonlinear controller is based on the robust backstepping technique, in which the robustness is provided via nonlinear damping terms. The boundedness of the tracking error is guaranteed with this method. In order to eliminate steady-state position error caused by the uncertainties and unmodeled dynamics, an integral term is added to the controller structure. After designing the proposed nonlinear controller, the overall closed-loop stability is accordingly analyzed with a Lyapunov-like function. Simulation studies are performed and the results are presented to test the success and the performance of the proposed controller.