Adaptive tracking control of a magnetic levitation system based on class K_∞ function

In this letter, an adaptive nonsingular terminal sliding mode (ANTSM) controller is proposed for a magnetic levitation system (MLS). Class K_∞ function is utilized for designing the adaptive gain and based on which, the sliding variable asymptotically converges to a neighborhood around zero whose size can be tuned to be arbitrarily small by tuning the function's parameters. Then, the introduced nonsingular terminal sliding function guarantees a resultant fast convergence of the system. Moreover, the class K_∞ function-based adaptive gain estimates the disturbance's variation without knowing its upper bound information a priori. In addition, the linearization of nonlinear system model is not required any longer and the controller is constructed based on the nonlinear one that will not sacrifice the control robustness. Lyapunov analysis verifies that under the proposed control, the tracking error of the ball's position is asymptotically bounded in an arbitrarily-small region. Finally, simulations are carried out to demonstrate the superiorities of the proposed method with higher precision and stronger robustness against the imposed disturbance force compared to conventional methods.