Discrete-Time Sliding Mode Controller For Magnetic Levitation System Using Minima Operator

This paper presents the development of a discrete-time sliding mode controller for a magnetic levitation system, incorporating a minimum operator approach. The primary objective is to precisely stabilize the position of a ferromagnetic ball above the ground within a finite time frame, achieved by utilizing an electromagnet to counteract the gravitational force. In pursuit of this goal, we have devised two discrete-time sliding mode controllers incorporating discrete-time reaching laws. Moreover, a novel formulation for discrete-time sliding mode control with a minimum operator, specifically tailored for this application, has been proposed to ensure finite-time tracking. Simulation results indicate that the proposed methodology, employing the minimum operator approach, delivers a superior response compared to conventional discrete-time sliding mode controllers. Furthermore, the issue of chattering, commonly observed in traditional discrete-time sliding mode controllers used for magnetic levitation systems, is effectively mitigated in our proposed approach.