Discrete Time Sliding Mode Control of Magnetic Levitation System with Enhanced Exponential Reaching Law

In this study, the control of magnetic levitation system in discrete time domain is considered. Magnetic ball levitation system model is identified, linearized near the equilibrium point and discretized in convenient sampling period. Discrete time sliding mode controller with enhanced exponential reaching law is designed and compared to traditional discrete time constant proportional rate reaching law for the magnetic ball levitation system which is subject to many control problems since it has unstable structure and it has nonlinear dynamics. The asymptotically stability of the system is analyzed by using Lyapunov stability condition with discrete time approach. In order to evaluate the performance of the considered control technique, simulations are conducted and the results show that discrete time enhanced exponential reaching law provides better performance in terms of both reference tracking and disturbance noise rejection as compared to conventional constant proportional rate reaching law techniques.