Discrete Time Sliding Mode Control Scheme for Nonlinear Systems With Bounded Uncertainties

Jalel Ghabi, Ahmed Rhif and Sundarapandian Vaidyanathan
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Jalel Ghabi: Higher Institute of Applied Sciences and Technology of Kairouan, University of Kairouan, Kairouan, Tunisia
Ahmed Rhif: Higher Institute of Applied Sciences and Technology of Kairouan, University of Kairouan, Kairouan, Tunisia
Sundarapandian Vaidyanathan: R & D Centre, Vel Tech University, Chennai, India

International Journal of System Dynamics Applications (IJSDA), 2018, vol. 7, issue 2, 15-33

Abstract: This article introduces a sliding mode controller to stabilize a discrete-time nonlinear system in the presence of uncertainties and external disturbances. The proposed controller is derived to guarantee the existence of a quasi-sliding mode, taking into account the upper bound of uncertainties. With this method, a recursive switching function is used, which allows for recovering lost invariance and robustness properties of a discrete sliding mode control. As for the system stability, it is found that the system is stabilized and finally restricted to a known region. This control scheme ensures robustness against parametric uncertainties and external disturbances as well as the elimination of chattering. In this article, after a detailed formalization of the proposed control design, a numerical example for an inverted pendulum is considered, proving the effectiveness of the control methodology.

Date: 2018
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