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

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

Jalel Ghabi, Ahmed Rhif, Sundarapandian Vaidyanathan
Copyright: © 2018 |Volume: 7 |Issue: 2 |Pages: 19
ISSN: 2160-9772|EISSN: 2160-9799|EISBN13: 9781522546603|DOI: 10.4018/IJSDA.2018040102
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MLA

Ghabi, Jalel, et al. "Discrete Time Sliding Mode Control Scheme for Nonlinear Systems With Bounded Uncertainties." IJSDA vol.7, no.2 2018: pp.15-33. http://doi.org/10.4018/IJSDA.2018040102

APA

Ghabi, J., Rhif, A., & Vaidyanathan, S. (2018). Discrete Time Sliding Mode Control Scheme for Nonlinear Systems With Bounded Uncertainties. International Journal of System Dynamics Applications (IJSDA), 7(2), 15-33. http://doi.org/10.4018/IJSDA.2018040102

Chicago

Ghabi, Jalel, Ahmed Rhif, and Sundarapandian Vaidyanathan. "Discrete Time Sliding Mode Control Scheme for Nonlinear Systems With Bounded Uncertainties," International Journal of System Dynamics Applications (IJSDA) 7, no.2: 15-33. http://doi.org/10.4018/IJSDA.2018040102

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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.

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