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Applications of Sliding Mode Control pp 233–268Cite as

Sliding Bifurcations and Sliding Mode Controller for a Two-Cell DC/DC Buck Converter

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Part of the Studies in Systems, Decision and Control book series (SSDC,volume 79)

Abstract

In this chapter, we analyze the sliding bifurcations that occur in the two-cell DC/DC buck converter controlled using a dynamic feedback controller, then we apply the sliding mode controller to the converter in order to inhibit bifurcations and chaotic behavior. We use a simplified discrete model to analyze the bifurcations in the two-cell converter, which can be regarded as a piecewise smooth nonlinear system with discontinuous iterated maps. Then, we give theoretical conditions of stability according to the parameters values of the dynamic feedback controller. The presence of discontinuities in the converter leads to several types of non-smooth bifurcations namely border collision bifurcation, degenerate flip bifurcation and sliding bifurcations such as switching-sliding, grazing-sliding and adding-sliding also called multi-sliding. Non-smooth bifurcations, and more particularly, sliding bifurcations are caused by structural changes in the system dynamics, then we apply the sliding mode controller which is a variable structure control system (VSCS) to avoid sliding modes in the DC/DC buck converter. Numerical simulations confirm the analytical results and explain the bifurcations and the strange phenomena encountered in the two-cell converter.

Keywords

  • Sliding bifurcations
  • Two-cell DC/DC buck converter
  • Dynamic feedback controller
  • Sliding mode controller

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  1. CEMLab, National Engineering School of Sfax, Sfax, Tunisia

    Karama Koubaâ

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  1. University of Sfax, Sfax, Tunisia

    Nabil Derbel

  2. University of Tunis Carthage, Urbain Nord, Tunisia

    Jawhar Ghommam

  3. University of the West of England, Bristol, United Kingdom

    Quanmin Zhu

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Koubaâ, K. (2017). Sliding Bifurcations and Sliding Mode Controller for a Two-Cell DC/DC Buck Converter. In: Derbel, N., Ghommam, J., Zhu, Q. (eds) Applications of Sliding Mode Control. Studies in Systems, Decision and Control, vol 79. Springer, Singapore. https://doi.org/10.1007/978-981-10-2374-3_13

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