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Sliding Mode Control of Class of Linear Uncertain Saturated Systems

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Advances and Applications in Sliding Mode Control systems

Part of the book series: Studies in Computational Intelligence ((SCI,volume 576))

Abstract

This chapter proposes a new design approach of continuous sliding mode control of linear systems in presence of uncertainty and saturation. The saturation constraint is reported on inputs vector and it is subject to constant limitations in amplitude. The uncertainty is being norm bounded reported on both dynamic and control matrices. In general, sliding mode control strategy consists on two essential phases. The design of the sliding surface is the first phase which is formulated as a pole assignment of linear uncertain and saturated system in a specific region through convex optimization. The solution to this problem is therefore numerically tractable via linear matrix inequalities (LMI) optimization. The controller design is the second phase of the sliding mode control design, which leads to the development of a continuous and non-linear control law. This nonlinear control law is build by choosing switched feedback gain capable of forcing the plant state trajectory to the sliding surface and maintaining a sliding mode condition. To give provider of robustness of the proposed nonlinear control, an approximation on the trajectory deviation of the uncertain saturated system compared to the ideal behavior is proposed. Finally, the validity and the applicability of this approach are illustrated by a multivariable numerical example of a robot pick and place.

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Author information

Authors and Affiliations

  1. School of Rural Equipment Engineers, ESIER, Medjez Elbeb, Tunisia

    Bourhen Torchani

  2. National Higher School of Engineering, ENSIT, Tunis, Tunisia

    Anis Sellami

  3. University of Toulouse, LAAS-CNRS, Toulouse, France

    Germain Garcia

Authors
  1. Bourhen Torchani
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  2. Anis Sellami
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  3. Germain Garcia
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Corresponding author

Correspondence to Bourhen Torchani .

Editor information

Editors and Affiliations

  1. Faculty of Computers and Information, Benha University, Benha, Egypt

    Ahmad Taher Azar

  2. Department of Engineering Design and Mathematics, University of the West of England, Bristol, United Kingdom

    Quanmin Zhu

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Torchani, B., Sellami, A., Garcia, G. (2015). Sliding Mode Control of Class of Linear Uncertain Saturated Systems. In: Azar, A., Zhu, Q. (eds) Advances and Applications in Sliding Mode Control systems. Studies in Computational Intelligence, vol 576. Springer, Cham. https://doi.org/10.1007/978-3-319-11173-5_5

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  • DOI: https://doi.org/10.1007/978-3-319-11173-5_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-11172-8

  • Online ISBN: 978-3-319-11173-5

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