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Synthesis of an Optimal Sliding Function Using LMIs Approach for Time Delay Systems

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Applications of Sliding Mode Control

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

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Abstract

During the reachability phase, the sliding mode control is sensitive to external disturbances and uncertainties. In this paper, we propose to determine coefficients of the sliding function using the technique of Linear Matrix Inequalities (LMIs) for single-input single-output time delay systems. This technique leads to an optimal choice of the sliding function to reduce the reachability phase. Using the proposed sliding function, a discrete second order sliding mode control is presented. The control law is based on an input–output model. Simulation results demonstrate that the proposed strategy leads to an optimal performance in terms of reduction of the reachability phase as well as the chattering phenomenon.

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Acknowledgments

This work has been supported by the Ministry of Higher Education and Scientific Research in Tunisia.

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Authors and Affiliations

  1. Research Unit: Numerical Control of Industrial Processes (CONPRI), National Engineering School of Gabes, University of Gabes, Gabes, Tunisia

    Houda Romdhane, Khadija Dehri & Ahmed Said Nouri

Authors
  1. Houda Romdhane
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  2. Khadija Dehri
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  3. Ahmed Said Nouri
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Corresponding author

Correspondence to Houda Romdhane .

Editor information

Editors and Affiliations

  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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Romdhane, H., Dehri, K., Nouri, A.S. (2017). Synthesis of an Optimal Sliding Function Using LMIs Approach for Time Delay Systems. 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_4

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  • DOI: https://doi.org/10.1007/978-981-10-2374-3_4

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-10-2373-6

  • Online ISBN: 978-981-10-2374-3

  • eBook Packages: EngineeringEngineering (R0)

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