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Saturated Feedback Control Using Different Higher-Order Sliding-Mode Algorithms

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Variable-Structure Systems and Sliding-Mode Control

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 271))

Abstract

In this chapter, a second-order system, which is subject to different disturbances, is considered. Feedback control laws adopting the continuous twisting and the twisting algorithms are designed such that continuous and saturated control signals are introduced to the system. In the case that a state variable is not available for measurement, estimate information obtained through the robust exact differentiator is incorporated into the design. For the closed loops of the aforementioned techniques, global stability properties are established. Effectiveness of the saturated continuous twisting approach using a comparison with the standard continuous twisting one is illustrated in a real-world application.

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Notes

  1. 1.

    As long as the function \(b(t)\ne 0\) is known, the discussed approach may be applied.

  2. 2.

    For other known upper bounds, the proposed technique may still be applied.

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Acknowledgements

The authors would like to appreciate the financial support of the European Union’s Horizon 2020 Research and Innovation Programme (H2020-MSCA-RISE-2016) under the Marie Sklodowska-Curie grant agreement No. 734832. The financial support of the Austrian Federal Ministry for Digital and Economic Affairs and the National Foundation for Research, Technology and Development is also gratefully acknowledged. Furthermore, L. Fridman would like to express his gratitude for the financial support of Consejo Nacional de Ciencia y Tecnología (CONACYT), grant No. 282013; Programa de Apoyo a Proyectos de Investigación e Innovación Tecnológica (PAPIIT-UNAM), grant No. IN 115419.

Author information

Authors and Affiliations

  1. Institute of Automation and Control, Graz University of Technology, Graz, Austria

    Mohammad Ali Golkani & Markus Reichhartinger

  2. Christian Doppler Laboratory for Model Based Control of Complex Test Bed Systems, Graz University of Technology, Graz, Austria

    Stefan Koch & Martin Horn

  3. Department of Control Engineering and Robotics, Division of Electrical Engineering, Engineering Faculty, National Autonomous University of Mexico, México D.F., Mexico

    Leonid Fridman

Authors
  1. Mohammad Ali Golkani
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  2. Stefan Koch
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  3. Markus Reichhartinger
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  4. Martin Horn
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  5. Leonid Fridman
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Corresponding author

Correspondence to Mohammad Ali Golkani .

Editor information

Editors and Affiliations

  1. Institute of Automation and Control, Graz University of Technology, Graz, Austria

    Martin Steinberger

  2. Institute of Automation and Control, Graz University of Technology, Graz, Austria

    Martin Horn

  3. Control Engineering and Robotics Department, National Autonomous University of Mexico, Mexico City, Distrito Federal, Mexico

    Leonid Fridman

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Golkani, M.A., Koch, S., Reichhartinger, M., Horn, M., Fridman, L. (2020). Saturated Feedback Control Using Different Higher-Order Sliding-Mode Algorithms. In: Steinberger, M., Horn, M., Fridman, L. (eds) Variable-Structure Systems and Sliding-Mode Control. Studies in Systems, Decision and Control, vol 271. Springer, Cham. https://doi.org/10.1007/978-3-030-36621-6_4

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