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Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties

Author

Listed:
  • Paweł Latosiński

    (Institute of Automatic Control, Lodz University of Technology, 18/22 Bohdana Stefanowskiego St., 90-924 Łódź, Poland
    These authors contributed equally to this work.)

  • Andrzej Bartoszewicz

    (Institute of Automatic Control, Lodz University of Technology, 18/22 Bohdana Stefanowskiego St., 90-924 Łódź, Poland
    These authors contributed equally to this work.)

Abstract

Sliding mode control strategies are well known for ensuring robustness of the system with respect to disturbance and model uncertainties. For continuous-time plants, they achieve this property by confining the system state to a particular hyperplane in the state space. Contrary to this, discrete-time sliding mode control (DSMC) strategies only drive the system representative point to a certain vicinity of that hyperplane. In established literature on DSMC, the width of this vicinity has always been strictly greater than zero in the presence of uncertainties. Thus, ideal sliding motion was considered impossible for discrete-time systems. In this paper, a new approach to DSMC design is presented with the aim of driving the system representative point exactly onto the sliding hyperplane even in the presence of uncertainties. As a result, the quasi-sliding mode band width is effectively reduced to zero and ideal discrete-time sliding motion is ensured. This is achieved with the proper selection of the sliding hyperplane, using the unique properties of relative degree two sliding variables. It is further demonstrated that, even in cases where selection of a relative degree two sliding variable is impossible, one can use the proposed technique to significantly reduce the quasi-sliding mode band width.

Suggested Citation

  • Paweł Latosiński & Andrzej Bartoszewicz, 2021. "Zero-Width Quasi-Sliding Mode Band in the Presence of Non-Matched Uncertainties," Energies, MDPI, vol. 14(11), pages 1-16, May.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:11:p:3011-:d:560230
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    References listed on IDEAS

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    1. Reza Sabzehgar & Yaser M. Roshan & Poria Fajri, 2020. "Modeling and Control of a Multifunctional Three-Phase Converter for Bidirectional Power Flow in Plug-In Electric Vehicles," Energies, MDPI, vol. 13(10), pages 1-19, May.
    2. Yubo Liu & Junlong Fang & Kezhu Tan & Boyan Huang & Wenshuai He, 2020. "Sliding Mode Observer with Adaptive Parameter Estimation for Sensorless Control of IPMSM," Energies, MDPI, vol. 13(22), pages 1-18, November.
    3. Enric Vidal-Idiarte & Carlos Restrepo & Abdelali El Aroudi & Javier Calvente & Roberto Giral, 2019. "Digital Control of a Buck Converter Based on Input-Output Linearization. An Interpretation Using Discrete-Time Sliding Control Theory," Energies, MDPI, vol. 12(14), pages 1-17, July.
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    Cited by:

    1. Katarzyna Adamiak & Andrzej Bartoszewicz, 2022. "Novel Power-Rate Reaching Law for Quasi-Sliding Mode Control," Energies, MDPI, vol. 15(15), pages 1-14, July.
    2. Pawel Latosinski & Andrzej Bartoszewicz, 2023. "Sliding Mode Controllers in Energy Systems and Other Applications," Energies, MDPI, vol. 16(3), pages 1-4, January.

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