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Reaching Law Based Sliding Mode Control of Sampled Time Systems

Author

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  • Piotr Leśniewski

    (Institute of Automatic Control, Łódź University of Technology, 18/22 Bohdana Stefanowskiego St., 90-924 Łódź, Poland)

  • Andrzej Bartoszewicz

    (Institute of Automatic Control, Łódź University of Technology, 18/22 Bohdana Stefanowskiego St., 90-924 Łódź, Poland)

Abstract

In this paper, discrete time reaching law-based sliding mode control of continuous time systems is considered. In sliding mode control methods, usually the assumption of bounded absolute values of disturbances is used. However in many cases, the rate of change of the disturbance is also bounded. In the presented approach, this knowledge is used to improve the control precision and reduce the undesirable chattering. Another advantage of the proposed method is that the disturbance does not have to satisfy the matching conditions. In the paper two new reaching laws are analyzed, one of them ensures the switching quasi-sliding motion and the other the non-switching motion. For both of them, the robustness is assessed by calculating the quasi-sliding mode band width, as well as the greatest possible state error values. Specifically, the state errors are not considered only at the sampling instants, as is usual for discrete time systems, but the bounds on the continuous values “between” the sampling instants are also derived. Then, the proposed approaches are compared and analyzed with respect to energy expenditure of the control signal.

Suggested Citation

  • Piotr Leśniewski & Andrzej Bartoszewicz, 2021. "Reaching Law Based Sliding Mode Control of Sampled Time Systems," Energies, MDPI, vol. 14(7), pages 1-19, March.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:7:p:1882-:d:526110
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    References listed on IDEAS

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    1. Anh-Tuan Tran & Bui Le Ngoc Minh & Van Van Huynh & Phong Thanh Tran & Emmanuel Nduka Amaefule & Van-Duc Phan & Tam Minh Nguyen, 2021. "Load Frequency Regulator in Interconnected Power System Using Second-Order Sliding Mode Control Combined with State Estimator," Energies, MDPI, vol. 14(4), pages 1-17, February.
    2. Quan-Quan Zhang & Rong-Jong Wai, 2021. "Robust Power Sharing and Voltage Stabilization Control Structure via Sliding-Mode Technique in Islanded Micro-Grid," Energies, MDPI, vol. 14(4), pages 1-27, February.
    3. Youpeng Chen & Wenshao Bu & Yanke Qiao, 2021. "Research on the Speed Sliding Mode Observation Method of a Bearingless Induction Motor," Energies, MDPI, vol. 14(4), pages 1-18, February.
    4. Peng Gao & Guangming Zhang & Xiaodong Lv, 2021. "Model-Free Control Using Improved Smoothing Extended State Observer and Super-Twisting Nonlinear Sliding Mode Control for PMSM Drives," Energies, MDPI, vol. 14(4), pages 1-15, February.
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    Cited by:

    1. 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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