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New Time-Varying Sliding Surface for Switching Type Quasi-Sliding Mode Control

Author

Listed:
  • Katarzyna Adamiak

    (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

This study considers the problem of energetical efficiency in switching type sliding mode control of discrete-time systems. The aim of this work is to reduce the quasi-sliding mode band-width and, as follows, the necessary control input, through an application of a new type of time-varying sliding hyperplane in quasi-sliding mode control of sampled time systems. Although time-varying sliding hyperplanes are well known to provide insensitivity to matched external disturbances and uncertainties of the model in the whole range of motion for continuous-time systems, their application in the discrete-time case has never been studied in detail. Therefore, this paper proposes a sliding surface, which crosses the system’s representative point at the initial step and then shifts in the state space according to the pre-generated demand profile of the sliding variable. Next, a controller for a real perturbed plant is designed so that it drives the system’s representative point to its reference position on the sliding plane in each step. Therefore, the impact of external disturbances on the system’s trajectory is minimized, which leads to a reduction of the necessary control effort. Moreover, thanks to a new reaching law applied in the reference profile generator, the sliding surface shift in each step is strictly limited and a switching type of motion occurs. Finally, under the assumption of boundedness and smoothness of continuous-time disturbance, a compensation scheme is added. It is proved that this control strategy reduces the quasi-sliding mode band-width from O ( T ) to O ( T 3 ) order from the very beginning of the regulation process. Moreover, it is shown that the maximum state variable errors become of O ( T 3 ) order as well. These achievements directly reduce the energy consumption in the closed-loop system, which is nowadays one of the crucial factors in control engineering.

Suggested Citation

  • Katarzyna Adamiak & Andrzej Bartoszewicz, 2021. "New Time-Varying Sliding Surface for Switching Type Quasi-Sliding Mode Control," Energies, MDPI, vol. 14(13), pages 1-20, June.
    • Handle: RePEc:gam:jeners:v:14:y:2021:i:13:p:3811-:d:581706
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    References listed on IDEAS

    as
    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. 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.
    3. Saleh Mobayen & Farhad Bayat & Chun-Chi Lai & Asghar Taheri & Afef Fekih, 2021. "Adaptive Global Sliding Mode Controller Design for Perturbed DC-DC Buck Converters," Energies, MDPI, vol. 14(5), pages 1-12, February.
    Full references (including those not matched with items on IDEAS)

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