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Adaptive Hierarchical Fractional-Order Sliding Mode Control of an Inverted Pendulum–Cart System

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Abstract

This paper designs an adaptive fractional-order sliding mode controller for an inverted pendulum–cart system. The input force is determined to stabilize the system and adjust the cart position and the pendulum angle to zero. A hierarchical sliding mode control approach with novel fractional-order sliding surfaces, including a fractional-order integral term, an ordinary derivative term, and a proportional term, is chosen to attain this purpose. The control signal is determined to ensure the sliding condition. In order to improve the robustness of the proposed controller against uncertainties in the cart friction coefficient and the pendulum’s viscous friction, the controller parameters are adapted according to an appropriate adaptation rule. The adaptation rule is attained using an appropriate Lyapunov-based approach. Numerical simulations confirm the feasibility and efficiency of the proposed control strategy.

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Authors and Affiliations

  1. Department of Electrical Engineering, Khomeinishahr Branch, Islamic Azad University, Isfahan, Iran

    Alireza Jafary Fesharaki & Mohammad Tabatabaei

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  1. Alireza Jafary Fesharaki
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  2. Mohammad Tabatabaei
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Correspondence to Mohammad Tabatabaei.

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The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Appendix

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Table 4 List of variables and their description
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Jafary Fesharaki, A., Tabatabaei, M. Adaptive Hierarchical Fractional-Order Sliding Mode Control of an Inverted Pendulum–Cart System. Arab J Sci Eng 47, 13927–13942 (2022). https://doi.org/10.1007/s13369-022-06613-y

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