In this paper, a novel fractional-order (FO) backstepping sliding-mode control is proposed for a class of FO nonlinear systems with mismatched disturbances. Here the matched/mismatched disturbances are estimated by an FO nonlinear disturbance observer (NDO). This FO NDO is proposed based on FO backstepping algorithm to estimate the mismatched disturbances. The stability of the closed-loop system is proved by the new extension of Lyapunov direct method for FO systems. Exponential reaching law considerably decreases the chattering and provides a high dynamic tracking performance. Finally, three simulation examples are presented to show the features and the effectiveness of the proposed method. Results show that this observer approximates the unknown mismatched disturbances successfully.
Fractional-Order Backstepping Sliding-Mode Control Based on Fractional-Order Nonlinear Disturbance Observer
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 18, 2018; final manuscript received August 22, 2018; published online September 17, 2018. Assoc. Editor: Bernard Brogliato.
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Delavari, H., and Heydarinejad, H. (September 17, 2018). "Fractional-Order Backstepping Sliding-Mode Control Based on Fractional-Order Nonlinear Disturbance Observer." ASME. J. Comput. Nonlinear Dynam. November 2018; 13(11): 111009. https://doi.org/10.1115/1.4041322
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