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Volume 9
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Article

Fractional-Order Sliding Mode Control Method for a Class of Integer-Order Nonlinear Systems

by
Wenjie Qing
1,*,
Binfeng Pan
1,
Yueyang Hou
2,
Shan Lu
2 and
Wenjing Zhang
2
1
School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China
2
Shanghai Aerospace Control Technology Institute, Shanghai 201109, China
*
Author to whom correspondence should be addressed.
Aerospace 2022, 9(10), 616; https://doi.org/10.3390/aerospace9100616
Submission received: 8 August 2022 / Revised: 8 October 2022 / Accepted: 11 October 2022 / Published: 17 October 2022
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Abstract

In this study, the problem of the stabilisation of a class of nonautonomous nonlinear systems was studied. First, a fractional stability theorem based on a fractional-order Lyapunov inequality was formulated. Then, a novel fractional-order sliding surface, which was a generalisation of integral, first-order, and second-order sliding surfaces with varying fractional orders, was proposed. Finally, a fractional-order sliding mode-based control for a class of nonlinear systems was designed. The stability property of the system with the proposed method was easily proven as a fractional Lyapunov direct method by the fractional stability theorem. As an illustration, the method was used as a fractional guidance law with an impact angle constraint for a manoeuvring target. Simulation results demonstrated the applicability and efficiency of the proposed method.
Keywords: fractional-order sliding surface; fractional-order sliding mode control; nonlinear systems; fractional stability theorem; fractional Lyapunov direct method fractional-order sliding surface; fractional-order sliding mode control; nonlinear systems; fractional stability theorem; fractional Lyapunov direct method

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MDPI and ACS Style

Qing, W.; Pan, B.; Hou, Y.; Lu, S.; Zhang, W. Fractional-Order Sliding Mode Control Method for a Class of Integer-Order Nonlinear Systems. Aerospace 2022, 9, 616. https://doi.org/10.3390/aerospace9100616

AMA Style

Qing W, Pan B, Hou Y, Lu S, Zhang W. Fractional-Order Sliding Mode Control Method for a Class of Integer-Order Nonlinear Systems. Aerospace. 2022; 9(10):616. https://doi.org/10.3390/aerospace9100616

Chicago/Turabian Style

Qing, Wenjie, Binfeng Pan, Yueyang Hou, Shan Lu, and Wenjing Zhang. 2022. "Fractional-Order Sliding Mode Control Method for a Class of Integer-Order Nonlinear Systems" Aerospace 9, no. 10: 616. https://doi.org/10.3390/aerospace9100616

APA Style

Qing, W., Pan, B., Hou, Y., Lu, S., & Zhang, W. (2022). Fractional-Order Sliding Mode Control Method for a Class of Integer-Order Nonlinear Systems. Aerospace, 9(10), 616. https://doi.org/10.3390/aerospace9100616

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