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Optimal Sliding Mode Robust Control for Fractional-Order Systems with Application to Permanent Magnet Synchronous Motor Tracking Control

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Abstract

This paper presents an optimal sliding mode output tracking control scheme for a class of fractional-order uncertain systems. Firstly, an augmented fractional-order system, composed of the original system and the external system, is constructed to transform the optimal output tracking issue into the design problem of linear quadratic regulator. The optimal tracking control problem for the nominal augmented fractional-order system is then studied. Secondly, the fractional-integral sliding mode controller is introduced to robustify the augmented fractional-order system, which satisfy the matching conditions. As a result, the original system output can track the external system output trajectory effectively even the uncertainties exist. Finally, the developed design techniques are applied to the tracking control of fractional-order permanent magnet synchronous motor. The simulation results demonstrate the validity of this approach.

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Acknowledgments

This work was supported by National Natural Science Foundation of People’s Republic of China (61573298, 61363073), Hunan Provincial Natural Science Foundation of China (14JJ2073) and Scientific Research Fund of Hunan Provincial Education Department (15B238).

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Authors and Affiliations

  1. Institute of Control Engineering, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Yong-Hong Lan

  2. School of Information Engineering, Xiangtan University, Xiangtan, 411105, Hunan, People’s Republic of China

    Liang-Liang Wang & Cai-Xue Chen

  3. School of Physics Science and Information Engineering, Jishou University, Jishou, 416000, Hunan, People’s Republic of China

    Ding Lei

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  1. Yong-Hong Lan
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  2. Liang-Liang Wang
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  3. Cai-Xue Chen
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  4. Ding Lei
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Correspondence to Yong-Hong Lan.

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Lan, YH., Wang, LL., Chen, CX. et al. Optimal Sliding Mode Robust Control for Fractional-Order Systems with Application to Permanent Magnet Synchronous Motor Tracking Control. J Optim Theory Appl 174, 197–209 (2017). https://doi.org/10.1007/s10957-015-0827-4

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  • DOI: https://doi.org/10.1007/s10957-015-0827-4

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