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

Yong-Hong Lan (), Liang-Liang Wang (), Cai-Xue Chen and Ding Lei ()
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Yong-Hong Lan: Xiangtan University
Liang-Liang Wang: Xiangtan University
Cai-Xue Chen: Xiangtan University
Ding Lei: Jishou University

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 1, No 13, 197-209

Abstract: 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.

Keywords: Fractional-order; Linear quadratic regulator; Sliding mode control; Permanent magnet synchronous motor; 49J15; 93C10 (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10957-015-0827-4

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