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Research Papers

Linear Matrix Inequality Based Fractional Integral Sliding-Mode Control of Uncertain Fractional-Order Nonlinear Systems

[+] Author and Article Information
Sara Dadras

Electrical and Computer Engineering Department,
Utah State University,
Logan, UT 84322
e-mail: s_dadras@ieee.org

Soodeh Dadras

Electrical and Computer Engineering Department,
Utah State University,
Logan, UT 84322

HamidReza Momeni

Automation and Instruments Lab,
Electrical Engineering Department,
Tarbiat Modares University,
P.O. Box 14115-143,
Tehran 14115, Iran

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received March 21, 2014; final manuscript received April 11, 2017; published online July 20, 2017. Editor: Joseph Beaman.

J. Dyn. Sys., Meas., Control 139(11), 111003 (Jul 20, 2017) (7 pages) Paper No: DS-14-1130; doi: 10.1115/1.4036807 History: Received March 21, 2014; Revised April 11, 2017

A design of linear matrix inequality (LMI)-based fractional-order surface for sliding-mode controller of a class of uncertain fractional-order nonlinear systems (FO-NSs) is proposed in this paper. A new switching law is achieved guaranteeing the reachability condition. This control law is established to obtain a sliding-mode controller (SMC) capable of deriving the state trajectories onto the fractional-order integral switching surface and maintain the sliding motion. Using LMIs, a sufficient condition for existence of the sliding surface is derived which ensures the tα asymptotical stability on the sliding surface. Through a numerical example, the superior performance of the new fractional-order sliding mode controller is illustrated in comparison with a previously proposed method.

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Figures

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Fig. 1

State trajectories

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Fig. 2

Sliding surface variables s1, s2, and s3

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Fig. 3

Control input variables u1, u2, and u3

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Fig. 4

Comparison of the evolution of the state trajectories

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Fig. 5

Comparison of the evolution of sliding surface

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