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Research Papers

Control of Fractional-Order Systems Using Chatter-Free Sliding Mode Approach

[+] Author and Article Information
Mohammad Pourmahmood Aghababa

Young Researchers and Elite Club,
Ahar Branch,
Islamic Azad University,
Ahar 51766, Iran
e-mail: m.pour13@gmail.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 10, 2013; final manuscript received August 22, 2013; published online February 13, 2014. Assoc. Editor: J. A. Tenreiro Machado.

J. Comput. Nonlinear Dynam 9(3), 031003 (Feb 13, 2014) (7 pages) Paper No: CND-13-1030; doi: 10.1115/1.4025771 History: Received February 10, 2013; Revised August 22, 2013

The problem of stabilization of nonlinear fractional systems in spite of system uncertainties is investigated in this paper. First, a proper fractional derivative type sliding manifold with desired stability and convergence properties is designed. Then, the fractional stability theory is adopted to derive a robust sliding control law to force the system trajectories to attain the proposed sliding manifold and remain on it evermore. The existence of the sliding motion is mathematically proven. Furthermore, the sign function in the control input, which is responsible to the being of harmful chattering, is transferred into the fractional derivative of the control input. Therefore, the resulted control input becomes smooth and free of the chattering. Some numerical simulations are presented to illustrate the efficient performance of the proposed chattering-free fractional variable structure controller.

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References

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Figures

Grahic Jump Location
Fig. 1

State trajectories of the controlled fractional-order Arneodo system (Eq. (31))

Grahic Jump Location
Fig. 2

Time response of the applied fractional sliding surface (Eq. (33))

Grahic Jump Location
Fig. 3

Time history of the adopted sliding control input (Eq. (34))

Grahic Jump Location
Fig. 4

State trajectories of the controlled fractional-order Arneodo system obtained by the method in Eq. (35)

Grahic Jump Location
Fig. 5

Time response of the applied fractional sliding surface obtained by the method in Eq. (35)

Grahic Jump Location
Fig. 6

Time history of the adopted sliding control input obtained by the method in Eq. (35)

Grahic Jump Location
Fig. 7

State trajectories of the controlled fractional-order Genesio system (Eq. (36))

Grahic Jump Location
Fig. 8

Time response of the applied fractional sliding surface (Eq. (37))

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Fig. 9

Time history of the adopted sliding control input (Eq. (38))

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