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Research Papers

Fractional-Order Backstepping Sliding-Mode Control Based on Fractional-Order Nonlinear Disturbance Observer

[+] Author and Article Information
Hadi Delavari

Department of Electrical Engineering,
Hamedan University of Technology,
Hamedan 65155, Iran
e-mail: delavari@hut.ac.ir

Hamid Heydarinejad

Department of Electrical Engineering,
Hamedan University of Technology,
Hamedan 65155, Iran
e-mail: hheydarinejad@yahoo.com

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 18, 2018; final manuscript received August 22, 2018; published online September 17, 2018. Assoc. Editor: Bernard Brogliato.

J. Comput. Nonlinear Dynam 13(11), 111009 (Sep 17, 2018) (13 pages) Paper No: CND-18-1068; doi: 10.1115/1.4041322 History: Received February 18, 2018; Revised August 22, 2018

In this paper, a novel fractional-order (FO) backstepping sliding-mode control is proposed for a class of FO nonlinear systems with mismatched disturbances. Here the matched/mismatched disturbances are estimated by an FO nonlinear disturbance observer (NDO). This FO NDO is proposed based on FO backstepping algorithm to estimate the mismatched disturbances. The stability of the closed-loop system is proved by the new extension of Lyapunov direct method for FO systems. Exponential reaching law considerably decreases the chattering and provides a high dynamic tracking performance. Finally, three simulation examples are presented to show the features and the effectiveness of the proposed method. Results show that this observer approximates the unknown mismatched disturbances successfully.

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Figures

Grahic Jump Location
Fig. 1

(a) Block diagram of FO backstepping algorithm with NDO and (b) block diagram of proposed FOBSMC-FNDO

Grahic Jump Location
Fig. 5

(a) Output response (y=z1) of the FO-MAGnetic LEVitation (MAGLEV) system via the proposed controller to the applied matched/mismatched disturbances, (b) the applied control law, and (c) the time response of the applied FO sliding surface

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Fig. 6

Disturbance and its estimation: (a) external mismatched disturbance d1and (b) external matched disturbance d3

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Fig. 7

(a) Output response (y=x1) of the microelectromechanical system, (b) output of the proposed controllers (control law), and (c) the time response of the applied FO sliding surfaces

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Fig. 2

(a) Output response (y=x1) of the FO Genesio–Tesi system under the FOBSMC and BSMC without FNDO and (b) output response (y=x1) of the FO Genesio–Tesi system under the FOBSMC-FNDO and the applied matched/mismatched disturbances

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Fig. 3

(a) Output response of the proposed controllers (control law) and (b) the applied FO sliding surface

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Fig. 4

Disturbance and its estimation: (a) external mismatched disturbance d1, (b) external mismatched disturbance d2, and (c) external matched disturbance d3

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Fig. 8

Disturbance and its estimation: (a) external mismatched disturbance d1 and (b) external matched disturbance d2

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