Research Papers

Finite Time Fractional-Order Sliding Mode-Based Tracking for a Class of Fractional-Order Nonholonomic Chained System

[+] Author and Article Information

Department of Electrical Engineering,
Punjab Engineering College (PEC)
(Deemed to be University),
Chandigarh 160012, India
e-mail: sharmadeepika504@gmail.com

Shiv Narayan

Department of Electrical Engineering,
Punjab Engineering College (PEC)
(Deemed to be University),
Chandigarh 160012, India

Sandeep Kaur

Department of Electrical Engineering,
Punjab Engineering College (PEC)
(Deemed to be University),
Chandigarh 160012, India

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 7, 2017; final manuscript received March 7, 2018; published online April 2, 2018. Assoc. Editor: Bernard Brogliato.

J. Comput. Nonlinear Dynam 13(5), 051006 (Apr 02, 2018) (9 pages) Paper No: CND-17-1408; doi: 10.1115/1.4039581 History: Received September 07, 2017; Revised March 07, 2018

This paper formulates a fractional-order finite time tracking scheme for a perturbed n-dimensional fractional-order extended chained form of nonholonomic system. First, the hierarchical sliding surfaces are properly selected, and then, a novel fractional-order sliding mode methodology is derived mathematically to accomplish the prescribed goal. With the introduction of new virtual controls, the proposed strategy renders finite time tracking of a fractional-order reference model in-spite of various system uncertainties. Further, the closed loop system stability is procured with the proposed method through fractional-Lyapunov and Mittag–Leffler-based stability theorems. It has also been verified analytically that the error dynamics converge to the chosen sliding surfaces in finite time. Finally, two examples including an engineering application of mobile robot are illustrated through matlab simulations to demonstrate the usefulness of the introduced control technique.

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Grahic Jump Location
Fig. 1

Simulations with the proposed method versus time in seconds for example 1: (a) tracking errors: x1e,x2e,x3e,x4e, (b) input errors with u1d=exp(−3t) and u2d=−3, and (c) convergence of sliding surfaces for both subsystems

Grahic Jump Location
Fig. 2

Tracking desired controls versus time in seconds, for example, 1: (a) u1 tracks u1d=exp(−3t) and (b) u2 tracks u2d=−3

Grahic Jump Location
Fig. 3

Simulations for the proposed method versus time in seconds, for example, 2: (a) x1e, (b) x2e, (c) x3e, (d) input tracking error 2 with u2d=1, (e) input tracking error 1 with u1d=1−e−t, and (f) convergence of all the sliding surfaces



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