Research Papers

Finite-Time Tracker Design for Uncertain Nonlinear Fractional-Order Systems

[+] Author and Article Information
Tahereh Binazadeh

Assistant Professor
Department of Electrical and
Electronic Engineering,
Shiraz University of Technology,
Modares Boulevard,
P.O. Box 71555-313
Shiraz, Iran
e-mail: binazadeh@sutech.ac.ir

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received September 13, 2015; final manuscript received May 6, 2016; published online May 24, 2016. Assoc. Editor: Brian Feeny.

J. Comput. Nonlinear Dynam 11(4), 041028 (May 24, 2016) (6 pages) Paper No: CND-15-1289; doi: 10.1115/1.4033606 History: Received September 13, 2015; Revised May 06, 2016

This paper considers the problem of finite-time output tracking for a class of nonautonomous nonlinear fractional-order (FO) systems in the presence of model uncertainties and external disturbances. The finite-time control methods indicate better properties in terms of robustness, disturbance rejection, and settling time. Thus, design of a robust nonsingular controller for finite-time output tracking of a time-varying reference signal is considered in this paper, and a novel FO nonsingular terminal sliding mode controller (TSMC) is designed, which can conquer the uncertainties and guarantees the finite-time convergence of the system output toward the desired time-varying reference signal. For this purpose, an appropriate nonsingular terminal sliding manifold is designed, where maintaining the system's states on this manifold leads to finite-time vanishing of error signal (i.e., ensures the finite-time occurrence of both reaching and sliding phases). Moreover, by tacking the fractional derivative of the sliding manifold, the convergence of system's trajectories into the terminal sliding manifold in a finite time is proven, and the convergence time is estimated. Finally, in order to verify the theoretical results, the proposed method is applied to an FO model of a horizontal platform system (FO-HPS), and the computer simulations show the efficiency of the proposed method in finite-time output tracking.

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Fig. 1

Physical model of the HPS

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Fig. 2

Phase portrait of the nominal unforced FO-HPS system

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Fig. 3

The block diagram of the control scheme

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Fig. 4

Time history of reference signal and controlled output for case 1

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Fig. 5

Time history of the terminal sliding manifold for case 1

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Fig. 6

Time history of the control input (FO-TSMC) for case 1

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Fig. 7

Time history of reference signal and controlled output for case 2

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Fig. 8

Time history of the sliding manifold for case 2

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Fig. 9

Time history of the control input for case 2




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