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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Bhat, S. P. , and Bernstein, D. S. , 1998, “ Continuous Finite-Time Stabilization of the Translational and Rotational Double Integrators,” IEEE Trans. Autom. Control, 43(5), pp. 678–682. [CrossRef]
Hong, Y. , Wang, J. , and Xi, Z. , 2005, “ Stabilization of Uncertain Chained Form Systems Within Finite Settling Time,” IEEE Trans. Autom. Control, 50(9), pp. 1379–1384. [CrossRef]
Polyakov, A. , Efimov, D. , and Perruquetti, W. , 2013, “ Finite-Time Stabilization Using Implicit Lyapunov Function Technique,” 9th Symposium on Nonlinear Control Systems, Toulouse, France.
Dorato, P. , 2006, “ An Overview of Finite-Time Stability,” Current Trends in Nonlinear Systems and Control: In Honor of Petar Kokotovic and Turi Nicosia, Birkhäuser, Boston, MA.
LaValle, S. M. , 2006, System Theory and Analytical Techniques, Cambridge University Press, Cambridge, UK.
Zhang, X. F. , Feng, G. , and Sun, Y. H. , 2012, “ Finite-Time Stabilization by State Feedback Control for a Class of Time-Varying Nonlinear Systems,” Automatica, 48(3), pp. 499–504. [CrossRef]
Khoo, S. , Yin, J. L. , Man, Z. H. , and Yu, X. H. , 2013, “ Finite-Time Stabilization of Stochastic Nonlinear Systems in Strict-Feedback Form,” Automatica, 49(5), pp. 1403–1410. [CrossRef]
Binazadeh, T. , and Shafiei, M. H. , 2014, “ A Novel Approach in the Finite-Time Controller Design,” Syst. Sci. Control Eng., 2(1), pp. 119–124. [CrossRef]
Binazadeh, T. , and Shafiei, M. H. , 2014, “ Nonsingular Terminal Sliding-Mode Control of a Tractor–Trailer System,” Syst. Sci. Control Eng., 2(1), pp. 168–174. [CrossRef]
Gao, F. , and Yuan, F. , 2014, “ Adaptive Finite-Time Stabilization for a Class of Uncertain High Order Nonholonomic Systems,” ISA Trans., 54, pp. 75–82. [CrossRef] [PubMed]
Zha, W. , Zhai, J. , and Fei, S. , 2015, “ Global Adaptive Finite-Time Control for Stochastic Nonlinear Systems Via State Feedback,” Circuits Syst. Signal Process., 34(12), pp. 3789–3809. [CrossRef]
Podlubny, I. , 1999, Fractional Differential Equations, Academic Press, New York.
Magin, R. L. , 2006, Fractional Calculus in Bioengineering, Begell House Redding, Danbury, CT.
Atanackovic, T. , Pilipovic, S. , and Zorica, D. , 2007, “ A Diffusion Wave Equation With Two Fractional Derivatives of Different Order,” J. Phys. A: Math. Theor., 40(20), pp. 5319–5334. [CrossRef]
Scalas, E. , 2008, “ On the Application of Fractional Calculus in Finance and Economics, Plenary Lecture Paper,” 3rd IFAC Workshop on Fractional Differentiation and its Applications, Ankara, Turkey.
Agrawal, O. P. , 2002, “ Formulation of Euler–Lagrange Equations for Fractional Variational Problems,” J. Math. Anal. Appl., 272(1), pp. 368–379. [CrossRef]
Mujumdar, A. , Tamhane, B. , and Kurode, S. , 2014, “ Fractional Order Modeling and Control of a Flexible Manipulator Using Sliding Modes,” American Control Conference (ACC), Portland, OR, June 4–6, pp. 2011–2016.
Bagley, R. L. , and Torvik, P. J. , 1986, “ On the Fractional Calculus Model of Viscoelastic Behavior,” J. Rheol., 30(1), pp. 133–155. [CrossRef]
Kamal, S. , Raman, A. , and Bandyopadhyay, B. , 2013, “ Finite-Time Stabilization of Fractional Order Uncertain Chain of Integrator: An Integral Sliding Mode Approach,” IEEE Trans. Autom. Control, 58(6), pp. 1597–1602. [CrossRef]
Xin, B. , and Zhang, J. , 2015, “ Finite-Time Stabilizing a Fractional-Order Chaotic Financial System With Market Confidence,” Nonlinear Dyn., 79(2), pp. 1399–1409. [CrossRef]
Binazadeh, T. , and Shafiei, M. H. , 2013, “ Output Tracking of Uncertain Fractional-Order Nonlinear Systems Via a Novel Fractional-Order Sliding Mode Approach,” Mechatronics, 23(7), pp. 888–892. [CrossRef]
Kilbas, A. A. , Srivastava, H. M. , and Trujillo, J. J. , 2006, Theory and Application of Fractional Differential Equations, North Holland Mathematics Studies, Elsevier, Amsterdam, The Netherlands.
Li, Y. , Chen, Y. Q. , and Podlubny, I. , 2010, “ Stability of Fractional Order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag-Leffler Stability,” Comput. Math. Appl., 59(5), pp. 1810–1821. [CrossRef]
Khalil, H. K. , 2002, Nonlinear Systems, 3rd ed., Prentice-Hall, Upper Saddle River, NJ.
Valerio, D. , 2005, “Toolbox Ninteger for matlab, V. 2.3.”
Aghababa, M. P. , 2014, “ Chaotic Behavior in Fractional-Order Horizontal Platform Systems and Its Suppression Using a Fractional Finite-Time Control Strategy,” J. Mech. Sci. Technol., 28(5), pp. 1875–1880. [CrossRef]


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Fig. 1

Physical model of the HPS

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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. 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. 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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