0
Research Papers

Adaptive Fuzzy Fractional-Order Nonsingular Terminal Sliding Mode Control for a Class of Second-Order Nonlinear Systems

[+] Author and Article Information
Tran Minh Duc

Division of Computational Mechatronics,
Institute for Computational Science,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Faculty of Electrical & Electronics Engineering,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam
e-mail: tranminhduc@tdt.edu.vn

Ngo Van Hoa

Division of Computational Mathematics
and Engineering,
Institute for Computational Science,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Faculty of Mathematics and Statistics,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam
e-mail: ngovanhoa@tdt.edu.vn

Thanh-Phong Dao

Division of Computational Mechatronics,
Institute for Computational Science,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam;
Faculty of Electrical & Electronics Engineering,
Ton Duc Thang University,
Ho Chi Minh City 700000, Vietnam
e-mail: daothanhphong@tdt.edu.vn

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received February 7, 2017; final manuscript received September 6, 2017; published online January 10, 2018. Assoc. Editor: Bernard Brogliato.

J. Comput. Nonlinear Dynam 13(3), 031004 (Jan 10, 2018) (8 pages) Paper No: CND-17-1056; doi: 10.1115/1.4038642 History: Received February 07, 2017; Revised September 06, 2017

This paper investigates a novel adaptive fuzzy fractional-order nonsingular terminal sliding mode controller (AFFO-NTSMC) for second-order nonlinear dynamic systems. The technique of fractional calculus and nonsingular terminal sliding mode control (NTSMC) are combined to establish fractional-order NTSMC (FO-NTSMC), in which a new fractional-order (FO) nonsingular terminal sliding mode (NTSM) surface is proposed. Then, a corresponding controller is designed to provide robustness, high performance control, finite time convergence in the presence of uncertainties and external disturbances. Furthermore, a fuzzy system with online adaptive learning algorithm is derived to eliminate the chattering phenomenon in conventional sliding mode control (SMC). The stability of the closed-loop system is rigorously proven. Numerical simulation results are presented to demonstrate the effectiveness of the proposed control method.

FIGURES IN THIS ARTICLE
<>
Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Arimoto, S. , 1984, “Stability and Robustness of PID Feedback Control for Robot Manipulators of Sensory Capability,” First International Symposium on Robotics Research, Bretton Woods, NH, Aug. 25–Sept. 2, pp. 783–799.
Abdallah, C. , Dawson, D. M. , Dorato, P. , and Jamshidi, M. , 1991, “Survey of Robust Control for Rigid Robots,” IEEE Control Syst., 11(2), pp. 24–30. [CrossRef]
Spong, M. W. , 1992, “On the Robust Control of Robot Manipulators,” IEEE Trans. Automatic Control, 37(11), pp. 1782–1786. [CrossRef]
Ortega, R. , and Spong, M. W. , 1988, “Adaptive Motion Control of Rigid Robots: A Tutorial,” 27th IEEE Conference on Decision and Control (CDC), Austin, TX, Dec. 7–9, pp. 1575–1584.
Slotine, J.-J. E. , and Li, W. , 1987, “On the Adaptive Control of Robot Manipulators,” Int. J. Rob. Res., 6(3), pp. 49–59. [CrossRef]
Chen, M. , Wu, Q.-X. , and Cui, R.-X. , 2013, “Terminal Sliding Mode Tracking Control for a Class of Siso Uncertain Nonlinear Systems,” ISA Trans., 52(2), pp. 198 –206. [CrossRef] [PubMed]
Feng, Y. , Yu, X. , and Man, Z. , 2002, “Non-Singular Terminal Sliding Mode Control of Rigid Manipulators,” Automatica, 38(12), pp. 2159–2167. [CrossRef]
Tran, M.-D. , and Kang, H.-J. , 2016, “A Novel Adaptive Finite-Time Tracking Control for Robotic Manipulators Using Nonsingular Terminal Sliding Mode and RBF Neural Networks,” Int. J. Precis. Eng. Manuf., 17(7), pp. 863–870. [CrossRef]
Jin, M. , Lee, J. , Chang, P. H. , and Choi, C. , 2009, “Practical Nonsingular Terminal Sliding-Mode Control of Robot Manipulators for High-Accuracy Tracking Control,” IEEE Trans. Ind. Electron., 56(9), pp. 3593–3601. [CrossRef]
Wu, Y. , Yu, X. , and Man, Z. , 1998, “Terminal Sliding Mode Control Design for Uncertain Dynamic Systems,” Syst. Control Lett., 34(5), pp. 281–287. [CrossRef]
Yu, X. , and Zhihong, M. , 2002, “Fast Terminal Sliding-Mode Control Design for Nonlinear Dynamical Systems,” IEEE Trans. Circuits Syst. I: Fundamental Theory Appl., 49(2), pp. 261–264. [CrossRef]
Yu, S. , Yu, X. , Shirinzadeh, B. , and Man, Z. , 2005, “Continuous Finite-Time Control for Robotic Manipulators With Terminal Sliding Mode,” Automatica, 41(11), pp. 1957–1964. [CrossRef]
Davila, J. , Fridman, L. , and Levant, A. , 2005, “Second-Order Sliding-Mode Observer for Mechanical Systems,” IEEE Trans. Autom. Control, 50(11), pp. 1785–1789. [CrossRef]
Rivera, J. , Garcia, L. , Mora, C. , Raygoza, J. J. , and Ortega, S. , 2011, “Super-Twisting Sliding Mode in Motion Control Systems,” Sliding Mode Control, A. Bartoszewicz, ed., InTech, Rijeka, Croatia. [CrossRef]
Utkin, V. , 1977, “Variable Structure Systems With Sliding Modes,” IEEE Trans. Autom. Control, 22(2), pp. 212–222. [CrossRef]
Zhihong, M. , and Yu, X. H. , 1997, “Terminal Sliding Mode Control of MIMO Linear Systems,” IEEE Trans. Circuits Syst. I: Fundamental Theory Appl., 44(11), pp. 1065–1070. [CrossRef]
Jiang, Y. , Wang, Q. , and Dong, C. , 2013, “A Reaching Law Based Neural Network Terminal Sliding-Mode Guidance Law Design,” TENCON 2013-2013 IEEE Region 10 Conference (31194), Xi'an, China, Oct. 22–25, pp. 1–5.
Sun, T. , Pei, H. , Pan, Y. , Zhou, H. , and Zhang, C. , 2011, “Neural Network-Based Sliding Mode Adaptive Control for Robot Manipulators,” Neurocomputing, 74(14), pp. 2377–2384. [CrossRef]
Li, H. , Wang, J. , Wu, L. , Lam, H.-K. , and Gao, Y. , 2017, “Optimal Guaranteed Cost Sliding Mode Control of Interval Type-2 Fuzzy Time-Delay Systems,” IEEE Trans. Fuzzy Syst., PP(99), p. 1.
Li, H. , Sun, X. , Wu, L. , and Lam, H.-K. , 2015, “State and Output Feedback Control of Interval Type-2 Fuzzy Systems With Mismatched Membership Functions,” IEEE Trans. Fuzzy Syst., 23(6), pp. 1943–1957. [CrossRef]
Roopaei, M. , and Jahromi, M. Z. , 2009, “Chattering-Free Fuzzy Sliding Mode Control in MIMO Uncertain Systems,” Nonlinear Anal.: Theory, Methods Appl., 71(10), pp. 4430–4437. [CrossRef]
Nguyen, S. D. , and Nguyen, Q. H. , 2017, “Design of Active Suspension Controller for Train Cars Based on Sliding Mode Control, Uncertainty Observer and Neuro-Fuzzy System,” J. Vib. Control, 23(8), pp. 1334–1353. [CrossRef]
Nguyen, S. D. , Vo, H. D. , and Seo, T.-I. , 2017, “Nonlinear Adaptive Control Based on Fuzzy Sliding Mode Technique and Fuzzy-Based Compensator,” ISA Trans., 70, pp. 309–321. [CrossRef] [PubMed]
Zhang, B. , Pi, Y. , and Luo, Y. , 2012, “Fractional Order Sliding-Mode Control Based on Parameters Auto-Tuning for Velocity Control of Permanent Magnet Synchronous Motor,” ISA Trans., 51(5), pp. 649–656. [CrossRef] [PubMed]
Zhong, J. , and Li, L. , 2015, “Tuning Fractional-Order Pid Controllers for a Solid-Core Magnetic Bearing System,” IEEE Trans. Control Syst. Technol., 23(4), pp. 1648–1656. [CrossRef]
Padula, F. , and Visioli, A. , 2012, “Optimal Tuning Rules for Proportional-Integral-Derivative and Fractional-Order Proportional-Integral-Derivative Controllers for Integral and Unstable Processes,” IET Control Theory Appl., 6(6), pp. 776–786. [CrossRef]
Ladaci, S. , and Charef, A. , 2006, “On Fractional Adaptive Control,” Nonlinear Dyn., 43(4), pp. 365–378. [CrossRef]
Cao, D. , and Fei, J. , 2016, “Adaptive Fractional Fuzzy Sliding Mode Control for Three-Phase Active Power Filter,” IEEE Access, 4, pp. 6645–6651. [CrossRef]
Dadras, S. , and Momeni, H. R. , 2012, “Fractional Terminal Sliding Mode Control Design for a Class of Dynamical Systems With Uncertainty,” Commun. Nonlinear Sci. Numer. Simul., 17(1), pp. 367–377. [CrossRef]
Delavari, H. , Ghaderi, R. , Ranjbar, A. , and Momani, S. , 2010, “Fuzzy Fractional Order Sliding Mode Controller for Nonlinear Systems,” Commun. Nonlinear Sci. Numer. Simul., 15(4), pp. 963–978. [CrossRef]
Nojavanzadeh, D. , and Badamchizadeh, M. , 2016, “Adaptive Fractional-Order Non-Singular Fast Terminal Sliding Mode Control for Robot Manipulators,” IET Control Theory Appl., 10(13), pp. 1565–1572. [CrossRef]
Wang, Y. , Luo, G. , Gu, L. , and Li, X. , 2016, “Fractional-Order Nonsingular Terminal Sliding Mode Control of Hydraulic Manipulators Using Time Delay Estimation,” J. Vib. Control, 22(19), pp. 3998–4011. [CrossRef]
Podlubny, I. , 1999, Fractional Differential Equations, Academic Press, San Diego, CA. [PubMed] [PubMed]
Kilbas, A. A. , Srivastava, H. M. , and Trujillo, J. J. , 2006, Theory and Applications of Fractional Differential Equations, Vol. 204, Elsevier, Amsterdam, The Netherlands. [CrossRef]
Li, Y. , Chen, Y. , and Podlubny, I. , 2009, “Mittag–Leffler Stability of Fractional Order Nonlinear Dynamic Systems,” Automatica, 45(8), pp. 1965–1969. [CrossRef]
Feng, Y. , Yu, X. , and Han, F. , 2013, “On Nonsingular Terminal Sliding-Mode Control of Nonlinear Systems,” Automatica, 49(6), pp. 1715–1722. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Block diagram of the proposed controller

Grahic Jump Location
Fig. 2

Two-link robot manipulator model

Grahic Jump Location
Fig. 3

Responses at joint 1: (a) output tracking and (b) tracking error

Grahic Jump Location
Fig. 4

Responses at joint 2: (a) output tracking and (b) tracking error

Grahic Jump Location
Fig. 5

Control input at joints 1 and 2

Grahic Jump Location
Fig. 6

Time responses of the terminal sliding mode surfaces; S1 and S2, respectively, correspond to joints 1 and 2

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In