Sliding Mode Control for Flexible-link Manipulators Based on Adaptive Neural Networks

  • Hong-Jun Yang
  • Min TanEmail author
Research Article


This paper mainly focuses on designing a sliding mode boundary controller for a single flexible-link manipulator based on adaptive radial basis function (RBF) neural network. The flexible manipulator in this paper is considered to be an Euler-Bernoulli beam. We first obtain a partial differential equation (PDE) model of single-link flexible manipulator by using Hamiltons approach. To improve the control robustness, the system uncertainties including modeling uncertainties and external disturbances are compensated by an adaptive neural approximator. Then, a sliding mode control method is designed to drive the joint to a desired position and rapidly suppress vibration on the beam. The stability of the closed-loop system is validated by using Lyapunov’s method based on infinite dimensional model, avoiding problems such as control spillovers caused by traditional finite dimensional truncated models. This novel controller only requires measuring the boundary information, which facilitates implementation in engineering practice. Favorable performance of the closed-loop system is demonstrated by numerical simulations.


Sliding mode control adaptive control neural network flexible manipulator partial differential equation (PDE) 


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The authors would like to thank the Editor-in-Chief, the Associate Editor, and the anonymous reviewers for their constructive comments, which helped to improve the quality and presentation of this paper.


  1. [1]
    T. Sangpet, S. Kuntanapreeda, R. Schmidt. Hysteretic nonlinearity observer design based on Kalman filter for piezoactuated flexible beams with control applications. International Journal of Automation and Computing, vol. 11, no. 6, pp. 627–634, 2014. DOI: 10.1007/s11633-014-0817-2.CrossRefGoogle Scholar
  2. [2]
    L. Zhang, S. Liu. Iterative learning control for flexible manipulator using Fourier basis function. International Journal of Automation and Computing, vol. 12, no. 6, pp. 639–647, 2015. DOI: 10.1007/s11633-015-0932-8.CrossRefGoogle Scholar
  3. [3]
    Z. H. Luo. Direct strain feedback control of flexible robot arms: New theoretical and experimental results. IEEE Transactions on Automatic Control, vol. 38, no. 11, pp. 1610–1622, 1993. DOI: 10.1109/9.262031.MathSciNetCrossRefzbMATHGoogle Scholar
  4. [4]
    A.A. Paranjape, J. Y. Guan, S. J. Chung, M. Krstic. PDE boundary control for flexible articulated wings on a robotic aircraft. IEEE Transactions on Robotics, vol. 29, no. 3, pp. 625–640, 2013. DOI: 10.1109/TRO.2013.2240711.CrossRefGoogle Scholar
  5. [5]
    W. He, T. T. Meng, D. Q. Huang, X. F. Li. Adaptive boundary iterative learning control for an Euler-Bernoulli beam system with input constraint. IEEE Transactions on Neural Networks and Learning Systems, to be published. DOI: 10.1109/TNNLS.2017.2673865.Google Scholar
  6. [6]
    H. J. Yang, J. K. Liu. Distributed piezoelectric vibration control for a flexible-link manipulator based on an observer in the form of partial differential equations. Journal of Sound and Vibration, vol. 363, pp. 77–96, 2016. DOI: 10.1016/j.jsv.2015.11.001.CrossRefGoogle Scholar
  7. [7]
    Z. J. Liu, J. K. Liu, W. He. Modeling and vibration control of a flexible aerial refueling hose with variable lengths and input constraint. Automatica, vol. 77, pp. 302–310, 2017. DOI: 10.1016/j.automatica.2016.11.002.MathSciNetCrossRefzbMATHGoogle Scholar
  8. [8]
    Z. J. Zhao, Y. Liu, W. He, F. Luo. Adaptive boundary control of an axially moving belt system with high acceleration/ deceleration. IET Control Theory & Applications, vol. 10, no. 11, pp. 1299–1306, 2016. DOI: 10.1049/ietcta. 2015.0753.MathSciNetCrossRefGoogle Scholar
  9. [9]
    W. He, S. Zhang. Control design for nonlinear flexible wings of a robotic aircraft. IEEE Transactions on Control Systems Technology, vol. 25, no. 1, pp. 351–357, 2017. DOI: 10.1109/TCST.2016.2536708.MathSciNetCrossRefGoogle Scholar
  10. [10]
    L. J. Zhang, J. K. Liu. Adaptive boundary control for flexible two-link manipulator based on partial differential equation dynamic model. IET Control Theory & Applications, vol. 7, no. 1, pp. 43–51, 2013. DOI: 10.1049/ietcta. 2011.0593.MathSciNetCrossRefGoogle Scholar
  11. [11]
    B. Z. Guo, F. F. Jin. The active disturbance rejection and sliding mode control approach to the stabilization of the Euler-Bernoulli beam equation with boundary input disturbance. Automatica, vol. 49, no. 9, pp. 2911–2918, 2013. DOI: 10.1016/j.automatica.2013.06.018.MathSciNetCrossRefzbMATHGoogle Scholar
  12. [12]
    T. Endo, F. Matsuno, H. Kawasaki. Simple boundary cooperative control of two one-link flexible arms for grasping. IEEE Transactions on Automatic Control, vol. 54, no. 10, pp. 2470–2476, 2009. DOI: 10.1109/TAC.2009.2029401.MathSciNetCrossRefzbMATHGoogle Scholar
  13. [13]
    Z. C. Qiu, J. D. Han, J. G. Liu. Experiments on fuzzy sliding mode variable structure control for vibration suppression of a rotating flexible beam. Journal of Vibration and Control, vol. 21, no. 2, pp. 343–358, 2015. DOI: 10.1177/1077546313487760.CrossRefGoogle Scholar
  14. [14]
    F. Duarte, F. Ullah, C. Bohn. Modeling and dual loop sliding mode control of a two flexible-link robot to reduce the transient response. In Proceedings of the 24th Mediterranean Conference on Control and Automation, IEEE, Athens, Greece, pp. 280–284, 2016. DOI: 10.1109/MED.2016.7536066.Google Scholar
  15. [15]
    A. Mujumdar, S. Kurode, B. Tamhane. Fractional order sliding mode control for single link flexible manipulator. In Proceedings of IEEE International Conference on Control Applications, IEEE, Hyderabad, India, pp. 288–293, 2013. DOI: 10.1109/CCA.2013.6662773.Google Scholar
  16. [16]
    S. Kurode, P. Dixit. Output feedback control of flexible link manipulator using sliding modes. In Proceedings of the 7th International Conference on Electrical & Computer Engineering, IEEE, Dhaka, Bangladesh, pp. 949–952, 2012. DOI: 10.1109/ICECE.2012.6471708.Google Scholar
  17. [17]
    G. Mamani, J. Becedas, V. Feliu. Sliding mode tracking control of a very lightweight single-link flexible robot robust to payload changes and motor friction. Journal of Vibration and Control, vol. 18, no. 8, pp. 1141–1155, 2012. DOI: 10.1177/1077546311416269.MathSciNetCrossRefGoogle Scholar
  18. [18]
    P. E. Kuo, A. Hosein, M. S. Farmanborda. Nonlinear output feedback control of a flexible link using adaptive neural network: Controller design. Journal of Vibration and Control, vol. 19, no. 11, pp. 1690–1708, 2013. DOI: 10.1177/1077546312445497.CrossRefzbMATHGoogle Scholar
  19. [19]
    A. Farmanbordar, S. M. Hoseini. Neural network adaptive output feedback control of flexible link manipulators. Journal of Dynamic Systems, Measurement, and Control, vol. 135, no. 2, Article number 021009, 2013. DOI: 10.1115/1.4007701.CrossRefGoogle Scholar
  20. [20]
    S. S. Ge, C. C. Hang, T. H. Lee, T. Zhang. Stable Adaptive Neural Network Control, Boston, MA, USA: Springer, 2013. DOI: 10.1007/978-1-4757-6577-9.zbMATHGoogle Scholar
  21. [21]
    T. R. Sun, H. L. Pei, Y. P. Pan, H. B. Zhou, C. H. Zhang. Neural network-based sliding mode adaptive control for robot manipulators. Neurocomputing, vol. 74, no. 14–15, pp. 2377–2384, 2011. DOI: 10.1016/j.neucom.2011.03.015.CrossRefGoogle Scholar
  22. [22]
    T. R. Sun, Y. P. Pan. Adaptive control for nonaffine nonlinear systems using reliable neural network approximation. IEEE Access, vol. 5, pp. 23657–23662, 2017. DOI: 10.1109/ACCESS.2017.2763628.CrossRefGoogle Scholar
  23. [23]
    T. R. Sun, H. L. Pei, Y. P. Pan, C. H. Zhang. Robust adaptive neural network control for environmental boundary tracking by mobile robots. International Journal of Robust and Nonlinear Control, vol. 23, no. 2, pp. 123–136, 2013. DOI: 10.1002/rnc.1816.MathSciNetCrossRefzbMATHGoogle Scholar
  24. [24]
    W. He, Y. H. Chen, Z. Yin. Adaptive neural network control of an uncertain robot with full-state constraints. IEEE Transactions on Cybernetics, vol. 46, no. 3, pp. 620–629, 2016. DOI: 10.1109/TCYB.2015.2411285.CrossRefGoogle Scholar
  25. [25]
    W. He, Y. T. Dong, C. Y. Sun. Adaptive neural impedance control of a robotic manipulator with input saturation. IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 46, no. 3, pp. 334–344, 2016. DOI: 10.1109/TSMC.2015.2429555.CrossRefGoogle Scholar
  26. [26]
    S. S. Ge, T. H. Lee, G. Zhu. Improving regulation of a single-link flexible manipulator with strain feedback. IEEE Transactions on Robotics and Automation, vol. 14, no. 1, pp. 179–185, 1998. DOI: 10.1109/70.660869.CrossRefGoogle Scholar
  27. [27]
    H. H. Lee, J. Prevost. A coupled sliding-surface approach for the trajectory control of a flexible-link robot based on a distributed dynamic model. International Journal of Control, vol. 78, no. 9, pp. 629–637, 2005. DOI: 10.1080/00207170500101664.MathSciNetCrossRefzbMATHGoogle Scholar
  28. [28]
    L. J. Zhang, J. K. Liu. Nonlinear PDE observer design for a flexible two-link manipulator. In Proceedings of American Control Conference, IEEE, Montreal, Canada, pp. 5336–5341, 2012. DOI: 10.1109/ACC.2012.6314625.Google Scholar
  29. [29]
    L. Zhang, J. Liu. Observer-based partial differential equation boundary control for a flexible two-link manipulator in task space. IET Control Theory & Applications, vol. 6, no. 13, pp. 2120–2133, 2012. DOI: 10.1049/ietcta. 2011.0545.MathSciNetCrossRefGoogle Scholar
  30. [30]
    A. P. Tzes, S. Yurkovich, F. D. Langer. Method for solution of the Euler-Bernoulli beam equation in flexible-link robotic systems. In Proceedings of IEEE International Conference on Systems Engineering, IEEE, Fairborn, USA, pp. 557–560, 1989. DOI: 10.1109/ICSYSE.1989.48736.Google Scholar

Copyright information

© Institute of Automation, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.State Key Laboratory of Management and Control for Complex Systems, Institute of AutomationChinese Academy of SciencesBeijingChina

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