Arabian Journal for Science and Engineering

, Volume 44, Issue 8, pp 7013–7021 | Cite as

Decoupled Backstepping Sliding Mode Control of Underactuated Systems with Uncertainty: Experimental Results

  • Baris AtaEmail author
  • Ramazan Coban
Research Article - Electrical Engineering


In this paper, a decoupled backstepping sliding mode control method is proposed to control underactuated systems under uncertainties and disturbances. The sliding mode control technique and the backstepping control technique are combined owing to their merits. Since the design methodology is based on the Lyapunov theorem, the stability of the system is guaranteed. The effectiveness of the proposed method is verified by the experimental results of the controller which is applied to a nonlinear, underactuated inverted pendulum system. The experimental results show that the decoupled backstepping sliding mode control achieves a satisfactory control performance rather than the decoupled sliding mode controller and the proposed method provides a robust performance to overcome parametric uncertainties where the decoupled sliding mode control fails.


Backstepping Sliding mode Decoupled sliding mode Underactuated systems Inverted pendulum on a cart 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Spong, M.W.: Underactuated Mechanical Systems. Control Problems in Robotics and Automation, pp. 135–150. Springer, London (1998). CrossRefGoogle Scholar
  2. 2.
    Man, W.; Lin, J.S.: Nonlinear control design for a class of underactuated systems. In: 2010 IEEE International Conference on Control Applications pp. 1439–1444 (2010).
  3. 3.
    Chen, Y.F.; Huang, A.C.: Controller design for a class of underactuated mechanical systems. IET Control Theory Appl. 6(1), 103 (2012). MathSciNetCrossRefGoogle Scholar
  4. 4.
    Adhikary, N.; Mahanta, C.: Integral backstepping sliding mode control for underactuated systems: swing-up and stabilization of the cart-pendulum system. ISA Trans. 52(6), 870–880 (2013). CrossRefGoogle Scholar
  5. 5.
    Shah, I.; Rehman, F.U.: Smooth second order sliding mode control of a class of underactuated mechanical systems. IEEE Access 6(c), 7759–7771 (2018). CrossRefGoogle Scholar
  6. 6.
    Isidori, A.: Nonlinear Control Systems. Communications and Control Engineering. Springer, London (1995). CrossRefzbMATHGoogle Scholar
  7. 7.
    She, J.; Zhang, A.; Lai, X.; Wu, M.: Global stabilization of 2-DOF underactuated mechanical systems-an equivalent-input-disturbance approach. Nonlinear Dyn. 69(1–2), 495–509 (2012). CrossRefGoogle Scholar
  8. 8.
    Zhang, A.; Lai, X.; Wu, M.; She, J.: Nonlinear stabilizing control for a class of underactuated mechanical systems with multi degree of freedoms. Nonlinear Dyn. 89(3), 2241–2253 (2017). MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Åström, K.J.; Furuta, K.: Swinging up a pendulum by energy control. Automatica 36(2), 287–295 (2000). MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ata, B.; Coban, R.: Artificial bee colony algorithm based linear quadratic optimal controller design for a nonlinear inverted pendulum. Int. J. Intell. Syst. Appl. Eng. 3(1), 1 (2015). CrossRefGoogle Scholar
  11. 11.
    Spong, M.W.: Energy based control of a class of underactuated mechanical systems. IFAC Proc Volumes 29(1), 2828–2832 (1996). CrossRefGoogle Scholar
  12. 12.
    Siuka, A.; Schöberl, M.: Applications of energy based control methods for the inverted pendulum on a cart. Robot. Auton. Syst. 57(10), 1012–1017 (2009). CrossRefGoogle Scholar
  13. 13.
    Chang, W.D.; Hwang, R.C.; Hsieh, J.G.: A self-tuning PID control for a class of nonlinear systems based on the Lyapunov approach. J. Process Control 12(2), 233–242 (2002). CrossRefGoogle Scholar
  14. 14.
    Subudhi, B.; Ghosh, A.; Krishnan, T.: Robust proportional-integral-derivative compensation of an inverted cart-pendulum system: an experimental study. IET Control Theory Appl. 6(8), 1145–1152 (2012). MathSciNetCrossRefGoogle Scholar
  15. 15.
    Lo, J.-C.; Kuo, Y.-H.: Decoupled fuzzy sliding-mode control. IEEE Trans. Fuzzy Syst. 6(3), 426–435 (1998). CrossRefGoogle Scholar
  16. 16.
    Mahjoub, S.; Mnif, F.; Derbel, N.: Second-order sliding mode approaches for the control of a class of underactuated systems. Int. J. Autom. Comput. 12(2), 134–141 (2015). CrossRefGoogle Scholar
  17. 17.
    Utkin, V.: Variable structure systems with sliding modes. IEEE Trans. Autom. Control 22(2), 212–222 (1977). MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Utkin, V.: Sliding Modes in Control and Optimization. Springer, Berlin (1992). CrossRefzbMATHGoogle Scholar
  19. 19.
    Coban, R.: Backstepping integral sliding mode control of an electromechanical system. Automatika 58(3), 266–272 (2018). CrossRefGoogle Scholar
  20. 20.
    Freeman, R.A.; Kokotovic, P.: Robust Nonlinear Control Design: State-Space and Lyapunov Techniques. Birkhäuser, Boston (1996)CrossRefzbMATHGoogle Scholar
  21. 21.
    Wang, Q.; Stengel, R.F.: Robust control of nonlinear systems with parametric uncertainty. Automatica 38, 1591 –1599 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Lu, C.H.; Hwang, Y.R.; Shen, Y.T.: Backstepping sliding mode tracking control of a vane-type air motor X-Y table motion system. ISA Trans. 50(2), 278–286 (2011). CrossRefGoogle Scholar
  23. 23.
    Coban, R.: Backstepping sliding mode tracking controller design and experimental application to an electromechanical system. J. Control Eng. Appl. Inform. 19(3), 88–96 (2017)Google Scholar
  24. 24.
    Ata, B.; Coban, R.: Linear quadratic optimal control of an inverted pendulum on a cart using artificial bee colony algorithm: an experimental study. Cukurova Univ. J. Fac. Eng. Archit. 32(2), 109–124 (2017). CrossRefGoogle Scholar
  25. 25.
    Coban, R.; Ata, B.: Decoupled sliding mode control of an inverted pendulum on a cart: an experimental study. In: IEEE/ASME International Conference on Advanced Intelligent Mechatronics, AIM (2017).
  26. 26.
    Feedback Instruments: 33-936s Digital Pendulum Control Experiments Manual. Tech. rep. (2006)Google Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2019

Authors and Affiliations

  1. 1.Department of Computer EngineeringCukurova UniversityAdanaTurkey

Personalised recommendations