Skip to main content
Log in

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

  • Research Article - Electrical Engineering
  • Published:
Arabian Journal for Science and Engineering Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Spong, M.W.: Underactuated Mechanical Systems. Control Problems in Robotics and Automation, pp. 135–150. Springer, London (1998). https://doi.org/10.1007/BFb0015081

    Book  Google Scholar 

  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). https://doi.org/10.1109/CCA.2010.5611126

  3. Chen, Y.F.; Huang, A.C.: Controller design for a class of underactuated mechanical systems. IET Control Theory Appl. 6(1), 103 (2012). https://doi.org/10.1049/iet-cta.2010.0667

    Article  MathSciNet  Google Scholar 

  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). https://doi.org/10.1016/j.isatra.2013.07.012

    Article  Google Scholar 

  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). https://doi.org/10.1109/ACCESS.2018.2806568

    Article  Google Scholar 

  6. Isidori, A.: Nonlinear Control Systems. Communications and Control Engineering. Springer, London (1995). https://doi.org/10.1007/978-1-84628-615-5

    Book  MATH  Google Scholar 

  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). https://doi.org/10.1007/s11071-011-0280-3

    Article  Google Scholar 

  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). https://doi.org/10.1007/s11071-017-3582-2

    Article  MathSciNet  MATH  Google Scholar 

  9. Åström, K.J.; Furuta, K.: Swinging up a pendulum by energy control. Automatica 36(2), 287–295 (2000). https://doi.org/10.1016/S0005-1098(99)00140-5

    Article  MathSciNet  MATH  Google Scholar 

  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). https://doi.org/10.18201/ijisae.87020

    Article  Google Scholar 

  11. Spong, M.W.: Energy based control of a class of underactuated mechanical systems. IFAC Proc Volumes 29(1), 2828–2832 (1996). https://doi.org/10.1016/S1474-6670(17)58105-7

    Article  Google Scholar 

  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). https://doi.org/10.1016/J.ROBOT.2009.07.016

    Article  Google Scholar 

  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). https://doi.org/10.1016/S0959-1524(01)00041-5

    Article  Google Scholar 

  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). https://doi.org/10.1049/iet-cta.2011.0251

    Article  MathSciNet  Google Scholar 

  15. Lo, J.-C.; Kuo, Y.-H.: Decoupled fuzzy sliding-mode control. IEEE Trans. Fuzzy Syst. 6(3), 426–435 (1998). https://doi.org/10.1109/91.705510

    Article  Google Scholar 

  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). https://doi.org/10.1007/s11633-015-0880-3

    Article  Google Scholar 

  17. Utkin, V.: Variable structure systems with sliding modes. IEEE Trans. Autom. Control 22(2), 212–222 (1977). https://doi.org/10.1109/TAC.1977.1101446

    Article  MathSciNet  MATH  Google Scholar 

  18. Utkin, V.: Sliding Modes in Control and Optimization. Springer, Berlin (1992). https://doi.org/10.1007/978-3-642-84379-2

    Book  MATH  Google Scholar 

  19. Coban, R.: Backstepping integral sliding mode control of an electromechanical system. Automatika 58(3), 266–272 (2018). https://doi.org/10.1080/00051144.2018.1426263

    Article  Google Scholar 

  20. Freeman, R.A.; Kokotovic, P.: Robust Nonlinear Control Design: State-Space and Lyapunov Techniques. Birkhäuser, Boston (1996)

    Book  MATH  Google Scholar 

  21. Wang, Q.; Stengel, R.F.: Robust control of nonlinear systems with parametric uncertainty. Automatica 38, 1591 –1599 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  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). https://doi.org/10.1016/J.ISATRA.2010.12.008

    Article  Google Scholar 

  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. 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). https://doi.org/10.21605/cukurovaummfd.358391

    Article  Google Scholar 

  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). https://doi.org/10.1109/AIM.2017.8014148

  26. Feedback Instruments: 33-936s Digital Pendulum Control Experiments Manual. Tech. rep. (2006)

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Baris Ata.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ata, B., Coban, R. Decoupled Backstepping Sliding Mode Control of Underactuated Systems with Uncertainty: Experimental Results. Arab J Sci Eng 44, 7013–7021 (2019). https://doi.org/10.1007/s13369-019-03754-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s13369-019-03754-5

Keywords

Navigation