Advertisement

Trajectory Tracking Control of a Class of Underactuated Mechanical Systems with Nontriangular Normal Form Based on Block Backstepping Approach

  • Mohammad-Reza Moghanni-Bavil-OlyaeiEmail author
  • Ahmad Ghanbari
  • Jafar Keighobadi
Article
  • 22 Downloads

Abstract

In this paper, the formulation of a block-backstepping control approach is presented to address the trajectory tracking problem for a general class of nonlinear n degrees of freedom (n-DOF) underactuated mechanical systems (UMSs) in nontriangular normal form. First, the Euler-Lagrange model of the general form of UMSs is transformed into block-strict feedback form. Then, control input for the n-DOF UMS will be obtainable by synthesis of the backstepping approach. Additionally, an integral action is incorporated to the proposed controller to enhance the steady state performance of the overall system and also to improve the trajectory tracking precision of the control system. Lyapunov theory is utilizable to prove the stability and convergence of the overall system. To demonstrate the effectiveness of the designed controller, the proposed control algorithm is applied through numerical simulation for the trajectory tracking of a single-link flexible-link flexible-joint manipulator (SFLFJM) as an UMS with the nontriangular normal form.

Keywords

Underactuated mechanical system Trajectory tracking Block-backstepping control Flexible-link flexible-joint manipulator 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Notes

References

  1. 1.
    Spong, M.W.: Underactuated mechanical systems. In: Control Problems in Robotics and Automation, pp. 135–150. Springer, Berlin (1998)Google Scholar
  2. 2.
    Liu, Y., Yu, H.: A survey of underactuated mechanical systems. IET Control Theor. Appl. 7(7), 921–935 (2013)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Olfati-Saber, R.: Nonlinear Control of Underactuated Mechanical Systems with Application to Robotics and Aerospace Vehicles. Massachusetts Institute of Technology (2001)Google Scholar
  4. 4.
    Fantoni, I., Lozano, R.: Non-linear Control for Underactuated Mechanical Systems. Springer Science & Business Media, London (2002)CrossRefGoogle Scholar
  5. 5.
    Aneke, N.P.I.: Control of Underactuated Mechanical Systems. Technische Universiteit Eindhoven (2003)Google Scholar
  6. 6.
    Maalouf, D., Moog, C.H., Aoustin, Y., Li, S.: Classification of two-degree-of-freedom underactuated mechanical systems. IET Control Theor. Appl. 9(10), 1501–1510 (2015)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Zhang, M., Ma, X., Rong, X., Tian, X., Li, Y.: Error tracking control for underactuated overhead cranes against arbitrary initial payload swing angles. Mech. Syst. Signal Process. 84, 268–285 (2017)CrossRefGoogle Scholar
  8. 8.
    Sepulchre, R., Jankovic, M., Kokotovic, P.V.: Constructive Nonlinear Control. Springer Science & Business Media (2012)Google Scholar
  9. 9.
    Kokotović, P., Arcak, M.: Constructive nonlinear control: a historical perspective. Automatica 37(5), 637–662 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Khalil, H.K.: Noninear Systems, vol. 2, pp. 5–1. Prentice-Hall, New Jersey (1996)Google Scholar
  11. 11.
    Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Nonlinear and Adaptive Control Design, vol. 222. Wiley, New York (1995)Google Scholar
  12. 12.
    Chang, Y., Cheng, C.-C.: Block backstepping control of multi-input nonlinear systems with mismatched perturbations for asymptotic stability. Int. J. Control 83(10), 2028–2039 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Rudra, S., Barai, R.K., Maitra, M.: Nonlinear state feedback controller design for underactuated mechanical system: a modified block backstepping approach. ISA Trans. 53(2), 317–326 (2014)CrossRefGoogle Scholar
  14. 14.
    Rudra, S., Barai, R.K., Maitra, M.: Block Backstepping Design of Nonlinear State Feedback Control Law for Underactuated Mechanical Systems. Springer, Berlin (2016)zbMATHGoogle Scholar
  15. 15.
    Chang, Y.: Block backstepping control of MIMO systems. IEEE Trans. Autom. Control 56(5), 1191–1197 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Rudra, S., Barai, R.K., Maitra, M.: Design and implementation of a block-backstepping based tracking control for nonholonomic wheeled mobile robot. Int. J. Robust Nonlinear Control 26(14), 3018–3035 (2016)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Dong, Z., Wan, L., Li, Y., Liu, T., Zhang, G.: Trajectory tracking control of underactuated USV based on modified backstepping approach. Int. J. Naval Archit. Ocean Eng. 7(5), 817–832 (2015)CrossRefGoogle Scholar
  18. 18.
    Vakil, M., Fotouhi, R., Nikiforuk, P.: A new method for dynamic modeling of flexible-link flexible-joint manipulators. J. Vib. Acoust. 134(1), 014503 (2012)CrossRefGoogle Scholar
  19. 19.
    Staufer, P., Gattringer, H., Bremer, H.: Comparative study on control concepts of a robot manipulator with multiple-link/joint flexibilities. PAMM 12(1), 79–80 (2012)CrossRefGoogle Scholar
  20. 20.
    Suklabaidya, S., Lochan, K., Roy, B.: Modeling and sliding mode control of flexible link flexible joint robot manipulator. In: Proceedings of the 2015 Conference on Advances in Robotics, p. 59. ACM (2015)Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringUniversity of TabrizTabrizIran
  2. 2.School of Engineering Emerging TechnologiesUniversity of TabrizTabrizIran

Personalised recommendations