Comparison of Backstepping-Based Sliding Mode and Adaptive Backstepping for a Robust Control of a Twin Rotor Helicopter

  • Saif Siddique Butt
  • Hao SunEmail author
  • Harald Aschemann
Part of the Mathematical Engineering book series (MATHENGIN)


In this contribution, two robust MIMO backstepping control approaches for a twin rotor aerodynamic system (TRAS) test-rig are considered. The TRAS represents a nonlinear system with significant couplings. A nonlinear multibody model of the TRAS with lumped unknown disturbance torques is derived using Lagrange’s equations. Herewith, both a backstepping-based sliding mode control and an adaptive backstepping control are designed to track desired trajectories for the azimuth angle and the pitch angle. An explicit expression is derived for the reaching time in the case of the backstepping-based sliding mode control. In order to estimate immeasurable angular velocities and unknown disturbance torques for the backstepping-based sliding mode control, a discrete-time extended Kalman filter (EKF) is employed. For the adaptive backstepping, a robust sliding mode differentiator is used instead to estimate the angular velocities. Moreover, in the adaptive backstepping control approach, the disturbance compensation is realised with the help of additional adaptive control parts driven by the tracking errors of the controlled variables. The overall stability of the proposed controllers in combination with the corresponding estimator is investigated thoroughly by simulations. Furthermore, in order to validate the proposed control schemes, experiments are performed on the dedicated test-rig and a comparison of the two proposed control structures is provided as well.


Lyapunov Function Tracking Error Pitch Angle Slide Mode Control Extend Kalman Filter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Ahmad S, Chipperfield A, Tokhi M (2000) Dynamic modeling and optimal control of a twin rotor MIMO system. In: Proceedings of the IEEE conference on national aerospace and electronics (NAECON), pp 391–398Google Scholar
  2. 2.
    Ahmad S, Shaheed M, Chipperfield A, Tokhi M (2000) Nonlinear modelling of a twin rotor MIMO system using radial basis function networks. In: Proceedings of the IEEE conference on national aerospace and electronics (NAECON), pp 313–320Google Scholar
  3. 3.
    Ahmed Q, Bhatti A, Iqbal S (2009) Nonlinear robust decoupling control design for twin rotor system. In: Proceedings of the 7th Asian Control Conference (ASCC), pp 937–942Google Scholar
  4. 4.
    Butt SS, Prabel R, Aschemann H (2014) Multi-variable flatness-based control of a two degrees of freedom helicopter. In: Proceedings of the international conference on control, decision and information technologies (CoDIT), pp 321–326Google Scholar
  5. 5.
    Butt SS, Prabel R, Aschemann H (2015) Multi-variable sliding mode control of a two degrees of freedom helicopter. In: Proceedings of the Vienna conference on mathematical modelling, (MATHMOD), pp 802–807Google Scholar
  6. 6.
    Chawda V, Celik O, O’Malley M (2011) Application of Levant’s differentiator for velocity estimation and increased Z-width in haptic iinterfaces. In: Proceedings of the IEEE world haptics conference (WHC), pp 403–408Google Scholar
  7. 7.
    Darus I, Aldebrez F, Tokhi M (2004) Parametric modelling of a twin rotor system using genetic algorithms. In: Proceedings of the first international symposium on control, communications and signal processing, pp 115–118Google Scholar
  8. 8.
    Dutka A, Ordys A, Grimble M (2003) Non-linear predictive control of 2 DOF helicopter model. In: Proceedings of the 42nd IEEE conference on decision and control (CDC), vol 4, pp 3954–3959Google Scholar
  9. 9.
    Goldstein H, Poole P, Safko J (2002) Classical mechanics. Addison Wesley, San FranciscozbMATHGoogle Scholar
  10. 10.
    INTECO (2013) Two rotor aero-dynamical system user’s manualGoogle Scholar
  11. 11.
    Jung-Hua Y, Wen-Chun H (2009) Adaptive backstepping control for electrically driven unmanned helicopter. Control Eng Pract 17(8):903–913CrossRefGoogle Scholar
  12. 12.
    Khalil HK (1996) Nonlinear systems. Prentice Hall, Upper Saddle RiverGoogle Scholar
  13. 13.
    Levant A (1998) Robust exact differentiation via sliding mode technique. Automatica 34(3):379–384MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Levant A (2003) Higher-order sliding modes, differentiation and output-feedback control. Int J Control 76(9):924–941MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lopez-Martinez M, Ortega M, Rubio F (2003) An H\(_\infty \) controller for a double rotor system. In: IEEE conference on emerging technologies and factory automation (ETFA), vol 1, pp 253–259Google Scholar
  16. 16.
    Lopez-Martinez M, Diaz JM, Ortega M, Rubio F (2004) Control of a laboratory helicopter using switched 2-step feedback linearization. In: Proceedings of the American control conference (ACC), vol. 5, pp 4330–4335Google Scholar
  17. 17.
    Lopez-Martinez M, Vivas C, Ortega M (2005) A multivariable nonlinear H\(_\infty \) controller for a laboratory helicopter. In: Proceedings of the 44th IEEE conference on decision and control, European control conference (CDC-ECC), pp 4065–4070Google Scholar
  18. 18.
    Rahideh A, Shaheed MH (2007) Mathematical dynamic modelling of a twin-rotor multiple input-multiple output system. Proc Inst Mech Eng, Part I: J Syst Control Eng 221(1):89–101CrossRefGoogle Scholar
  19. 19.
    Shaheed M (2004) Performance analysis of 4 types of conjugate gradient algorithms in the nonlinear dynamic modelling of a TRMS using feedforward neural networks. In: Proceedings of the IEEE international conference on systems, man and cybernetics, vol 6, pp 5985–5990Google Scholar
  20. 20.
    Slotine J, Li W (1991) Applied nonlinear control. Prentice-Hall Inc, Upper Saddle RiverzbMATHGoogle Scholar
  21. 21.
    Stengel R (1994) Optimal control and estimation. Dover Publications Inc, New YorkzbMATHGoogle Scholar
  22. 22.
    Utkin VI, Guldner J, Shi J (1999) Sliding mode control in electromechanical systems. The Taylor & Francis systems and control book series. Taylor & Francis, LondonGoogle Scholar
  23. 23.
    Young K, Utkin V, Ozguner U (1999) A control engineer’s guide to sliding mode control. IEEE Trans Control Syst Technol 7(3):328–342CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Saif Siddique Butt
    • 1
  • Hao Sun
    • 1
    Email author
  • Harald Aschemann
    • 1
  1. 1.Chair of MechatronicsUniversity of RostockRostockGermany

Personalised recommendations