Robust Output Tracking of a 3DOF Helicopter via High-Order Sliding Mode Observers

  • Alejandra Ferreira de LozaEmail author
  • Jérome Cieslak
  • David Henry
  • Ali Zolghadri
  • Leonid Fridman


This paper tackles the output tracking problem of a MIMO system subjected to actuator faults and unmatched perturbations. The proposed methodology is based on high order sliding mode observation and identification techniques. A dynamic sliding surface is proposed using a nested-backward design strategy in order to counteract the effects of the unmatched perturbations. A super-twisting control is used to steer the state to the sliding surface. The identified value of the fault is injected to alleviate the control gain while accomplishing fault accommodation. As a consequence, the chattering is attenuated. A simulation example for a 3-DOF helicopter highlights the efficiency of the present method.


Unknown Input Actuator Fault Fault Tolerant Control Successive Derivative Robust Output 
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.


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  1. 1.
    Edwards, C., Lombaerts, T., Smaili, H.: Fault Tolerant Flight Control: A Benchmark Challenge. Springer (2010)Google Scholar
  2. 2.
    Berdjag, D., Cieslak, J., Zolghadri, A.: Fault diagnosis and monitoring of oscillatory failure case in aircraft inertial system. Control Engineering Practice 20, 1410–1425 (2012)CrossRefGoogle Scholar
  3. 3.
    Ferreira de Loza, A., Cieslak, J., Henry, D., Dvila, J., Zolghadri, A.: Sensor fault diagnosis using a non-homogeneous high-order sliding mode observer with application to a transport aircraft. IET Control Theory and Applications (2015), doi:10.1049/iet-cta.2014.0226Google Scholar
  4. 4.
    Cieslak, J., Efimov, D., Henry, D.: Transient management of a supervisory fault-tolerant control scheme based on dwell-time conditions. Int. J. Adapt. Control Signal Process (2014), doi:10.1002/acs.2465Google Scholar
  5. 5.
    Efimov, D., Cieslak, J., Henry, D.: Supervisory faulttolerant control with mutual performance optimization. Int. J. Adapt. Control Signal Process. 27, 251–279 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Cieslak, J., Henry, D., Zolghadri, A.: Fault tolerant flight control: from theory to piloted flight simulator experiments. IET Control Theory and Applications 4, 1451–1464 (2010)CrossRefGoogle Scholar
  7. 7.
    Utkin, V.I.: Sliding modes in control and optimization. Springer, Berlin (1992)CrossRefzbMATHGoogle Scholar
  8. 8.
    Corradini, M.L., Monteriu, A., Orlando, G.: An actuator failure tolerant control scheme for an underwater remotely operated vehicle. IEEE Trans. on Control Systems Technology 19, 1036–1046 (2011)CrossRefGoogle Scholar
  9. 9.
    Alwi, H., Edwards, C.: Fault Detection and Fault-Tolerant Control Using Sliding Modes. AIC. Springer, New York (2011)Google Scholar
  10. 10.
    Hamayun, M.T., Edwards, C., Alwi, H.: A fault tolerant control allocation scheme with output integral sliding modes. Automatica 49, 1830–1837 (2013)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Efimov, D., Zolghadri, A., Rassi, T.: Actuator fault detection and compensation under feedback control. Automatica 47, 1699–1705 (2011)CrossRefzbMATHGoogle Scholar
  12. 12.
    Davila, J.: Exact tracking using backstepping control design and high-order sliding modes. IEEE Trans. on Automat. Control 58, 2077–2081 (2013)CrossRefMathSciNetGoogle Scholar
  13. 13.
    Ferreira, A., Fridman, L., Punta, E., Bartolini, G.: Output nested backward compensation of unmatched effects of unknown inputs. In: Proc. of the IEEE Conference on Decision and Control, pp. 1448–1453 (2010)Google Scholar
  14. 14.
    Utkin, V.I.: Sliding modes in control and optimization. Springer, Berlin (1992)CrossRefzbMATHGoogle Scholar
  15. 15.
    Wang, W., Wen, C.: Adaptive compensation for infinite number of actuator failures or faults. Automatica 47, 2197–2210 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Basin, M.V., Loukianov, A.G., Hernandez-Gonzalez, M.: Joint state and parameter estimation for uncertain stochastic nonlinear polynomial systems. Int. J. Systems Science 44, 1200–1208 (2013)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    Bejarano, F.J., Figueroa, M., Pacheco, J., De Jesus Rubio, J.: Robust fault diagnosis of disturbed linear systems via a sliding mode high order differentiator. Int. J. of Control 85, 648–659 (2012)CrossRefzbMATHGoogle Scholar
  18. 18.
    Fridman, L., Davila, J., Levant, A.: High-order sliding-mode observation for linear systems with unknown inputs. Nonlinear Analysis: Hybrid Systems 5, 337–347 (2011)MathSciNetGoogle Scholar
  19. 19.
    Ferreira de Loza, A., Rios, H., Rosales, A.: Robust regulation for a 3DOF helicopter via sliding-mode observation and identification. Journal of the Franklin Institute 349, 700–718 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  20. 20.
    Zolghadri, A., Henry, D., Cieslak, J., Efimov, D., Goupil, P.: Fault Diagnosis and Fault-Tolerant Control and Guidance for Aerospace Vehicles: From theory to application. Advances in Industrial Control. Springer (2014) ISBN 978-1-4471-5312-2Google Scholar
  21. 21.
    Levant, A.: Higher-order sliding modes, differentiation and output feedback control. Int. J. of Control 76, 924–941 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Loukyanov, A., Utkin, V.: Methods of reducing equations for dynamic systems to a regular form. Automatic and Remote Control 42, 413–420 (1993)Google Scholar
  23. 23.
    Drakunov, S.V., Izosimov, D.B., Lukyanov, A.G., Utkin, V.I.: Block control principle I. Automation and Remote Control 51, 601–609 (1990)zbMATHMathSciNetGoogle Scholar
  24. 24.
    Polyakov, A.: Nonlinear feedback design for fixed-time stabilization of linear control systems. IEEE Transactions on Automatic Control 57, 2106–2110 (2012)CrossRefMathSciNetGoogle Scholar
  25. 25.
    Levant, A.: Sliding order and sliding accuracy in sliding mode control. Int. J. of Control 58, 1247–1263 (1993)CrossRefzbMATHMathSciNetGoogle Scholar
  26. 26.
    Moreno, J.A., Osorio, M.: Strict Lyapunov functions for the supertwisting algorithm. IEEE Trans. on Automat. Control 57, 1035–1040 (2012)CrossRefMathSciNetGoogle Scholar
  27. 27.
    Cieslak, J., Efimov, D., Zolghadri, A., Henry, D., Goupil, P.: Design of a non-homogeneous differentiator for actuator oscillatory failure case reconstruction in noisy environment. Proc. IMechE Part I: J Systems and Control Engineering (2014), doi:10.1177/0959651814561091Google Scholar
  28. 28.
    Krstic, M., Kanellakopoulos, I., Kokotovic, P.V.: Nonlinear and adaptive control design. Wiley, New York (1995)Google Scholar
  29. 29.
    Quanser Inc. 3-DOF Helicopter Reference Manual, Document Number 644, Revision 2.1Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Alejandra Ferreira de Loza
    • 1
    Email author
  • Jérome Cieslak
    • 2
  • David Henry
    • 2
  • Ali Zolghadri
    • 2
  • Leonid Fridman
    • 3
  1. 1.Instituto Politecnico NacionalTijuanaMexico
  2. 2.CNRS, IMS-labUniversité de BordeauxTalence cedexFrance
  3. 3.Department of Control, Engineering FacultyUniversidad Nacional Autonoma de Mexico (UNAM)Mexico D.FMexico

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