International Journal of Fuzzy Systems

, Volume 19, Issue 5, pp 1444–1463 | Cite as

Interval Type-2 Fuzzy Sliding Mode Controller Based on Nonlinear Observer for a 3-DOF Helicopter with Uncertainties

  • Samir Zeghlache
  • Tarak Benslimane
  • Nourredine Amardjia
  • Abderrahmen Bouguerra


In this paper, a robust controller for a three degree of freedom helicopter control is proposed in presence of modeling error and disturbance. In this frame, interval type-2 fuzzy logic control approach (IT2FLC) and sliding mode control (SMC) techniques are used to design a controller named interval type-2 fuzzy sliding mode controller (IT2FSMC). Elevation, pitch and travel angles are considered measurable, whereas unmeasured states are estimated by using a nonlinear observer. The proposed control scheme can not only attenuate the chattering effect of the SMC, but also it reduces the rules number of the fuzzy controller. As for stability, it is exponentially guaranteed by using the Lyapunov criteria. The simulation results show that the IT2FSMC significantly alleviates the chattering effect and provides a good tracking performance, in the presence of modeling error and disturbance. They also illustrate that the IT2FSMC achieves the best tracking performance in comparison with the type-1 fuzzy logic controller, the IT2FLC and the type-1 fuzzy sliding mode controller.


Type-2 fuzzy logic Sliding mode controller 3-DOF helicopter Nonlinear observer Stability 


  1. 1.
    Westerberg, S., Mettin, U., Shiriaev, A: Motion planning and control of an underactuated 3-DOF helicopter. In: Proceedings of the IEEE International on Intelligent Robots and Systems, pp. 3759–3764 (2010)Google Scholar
  2. 2.
    3-DOF Helicopter experiment manual. Quanser Consulting, Canada (1998).
  3. 3.
    Starkov, K.K., Aguilar, L.T., Orlov, Y.: Sliding mode control synthesis of a 3-DOF helicopter prototype using position feedback. In: Proceedings of the IEEE International Workshop on Variable Structure Systems, pp. 233–237 (2008)Google Scholar
  4. 4.
    Thomas, K., Knut, G., Andreas, K.: Trajectory tracking of a 3-DOF laboratory helicopter under input and state constraints. IEEE Trans. Control Syst. Technol. 18, 944–952 (2010)CrossRefGoogle Scholar
  5. 5.
    Shan, J., Liu, H.T., Nowotny, S.: Synchronised trajectory-tracking control of multiple 3-DOF experimental helicopters. IEE Proc. Control Theory Appl. 152, 683–692 (2005)CrossRefGoogle Scholar
  6. 6.
    Fang, Z., Weinan, G., Lei, Z.: Robust adaptive integral backstepping control of a 3-DOF helicopter. Int. J. Adv. Robot. Syst. 9, 1–8 (2012)CrossRefGoogle Scholar
  7. 7.
    Kutay, A.T., Anthony, J.C., Naira, H.: Experimental results on adaptive output feedback control using a laboratory model helicopter. IEEE Trans. Control Syst. Technol. 13, 196–202 (2005)CrossRefGoogle Scholar
  8. 8.
    Yu, Y., Hong, Y.Z.: Robust attitude control of a 3-DOF helicopter with multi-operation points. J. Syst. Sci. Complex. 22, 207–219 (2009)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mitsuaki, I., Masatoshi, N., Kazuhide, N.: Nonlinear adaptive model following control for a 3-DOF tandem-rotor model helicopter. Control Eng. Pract. 18, 936–943 (2010)CrossRefGoogle Scholar
  10. 10.
    Xiafu, W., Geng, L., Yisheng, Z.: Robust H attitude control of a laboratory helicopter. Robot. Auton. Syst. 61, 1247–1257 (2013)CrossRefGoogle Scholar
  11. 11.
    Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, Berlin (2008)MATHGoogle Scholar
  12. 12.
    de Loza, A.F., Ríos, H., Rosales, A.: Robust regulation for a 3-DOF helicopter via sliding-mode observation and identification. J. Frankl. Inst. 349, 700–718 (2012)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Marlen, M.S., Luis, T.A., Yury, O.: Output sliding mode-based stabilization of underactuated 3-DOF helicopter prototype and its experimental verification. J. Frankl. Inst. (2015). doi: 10.1016/j.jfranklin.2015.01.010 MathSciNetGoogle Scholar
  14. 14.
    Meza-Sanchez, I.M., Orlov, Y., Aguilar, L.T.: Stabilization of a 3-DOF underactuated helicopter prototype: second order sliding mode algorithm synthesis, stability analysis, and numerical verification. In: Proceedings of the IEEE International Workshop on Variable Structure Systems, pp. 361–366 (2012)Google Scholar
  15. 15.
    Junshan, G., Xinghu, X., Chen, H.: A study on the control methods based on 3-DOF helicopter model. J. Comput. 7, 2526–2533 (2012)Google Scholar
  16. 16.
    Arbab, N.K., Yaping, D., Xu, X.Y.: Simpler fuzzy logic controller (SFLC) design for 3-DOF laboratory scaled helicopter. Int. J. Res. Rev. Appl. Sci. 15, 228–241 (2013)Google Scholar
  17. 17.
    Lei, Y., Lidong, Z., Qing, L.: Design and application of fuzzy sliding mode control in the 3-DOF helicopter. In: Proceedings of the IEEE International on Intelligent Systems and Applications, pp. 1–5 (2009)Google Scholar
  18. 18.
    Li, H., Chengwei, W., Peng, S.: Control of nonlinear networked systems with packet dropouts: interval type-2 fuzzy model-based approach. IEEE Trans. Cybern. (2015). doi: 10.1109/TCYB.2014.2371814 Google Scholar
  19. 19.
    Li, H., Wu, C., Wu, L., Lam, H.-K., Gao, Y.: Filtering of interval type-2 fuzzy systems with intermittent measurements. IEEE Trans. Cybern. (2016). doi: 10.1109/TCYB.2015.2413134 Google Scholar
  20. 20.
    Li, H., Sun, X., Wu, L., Lam, H.: State and output feedback control of a class of fuzzy systems with mismatched membership functions. IEEE Trans. Fuzzy Syst. (2015). doi: 10.1109/TFUZZ.2014.2387876 Google Scholar
  21. 21.
    Li, H., Pan, Y., Zhou, Q.: Filter design for interval type-2 fuzzy systems with D stability constraints under a unified frame. IEEE Trans. Fuzzy Syst. (2015). doi: 10.1109/TFUZZ.2014.2315658 Google Scholar
  22. 22.
    Ahsene, B., Salim, L., Fares, B., Franck, P.: Design and experimentation of a self-tuning PID control applied to the 3-DOF helicopter. Arch. Control Sci. 23, 311–331 (2013)MathSciNetMATHGoogle Scholar
  23. 23.
    Héctor, R., Antonio, R., Alejandro, D.: Global non-homogeneous quasi-continuous controller for a 3-DOF helicopter. In: Proceedings of the IEEE International Workshop on Variable Structure Systems, pp. 475–480 (2010)Google Scholar
  24. 24.
    Fabrício, G.M., Elder, M.H.: Adaptive elevation control of a three degrees-of-freedom model helicopter using neural networks by state and output feedback. ABCM Symp. Ser. Mechatron. 3, 106–113 (2008)Google Scholar
  25. 25.
    Kamil, K., Yusuf, T., Mehmet, T., Kemal, U., Giilay, O.: Controlling 3-DOF helicopter via fuzzy PID controller. In: Proceedings of the IEEE International on Electrical and Electronics Engineering, pp. 869–873 (2015)Google Scholar
  26. 26.
    Liu, H., Yu, Y., Lu, G., Zhong, Y.: Robust LQR attitude control of 3-DOF helicopter. In: Proceedings of the IEEE International on Chinese Control Conference, pp. 529–534 (2010)Google Scholar
  27. 27.
    Bharathi, M., Golden, K.: An LQR controller design approach for pitch axis stabilization of 3-DOF helicopter system. Int. J. Sci. Eng. Res. 4, 1398–1409 (2013)Google Scholar
  28. 28.
    Boukhnifer, M., Chaibet, A., Larouci, C.: H-infinity robust control of 3-DOF helicopter. In: Proceedings of the IEEE International on Systems, Signals and Devices, pp. 1–6 (2012)Google Scholar
  29. 29.
    Wang, X., Zhao, C., Li, Z.: Robust H-infinity tracing control of 3-DOF helicopter model. In: Proceedings of the IEEE International Measuring Technology and Mechatronics Automation, pp. 279–282 (2010)Google Scholar
  30. 30.
    Yao, Y., Geng, L., Changyin, S., Hao, L.: Robust backstepping decentralized tracking control for a 3-DOF helicopter. Nonlinear Dyn. 82, 947–960 (2015)MathSciNetCrossRefMATHGoogle Scholar
  31. 31.
    Konstantin, K.S., Aguilar, L.T., Yury, O.: Sliding mode control synthesis of a 3-DOF helicopter prototype using position feedback. In: Proceedings of the IEEE International Workshop on Variable Structure Systems, pp. 233–237 (2008)Google Scholar
  32. 32.
    Héctor, R., Antonio, R., Alejandra, F., Alejandro, D.: Robust regulation for a 3-DOF helicopter via sliding-modes control and observation techniques. In: Proceedings of American Control Conference, pp. 4427–4432 (2010)Google Scholar
  33. 33.
    Franck, P., Abdelhamid, C.: A robust controller based on adaptive super-twisting algorithm for a 3-DOF Helicopter. In: Proceedings of the IEEE International on Decision and Control, pp. 7095–7100 (2012)Google Scholar
  34. 34.
    Boris, A., Dimitri, P., Alexander, L.: Adaptive control of 3-DOF motion for LAAS helicopter benchmark: design and experiments. In: Proceedings of the IEEE International on American Control Conference, pp. 3312–3317 (2007)Google Scholar
  35. 35.
    Masatoshi, N., Mitsuaki, I., Kazuhide, N.: Nonlinear adaptive control system design and experiment for a 3-DOF model helicopter. Artif. Life Robot. 13, 50–53 (2008)CrossRefGoogle Scholar
  36. 36.
    Rafael, P.B., Elder, M.H.: Adaptive control of a 3-DOF helicopter model using neural networks. In: Proceedings of the International Congress of Mechanical Engineering, pp. 1–8 (2007)Google Scholar
  37. 37.
    Li, Y., Shaocheng, T., Tieshan, L.: Composite adaptive fuzzy output feedback control design for uncertain nonlinear strict-feedback systems with input saturation. IEEE Trans. Cybern. 45, 2299–2308 (2015)CrossRefGoogle Scholar
  38. 38.
    Li, Y., Shuai, S., Shaocheng, T.: Adaptive fuzzy control design for stochastic nonlinear switched systems with arbitrary switchings and unmodeled dynamics (2016). doi: 10.1109/TCYB.2016.2518300
  39. 39.
    Li, Y., Tong, S.: Adaptive fuzzy output-feedback stabilization control for a class of switched nonstrict-feedback nonlinear systems (2016). doi: 10.1109/TCYB.2016.2536628
  40. 40.
    Hongyi, L., Jiahui, W., Peng, S.: Output-feedback based sliding mode control for fuzzy systems with actuator saturation (2015). doi: 10.1109/TFUZZ.2015.2513085
  41. 41.
    Hongyi, L., Yabin, G., Peng, S., Hak-Keung, L.: Observer-based fault detection for nonlinear systems with sensor fault and limited communication capacity (2015). doi: 10.1109/TAC.2015.2503566
  42. 42.
    Yongping, P., Meng, J., Daoping, H., Qinruo, W.: Fire-rule-based direct adaptive type-2 fuzzy H tracking control. Eng. Appl. Artif. Intell. 24, 1174–1185 (2011)CrossRefGoogle Scholar
  43. 43.
    Faa-Jeng, L., Po-Huan, C.: Adaptive control of two-axis motion control system using interval type-2 fuzzy neural network. IEEE Trans. Ind. Electron. 56, 178–193 (2009)CrossRefGoogle Scholar
  44. 44.
    Irem, U.S., Cengiz, K.: Interval type-2 fuzzy capital budgeting. Int. J. Fuzzy Syst. (2015). doi: 10.1007/s40815-015-0040-5 MathSciNetGoogle Scholar
  45. 45.
    Roopaei, M., Zolghadri, J.: Chattering-free fuzzy sliding mode control in MIMO uncertain system. Nonlinear Anal. Theory Methods Appl. 71, 4430–4437 (2009)MathSciNetCrossRefMATHGoogle Scholar
  46. 46.
    Hongyi, L., Yingnan, P., Peng, S.: Switched fuzzy output feedback control and its application to mass-spring-damping system (2015). doi: 10.1109/TFUZZ.2015.2505332
  47. 47.
    Hongyi, L., Jiahui, W., Hak-Keung, L., Qi, Z., Haiping, D.: Adaptive sliding mode control for interval type-2 fuzzy systems (2016). doi: 10.1109/TSMC.2016.2531676
  48. 48.
    Kheireddine, C., Lamir, S., Mouna, G., Khier, B.: Indirect adaptive interval type-2 fuzzy control for nonlinear systems. Int. J. Model. Identif. Control 2, 106–119 (2007)CrossRefMATHGoogle Scholar
  49. 49.
    Tao, C.W., Chang, C.W., Taur, J.S.: A simplify type reduction for interval type-2 fuzzy sliding controllers. Int. J. Fuzzy Syst. 15, 460–470 (2013)Google Scholar
  50. 50.
    Wang, L., Liu, Z., Zhang, Y., Chan, C.L.P., Chen, X.: Type-2 fuzzy logic controller using SRUKF-based state estimations for biped walking robots. Int. J. Fuzzy Syst. 15, 423–434 (2013)MathSciNetGoogle Scholar
  51. 51.
    Meng-Tzu, H., Ching-Hung, L., Chin-Min, L.: Type-2 fuzzy cerebellar model articulation controller-based learning rate adjustment for blind source separation. Int. J. Fuzzy Syst. 16, 411–421 (2014)Google Scholar
  52. 52.
    Castillo, O., Melin, P.: A review on the design and optimization of interval type-2 fuzzy controllers. Appl. Soft Comput. 12, 1267–1278 (2012)CrossRefGoogle Scholar
  53. 53.
    Lu, X.-G., Liu, M., Liu, J.-X.: Design and optimization of interval type-2 fuzzy logic controller for delta parallel robot trajectory control. Int. J. Fuzzy Syst. (2016). doi: 10.1007/s40815-015-0131-3 Google Scholar
  54. 54.
    Jafar, T., Amir, A.S., Mohammad, B.M.: Stability analysis of a class of MIMO recurrent type-2 fuzzy systems. Int. J. Fuzzy Syst. (2016). doi: 10.1007/s40815-016-0188-7 Google Scholar
  55. 55.
    Castillo, O., Melin, P.: Type-2 Fuzzy Logic: Theory and Applications. Studies in Fuzziness and Soft Computing, vol. 223. Springer, Berlin (2008)Google Scholar

Copyright information

© Taiwan Fuzzy Systems Association and Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Samir Zeghlache
    • 1
  • Tarak Benslimane
    • 1
  • Nourredine Amardjia
    • 2
    • 3
  • Abderrahmen Bouguerra
    • 1
  1. 1.LASS Laboratory, Department of Electrical Engineering, Faculty of TechnologyUniversity of MSilaIchbiliaAlgeria
  2. 2.Department of Electronics, Faculty of TechnologyUniversity Ferhat AbbasSétifAlgeria
  3. 3.LIS LaboratoryUniversity Ferhat AbbasSétifAlgeria

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