Skip to main content
Springer Nature Link
Log in

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

  • Published:
International Journal of Fuzzy Systems Aims and scope Submit manuscript

Abstract

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.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  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)

  2. 3-DOF Helicopter experiment manual. Quanser Consulting, Canada (1998). http://www.lehigh.edu/~inconsy/lab/experiments/QUANSER-3DOFHelicopter_Reference_Manual.pdf

  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)

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  10. Xiafu, W., Geng, L., Yisheng, Z.: Robust H ∞ attitude control of a laboratory helicopter. Robot. Auton. Syst. 61, 1247–1257 (2013)

    Article  Google Scholar 

  11. Utkin, V.I.: Sliding Modes in Control and Optimization. Springer, Berlin (2008)

    MATH  Google Scholar 

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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

    MathSciNet  Google Scholar 

  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)

  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. 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. 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)

  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. 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. 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. 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. 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)

    MathSciNet  MATH  Google Scholar 

  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)

  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. 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)

  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)

  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. 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)

  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)

  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)

    Article  MathSciNet  MATH  Google Scholar 

  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)

  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)

  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)

  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)

  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)

    Article  Google Scholar 

  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)

  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)

    Article  Google Scholar 

  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. 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. 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. 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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  44. Irem, U.S., Cengiz, K.: Interval type-2 fuzzy capital budgeting. Int. J. Fuzzy Syst. (2015). doi:10.1007/s40815-015-0040-5

    MathSciNet  Google Scholar 

  45. Roopaei, M., Zolghadri, J.: Chattering-free fuzzy sliding mode control in MIMO uncertain system. Nonlinear Anal. Theory Methods Appl. 71, 4430–4437 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  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. 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. 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)

    Article  MATH  Google Scholar 

  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. 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)

    MathSciNet  Google Scholar 

  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. Castillo, O., Melin, P.: A review on the design and optimization of interval type-2 fuzzy controllers. Appl. Soft Comput. 12, 1267–1278 (2012)

    Article  Google Scholar 

  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. 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. Castillo, O., Melin, P.: Type-2 Fuzzy Logic: Theory and Applications. Studies in Fuzziness and Soft Computing, vol. 223. Springer, Berlin (2008)

Download references

Author information

Authors and Affiliations

  1. LASS Laboratory, Department of Electrical Engineering, Faculty of Technology, University of MSila, BP 166, Ichbilia, Msila, Algeria

    Samir Zeghlache, Tarak Benslimane & Abderrahmen Bouguerra

  2. Department of Electronics, Faculty of Technology, University Ferhat Abbas, Sétif, Algeria

    Nourredine Amardjia

  3. LIS Laboratory, University Ferhat Abbas, Sétif, Algeria

    Nourredine Amardjia

Authors
  1. Samir Zeghlache
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Tarak Benslimane
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Nourredine Amardjia
    View author publications

    You can also search for this author inPubMed Google Scholar

  4. Abderrahmen Bouguerra
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Samir Zeghlache.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zeghlache, S., Benslimane, T., Amardjia, N. et al. Interval Type-2 Fuzzy Sliding Mode Controller Based on Nonlinear Observer for a 3-DOF Helicopter with Uncertainties. Int. J. Fuzzy Syst. 19, 1444–1463 (2017). https://doi.org/10.1007/s40815-016-0226-5

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40815-016-0226-5

Keywords