Skip to main content
Log in

Composite Anti-Disturbance Reference Model L2-\(L_{\infty }\) Control for Helicopter Slung Load System

  • Regular Paper
  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

This work considers the anti-disturbance model reference L2-\(L_{\infty }\) control for the helicopter slung load system subject to unknown disturbances. Initially, a linear model is derived based on the nonlinear dynamics of a helicopter with slung load. The uncertainty and disturbances are jointly considered in the controller design. Then, by designing a disturbance observer and using robust L2-\(L_{\infty }\) control method, the state feedback control and dynamic output feedback control are respectively analyzed, and two sufficient conditions on deriving the observer gain and controller one are presented via the linear matrix inequality (LMI) form, which can guarantee the helicopter slung load system to asymptotically track the reference model with L2-\(L_{\infty }\) performance. Finally, some simulation results are presented to show the effectiveness of the proposed methods.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Raptis, I.A., Valavanis, K.P.: Linear and nonlinear control of small-scale unmanned helicopters. Springer, Netherlands (2011)

    Book  Google Scholar 

  2. Isidori, A., Marconi, L., Serrani, A.: Robust nonlinear motion control of a helicopter. IEEE Trans. Autom. Control 48(3), 413–426 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  3. Marconi, L., Naldi, R.: Robust full degree-of-freedom tracking control of a helicopter. Automatica 43(11), 1909–1920 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  4. Yang, Y.D.: Helicopter flight control. National Defense Industry Press, Beijing (2007)

    Google Scholar 

  5. Raptis, I.A., Valavanis, K.P., Vachtsevanos, G.J.: Linear tracking control for small-scale unmanned helicopters. IEEE Trans. Control Syst. Technol. 20(4), 995–1010 (2012)

    Article  Google Scholar 

  6. Xian, B., Guo, J., Zhang, Y., Zhao, B.: Sliding mode tracking control for miniature unmanned helicopters. Chin. J. Aeronaut. 28(1), 277–284 (2015)

    Article  Google Scholar 

  7. Alvarenga, J., Vitzilaios, N.I., Valavanis, K.P., et al.: Survey of unmanned helicopter model-based navigation and control techniques. J. Intell. Robot. Sys. 80(1), 87–138 (2015)

    Article  Google Scholar 

  8. Zhong, Y., Zhang, W., Zhang, Y., et al.: Sensor fault detection and diagnosis for an unmanned quadrotor helicopter. J. Intell. Robot Sys 96(3-4), 555–572 (2019)

    Article  Google Scholar 

  9. Manwaring, J.C., Conway, G.A., Garrett, L.C.: Epidemiology and prevention of helicopter external load accidents. J. Safety Res. 29(2), 107–121 (1998)

    Article  Google Scholar 

  10. Shi, D., Wu, Z., Chou, W.: Harmonic extended state observer based anti-swing attitude control for quadrotor with slung load. Electronics 7(6), 1–18 (2018)

    Article  Google Scholar 

  11. Guglieri, G., Marguerettaz, P.: Dynamic stability of a helicopter with an external suspended load. J. Am. Helicopter Soc. 59(4), 1–12 (2014)

    Article  Google Scholar 

  12. Fusato, D., Guglieri, G., Celi, R.: Flight dynamics of an articulated rotor helicopter with an external slung load. J. Am. Helicopter Soc. 46(1), 3–14 (2001)

    Article  Google Scholar 

  13. Cao, Y., Qi, Q.: Trims, controllability, and flying qualities of a Tilt-Rotor aircraft slung-load system. J. Aero. Eng. 31(2), 06017006 (2017)

    Article  Google Scholar 

  14. Cao, Y., Wang, Z.: Equilibrium characteristics and stability analysis of helicopter slung-load system. J. Beijing Univ. Aeronaut. Astronaut. 40(9), 1219–1224 (2017)

    Google Scholar 

  15. Potter, J., Singhose, W.E., Costelloy, M.: Reducing swing of model helicopter sling load using input shaping. 9th IEEE International Conference on Control and Automation, pp 19–21 (2011)

  16. Thanapalan, K., Wong, T.M.: Modeing of a helicopter with an under-slung load system. Proceedings of the 29th Chinese Control Conference, pp 1451–1456 (2010)

  17. Thanapalan, K.: Nonlinear controller design for a helicopter with an external slung load system. Syst. Sci. Control Eng. 5(1), 97–107 (2017)

    Article  Google Scholar 

  18. Guerrero-Sánchez, M.E., Mercado-Ravell, D.A., Lozano, R., et al.: Swing-attenuation for a quadrotor transporting a cable-suspended payload. ISA Trans. 68, 433–449 (2017)

    Article  Google Scholar 

  19. Omar, H.M.: Designing anti-swing fuzzy controller for helicopter slung-load system near hover by particle swarms. Aerosp. Sci. Technol. 29(1), 223–234 (2013)

    Article  Google Scholar 

  20. El-Ferik, S., Syed, A.H., Omar, H.M., et al.: Nonlinear forward path tracking controller for helicopter with slung load. Aerosp. Sci. Technol. 69, 602–608 (2017)

    Article  Google Scholar 

  21. Klausen, K., Fossen, T.I., Johansen, T.A.: Nonlinear control with swing damping of a multirotor UAV with suspended load. J. Intell. Robot. Syst. 88(2-4), 379–394 (2017)

    Article  Google Scholar 

  22. Ren, Y., Chen, M.: Anti-swing control for a suspension cable system of a helicopter with cable swing constraint and unknown dead-zone. Neurocomputing 356, 257–267 (2019)

    Article  Google Scholar 

  23. Ren, Y., Chen, M., Liu, J.: Unilateral boundary control for a suspension cable system of a helicopter with horizontal motion. IET. Contr. Theory Appl. 13(4), 467–476 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  24. Ren, Y., Chen, M., Wu, Q.X.: Disturbance observer-based boundary control for a suspension cable system moving in the horizontal plane. Trans. Inst. Meas. Control 41(2), 340–349 (2019)

    Article  Google Scholar 

  25. Liu, S., Xiang, Z.: Exponential output tracking control for positive switched linear systems with time-varying delays. Nonlinear Anal. Hybrid Syst. 11, 118–128 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  26. Xie, J., Zhao, J.: Model reference adaptive control for switched LPV systems and its application. IET Contr. Theory Appl. 10(17), 2204–2212 (2016)

    Article  MathSciNet  Google Scholar 

  27. Chen, Y., Wei, Y., Liang, S., et al.: Indirect model reference adaptive control for a class of fractional order systems. Commun. Nonlinear Sci. Numer. Simul. 39, 458–471 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  28. Chen, M., Li, Y.: Model reference resilient control for the helicopter with time-varying disturbance. Int. J. Robust Nonlinear Control. 29, 5095–5117 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  29. Yu, L.: Robust Control Linear Matrix Inequality Processing Method. Tsinghua University Press, Beijing (2002)

    Google Scholar 

  30. Chen, M., Ge, S.S., How, B.V.E.: Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities. IEEE Trans. Neural Netw. 21(5), 796–812 (2010)

    Article  Google Scholar 

  31. Vafamand, N., Arefi, M.M., Khooban, M.H., et al.: Nonlinear model predictive speed control of electric vehicles represented by linear parameter varying models with bias terms. IEEE J. Emerg. Sel. Topics Power Electron. 7(3), 2081–2089 (2019)

    Article  Google Scholar 

  32. Vafamand, N., Rakhshan, M.: Dynamic model-based fuzzy controller for maximum power point tracking of photovoltaic systems: a linear matrix inequality approach. Dyn. Syst. Meas. Control. 139(5), 051010 (2017)

    Article  Google Scholar 

  33. Vafamand, N., Asemani, M.H., Khayatian, A., et al.: TS fuzzy robust L1 control for nonlinear systems with persistent bounded disturbances. J. Frankl. Inst 354(14), 5854–5876 (2017)

    Article  MATH  Google Scholar 

  34. Vafamand, N., Asemani, M.H., Khayatiyan, A., et al.: TS Fuzzy Model-Based Controller design for a class of nonlinear systems including nonsmooth functions. IEEE Trans. Syst. Man. Cybern. Syst. 50 (1), 233–243 (2020)

    Article  Google Scholar 

  35. Vafamand, N., Yousefizadeh, S., Khooban, M.H., et al.: Adaptive TS fuzzy-based MPC for DC microgrids with dynamic CPLs: nonlinear power observer approach. IEEE Syst. J. 13(3), 3203–3210 (2019)

    Article  Google Scholar 

  36. Chen, W.H.: Nonlinear disturbance observer-enhanced dynamic inversion control of missiles. J. Guid. Control Dyn. 26(1), 161–166 (2003)

    Article  Google Scholar 

  37. Chen, W.H.: Disturbance observer based control for nonlinear systems. IEEE/ASME Trans Mechatron. 9(4), 706–710 (2004)

    Article  Google Scholar 

  38. Sun, H., Li, S.: Composite control method for stabilizing spacecraft attitude in terms of Rodrigues parameters. Chin. J. Aeronaut. 26(3), 687–696 (2013)

    Article  Google Scholar 

  39. Chen, M., Chen, S.D., Wu, Q.X.: Sliding mode disturbance observer-based adaptive control for uncertain MIMO nonlinear systems with dead-zone. Int. J. Adapt. Control Signal Process. 31(7), 1003–1018 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  40. Smith, J., Su, J., Liu, C., Chen, W.H.: Disturbance observer based control with anti-windup applied to a small fixed wing uav for disturbance rejection. J. Intell. Robot. Sys. 88, 329–346 (2017)

    Article  Google Scholar 

  41. Chen, W.H., Ding, K., Lu, X.: Disturbance-observer-based control design for a class of uncertain systems with intermittent measurement. J. Frankl. Inst. 354(13), 5266–5279 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  42. Sun, H., Guo, L.: Neural network-based DOBC for a class of nonlinear systems with unmatched disturbances. IEEE Trans. Neural Netw. Learn. Syst. 28(2), 482–489 (2017)

    Article  MathSciNet  Google Scholar 

  43. Li, Y., Sun, H., Zong, G., Hou, L.: Anti-disturbance control for time-varying delay Markovian jump nonlinear systems with multiple disturbances. Int. J. Syst. Sci. 48(15), 3186–3200 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  44. Wei, X., Guo, L.: Composite disturbance-observer-based control and \(H_{\infty }\) control for complex continuous models. Int. J. Robust Nonlinear Control 20(1), 106–118 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  45. Wei, X., Chen, N., Li, W.: Composite adaptive disturbance observer-based control for a class of nonlinear systems with multisource disturbance. Int. J. Adapt. Control Signal Process. 27(3), 199–208 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  46. Zhang, R., Li, T., Guo, L.: Disturbance observer based \(H_{\infty }\) control for flexible spacecraft with time-varying input delay. Adv. Difference Equ. 2013(1), 1–12 (2013)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

This work was supported in part by the National Natural Science Foundation of China under Grant 61803207; in part by the Key R & D projects (Social Development) in Jiangsu Province of China under Grant BE2020704; in part by the Joint fund of China Electronics Technology for Equipment Preresearch 6141B08231110a; in part by Jiangsu Province “333” project under Grant BRA2019051.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mou Chen.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, L., Chen, M., Li, T. et al. Composite Anti-Disturbance Reference Model L2-\(L_{\infty }\) Control for Helicopter Slung Load System. J Intell Robot Syst 102, 15 (2021). https://doi.org/10.1007/s10846-020-01276-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-020-01276-z

Keywords

Navigation