International Journal of Fuzzy Systems

, Volume 19, Issue 4, pp 1227–1237 | Cite as

A Systematic Approach to Fuzzy-model-based Robust \(H_\infty\) Control Design for a Quadrotor UAV Under Imperfect Premise Matching

Article
First Online:
Received:
Revised:
Accepted:

Abstract

In this paper, a systematic procedure to design a robust \(H_\infty\) controller for a quadrotor unmanned aerial vehicle is proposed. To do this, the nonlinear dynamic behavior of the quadrotor attitude system is represented as the Takagi–Sugeno (T–S) fuzzy model. Using the derived T–S fuzzy model, a sufficient condition guaranteeing the asymptotic stability and \(H_\infty\) disturbance attenuation performance is proposed based on an linear matrix inequality. Unlike the previous studies employing the parallel-distributed-compensation concept, in this paper, the robust \(H_\infty\) controller is designed under the imperfect premise matching condition in which the fuzzy controller uses the different membership functions from those of the fuzzy system. Thus, compared to the conventional methods, the hardware implementation cost of the proposed fuzzy controller is decreased even if the membership functions of the fuzzy system are complicated. Finally, some numerical examples are given to show the effectiveness of the proposed method.

Keywords

Takagi–Sugeno fuzzy system Quadrotor Disturbance attenuation \(H_\infty\) control 
This is a preview of subscription content, log in to check access.

Notes

Acknowledgments

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2015R1A2A2A05001610) and by the D2 Innovation funded by the Agency for Defense Development, Grant No. UC150001ID.

References

  1. 1.
    Yoo, D.W., Oh, H.D., Won, D.Y., Tahk, M.J.: Dynamic modeling and stabilization techniques for tri-rotor unmanned aerial vehicles. Int. J. Aeronaut. Space Sci. 11(3), 167–174 (2010)Google Scholar
  2. 2.
    Romero, H., Salazar, S., Lozano, R.: Real-time stabilization of an eight-rotor UAV using optical flow. IEEE Trans. Robot. 25(4), 809–817 (2009)CrossRefGoogle Scholar
  3. 3.
    Choi, Y.C., Ahn, H.S.: Nonlinear control of quadrotor for point tracking: actual implementation and experimental tests. IEEE Trans. Mechatron. 20(3), 1179–1192 (2015)CrossRefGoogle Scholar
  4. 4.
    Santana, L.V. Brandao, A.S. Filho, M.S., Carelli, R.: A trajectory tracking and 3d positioning controller for the ar.drone quadrotor. In: ICUAS’14, pp. 756–767 (2014)Google Scholar
  5. 5.
    Ji, Y., Yu, Y., Zhang, W., Sun, C.: Attitude control of a quadrotor unmanned aerial vehicle based on linear extended state observer. In: CCDC’15, pp. 1350–1355 (2015)Google Scholar
  6. 6.
    Ryan, T., Kim, H.J.: LMI-based gain synthesis for simple robust quadrotor control. IEEE Trans. Autom. Sci. Eng. 10(4), 1173–1178 (2013)CrossRefGoogle Scholar
  7. 7.
    Yacef, F., Bouhali, O., Khebbache, H., Boudjema, F.: Takagi-Sugeno model for quadrotor modelling and control using nonlinear state feedback controller. Int. J. Control Theory Comput. Model. 2(3), 9–24 (2012)CrossRefGoogle Scholar
  8. 8.
    Kushleyev, A., Mellinger, D., Powers, C., Kumar, V.: Towards a swarm of agile micro quadrotors. Auton. Robot 35(4), 287–300 (2013)CrossRefGoogle Scholar
  9. 9.
    Bouabdallah, S., Noth, A., Siegwart, R.: PID vs LQ control techniques applied to an imdoor micro quadrotor. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2451–2456 (2004)Google Scholar
  10. 10.
    Xu, R., Umit, O.: Sliding mode control of a quadrotor helicopter. In: CDC’06, pp. 4957–4962 (2006)Google Scholar
  11. 11.
    Su, S.F., Hsueh, Y.C., Tseng, C.P., Chen, S.S., Lin, Y.S.: Direct adaptive fuzzy sliding mode control for under-actuated uncertain systems. Int. J. Fuzzy Logic Intel. Syst. 15(4), 240–250 (2015)CrossRefGoogle Scholar
  12. 12.
    Nicol, C., Macnab, C.J.B., Ramirez, A.: Robust adaptive control of a quadrotor helicopter. Mechatronics 21(6), 927–938 (2011)CrossRefMATHGoogle Scholar
  13. 13.
    Bouabdallah, S., Siegwart, R.: Backstepping and sliding-mode techniques applied to an indoor micro quadrotor. In: ICRA’05, pp. 2247–2252 (2005)Google Scholar
  14. 14.
    Razinkova, A., Kang, B.J., Cho, H.C., Jeon, H.T.: Constant altitude flight control for quadrotor UAVs with dynamic feedforward compensation. Int. J. Fuzzy Logic Intel. Syst. 14(1), 26–33 (2014)CrossRefGoogle Scholar
  15. 15.
    Takagi, T., Sugeno, M.: Fuzzy identification of systems and its applications to modeling and control. IEEE Trans. Syst. Man Cybern. 15(1), 116–132 (1985)CrossRefMATHGoogle Scholar
  16. 16.
    Tanaka, K., Wang, H.O.: Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Wiley, New York (2001)CrossRefGoogle Scholar
  17. 17.
    Lee, D.H., Joo, Y.H., Tak, M.H.: LMI conditions for local stability and stabilization of continuous-time T–S fuzzy systems. Int. J. Control Autom. Syst. 13(4), 986–994 (2015)CrossRefGoogle Scholar
  18. 18.
    Wang, H.O., Tanaka, K., Griffin, M.F.: An approach to fuzzy control of nonlinear systems: stability and the design issues. IEEE. Trans. Fuzzy Syst. 4(1), 14–23 (1996)CrossRefGoogle Scholar
  19. 19.
    Lee, H.J., Park, J.B., Joo, Y.H.: Robust fuzzy control of nonlinear systems with parametric uncertainties. IEEE Trans. Fuzzy Syst. 9(2), 369–379 (2001)CrossRefGoogle Scholar
  20. 20.
    Kim, H.S., Park, J.B., Joo, Y.H.: Robust stabilization condition for a polynomial fuzzy system with parametric uncertainties. In: ICCAS, pp. 107–111 (2012)Google Scholar
  21. 21.
    Son, H.S., Park, J.B., Joo, Y.H.: Segmentalized FCM-based tracking algorithm for zigzag maneuvering target. Int. J. Control Autom. Syst. 13(1), 231–237 (2015)CrossRefGoogle Scholar
  22. 22.
    Tseng, C.S., Chen, B.S., Uang, H.J.: Fuzzy tracking control design for nonlinear dynamic systems via T–S fuzzy model. IEEE Trans. Fuzzy Syst. 9(3), 381–392 (2001)CrossRefGoogle Scholar
  23. 23.
    Tanaka, K., Ikeda, T., Wang, H.O.: Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs. IEEE Trans. Fuzzy Syst. 6(2), 250–265 (1998)CrossRefGoogle Scholar
  24. 24.
    Lee, D., Joo, Y.H., Ra, I.H.: Local stability and local stabilization of discrete-time T–S fuzzy systems with time-delay. Int. J. Control Autom. Syst. 14(1), 29–38 (2016)CrossRefGoogle Scholar
  25. 25.
    Cao, Y.Y., Frank, P.M.: Robust \(H_\infty\) disturbance attenuation for a class of uncertain discrete-time fuzzy systems. IEEE Trans. Fuzzy Syst. 8(4), 406–415 (2000)CrossRefGoogle Scholar
  26. 26.
    Hong, S.K., Langari, R.: An LMI-based \(H_\infty\) fuzzy control system design with TS framework. Inf. Sci. 123, 163–179 (2000)CrossRefMATHGoogle Scholar
  27. 27.
    Lee, D.H., Park, J.B., Joo, Y.H., Kim, S.K.: Local \(H_\infty\) controller design for continuous-time T–S fuzzy systems. Int. J. Control Autom. Syst. 13(6), 1499–1507 (2015)CrossRefGoogle Scholar
  28. 28.
    Lee, D.H., Park, J.B., Joo, Y.H., Lin, K.C., Ham, C.H.: Robust \(H_\infty\) control for uncertain nonlinear active magnetic bearing systems via Takagi-Sugeno fuzzy models. Int. J. Control Autom. Syst. 8(3), 636–646 (2010)CrossRefGoogle Scholar
  29. 29.
    Lam, H.K., Narimani, M.: Stability analysis and performance design for fuzzy-model-based control system under imperfect premise matching. IEEE Trans. Fuzzy Syst. 17(4), 949–961 (2009)CrossRefGoogle Scholar
  30. 30.
    Lfberg, J.: Yalmip: a toolbox for modeling and optimization in MATLAB. In: Proceedings of the CACSD’04, pp. 284–289 (2004)Google Scholar
  31. 31.
    Lee, D.H., Joo, Y.H.: LMI-based robust sampled-data stabilization of polytopic LTI systems: a truncated power series expansion approach. Int. J. Control Autom. Syst. 13(2), 284–291 (2015)CrossRefGoogle Scholar
  32. 32.
    Lee, D.H., Joo, Y.H., Kim, S.K.: \(H_\infty\) digital redesign for LTI systems. Int. J. Control Autom. Syst. 13(3), 603–610 (2015)CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  1. 1.School of Electrical and Electronic EngineeringYonsei UniversitySeoulKorea
  2. 2.Department of Control and Robotics EngineeringKunsan National UniversityGunsan-siKorea

Personalised recommendations