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Adaptive fuzzy global sliding mode control for trajectory tracking of quadrotor UAVs

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Abstract

In this paper, an adaptive fuzzy-based global sliding mode control strategy is proposed for quadrotor unmanned aerial vehicles (UAVs) in robust trajectory tracking against parameter uncertainties and external disturbances. Compared with the conventional sliding mode control, the reaching phase and the control chattering are eliminated in the control scheme, and requirements of the upper bound of the uncertainties are removed. More specifically, in order to counteract the disturbances, the fuzzy system with multiple-input variables and continuous membership functions is adopted rather than the switching term, which softens the control signals greatly. Besides, the use of specific singletons membership functions for the multiple-output fuzzy sets simplifies the defuzzification and reduces the computation burden significantly. Additionally, an adaptive tuner is employed, and the optimal control efforts can be achieved. Finally, comparative flight performances under different controllers for the quadrotor UAVs are demonstrated to verify the effectiveness and superiority of the proposed control approach.

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References

  1. Abdollahi, T., Salehfard, S., Xiong, C., Ying, J.: Simplified fuzzy-Padé controller for attitude control of quadrotor helicopters. IET Control Theory Appl. 12(2), 310–317 (2018)

    Article  MathSciNet  Google Scholar 

  2. Zhu, W., Du, H., Cheng, Y., Cheng, Y., Chu, Z.: Hovering control for quadrotor aircraft based on finite-time control algorithm. Nonlinear Dyn. 88(4), 2359–2369 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  3. Cabecinhas, D., Naldi, R., Silvestre, C., Cunha, R., Marconi, L.: Robust landing and sliding maneuver hybrid controller for a quadrotor vehicle. IEEE Trans. Control Syst. Technol. 24(2), 400–412 (2016)

    Article  Google Scholar 

  4. Liang, X., Fang, Y., Sun, N., Lin, H.: Nonlinear hierarchical control for unmanned quadrotor transportation systems. IEEE Trans. Ind. Electron. 65(4), 3395–3405 (2018)

    Article  Google Scholar 

  5. Nguyen, H., Ha, C., Lee, D.: Mechanics, control and internal dynamics of quadrotor tool operation. Automatica 61(C), 289–301 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  6. Tofigh, M., Mahjoob, M., Ayati, M.: Dynamic modeling and nonlinear tracking control of a novel modified quadrotor Int. J. Robust Nonlinear Control 28, 552–567 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zou, Y., Zhu, B.: Adaptive trajectory tracking controller for quadrotor systems subject to parametric uncertainties. J. Frankl. Inst. Eng. Appl. Math. 355(15), 6724–6746 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  8. Sanz, R., García, P., Zhong, Q., Albertos, P.: Predictor-based control of a class of time-delay systems and its application to quadrotors. IEEE Trans. Ind. Electron. 64(1), 459–469 (2016)

    Article  Google Scholar 

  9. Li, S., Wang, Y., Tan, J.: Adaptive and robust control of quadrotor aircrafts with input saturation. Nonlinear Dyn. 89(1), 255–265 (2017)

    Article  MATH  Google Scholar 

  10. Zhao, B., Xian, B., Zhang, Y., Zhang, X.: Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology. IEEE Trans. Ind. Electron. 62(5), 2891–2902 (2015)

    Article  Google Scholar 

  11. Rinaldi, F., Chiesa, S., Quagliotti, F.: Linear quadratic control for quadrotors UAVs dynamics and formation flight. J. Intell. Robot. Syst. 70(1–4), 203–220 (2013)

    Article  Google Scholar 

  12. Islam, M., Okasha, M., Mohammad Idres, M.: Trajectory tracking in quadrotor platform by using PD controller and LQR control approach. In: IEEE International Conference on Information and Automation, pp. 1–8 (2017)

  13. Duc, M., Trong, T., Yang, S.: The quadrotor MAV system using PID control. In: IEEE International Conference on Mechatronics and Automation, pp. 506–510 (2015)

  14. Khatoon, S., Shahid, M., Ibraheem, Chaudhary, H.: Dynamic modeling and stabilization of quadrotor using PID controller. In: IEEE International Conference on Advances in Computing, Communications and Informatics, pp. 746–750 (2014)

  15. Wang, R., Liu, J.: Trajectory tracking control of a 6-DOF quadrotor UAV with input saturation via backstepping. J. Frankl. Inst. Eng. Appl. Math. 355(7), 3288–3309 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  16. Wei, Y., Li, C., Sun, Y., Ma, G.: Backstepping approach for controlling a quadrotor using Barrier Lyapunov Functions. In: Proceedings of the 36th Chinese Control Conference, pp. 6235–6239. IEEE (2017)

  17. Madani, T., Benallegue, A.: Sliding mode observer and backstepping control for a quadrotor unmanned aerial vehicles. In: American Control Conference, 2007. ACC’07, pp. 5887–5892. IEEE (2007)

  18. Chen, F., Jiang, R., Zhang, K., Jiang, B., Tao, G.: Robust backstepping sliding-mode control and observer-based fault estimation for a quadrotor UAV. IEEE Trans. Ind. Electron. 63(8), 5044–5056 (2016)

    Article  Google Scholar 

  19. Li, S., Wang, Y., Tan, J., Zheng, Y.: Adaptive RBFNNs/integral sliding mode control for a quadrotor aircraft. Neurocomputing 216(C), 126–134 (2016)

    Article  Google Scholar 

  20. Besnard, L., Shtessel, Y., Landrum, B.: Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer. J. Frankl. Inst. Eng. Appl. Math. 349(2), 658–684 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  21. Zhao, B., Xian, B., Zhang, Y., Zhang, X.: Nonlinear robust sliding mode control of a quadrotor unmanned aerial vehicle based on immersion and invariance method. Int. J. Robust Nonlinear Control 25(18), 3714–3731 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  22. Ma, D., Xia, Y., Shen, G., Jia, Z., Li, T.: Flatness-based adaptive sliding mode tracking control for a quadrotor with disturbances. J. Frankl. Inst. Eng. Appl. Math. 355(14), 6300–6322 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  23. Aboudonia, A., El-Badawy, A., Rashad, R.: Active anti-disturbance control of a quadrotor unmanned aerial vehicle using the command-filtering backstepping approach. Nonlinear Dyn. 90, 581–597 (2017)

    Article  MATH  Google Scholar 

  24. Yang, H., Cheng, L., Xia, Y., Yuan, Y.: Active disturbance rejection attitude control for a dual closed-loop quadrotor under gust wind. IEEE Trans. Control Syst. Technol. 26(4), 1400–1405 (2018)

    Article  Google Scholar 

  25. Castillo, A., Sanz, R., Garcia, P., Albertos, P.: A quaternion-based and active disturbance rejection attitude control for quadrotor. In: IEEE International Conference on Information and Automation, pp. 240–245 (2017)

  26. Aboudonia, A., Rashad, R., El-Badawy, A.: Composite hierarchical anti-disturbance control of a quadrotor UAV in the presence of matched and mismatched disturbances. J. Intell. Robot. Syst. 90, 201–216 (2018)

    Article  Google Scholar 

  27. Islam, S., Liu, P.X., El Saddik, A.: Robust control of four-rotor unmanned aerial vehicle with disturbance uncertainty. IEEE Trans. Ind. Electron. 62(3), 1563–1571 (2015)

    Article  Google Scholar 

  28. Wang, X., Shirinzadeh, B.: Nonlinear augmented observer design and application to quadrotor aircraft. Nonlinear Dyn. 80(3), 1463–1481 (2015)

    Article  MATH  Google Scholar 

  29. Kuo, C., Tsai, C.: Quaternion-based adaptive backstepping RFWNN control of quadrotors subject to model uncertainties and disturbances. Int. J. Fuzzy Syst. 20(6), 1745–1755 (2018)

    Article  MathSciNet  Google Scholar 

  30. Kayacan, E., Maslim, R.: Type-2 fuzzy logic trajectory tracking control of quadrotor VTOL aircraft with elliptic membership functions. IEEE-ASME Trans. Mechatron. 22(1), 339–348 (2017)

    Article  Google Scholar 

  31. Xian, B., Diao, C., Zhao, B., Zhang, Y.: Nonlinear robust output feedback tracking control of a quadrotor UAV using quaternion representation. Nonlinear Dyn. 79(4), 2735–2752 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  32. Alsmadi, Y., Utkin, V., Hajahmed, M., Xu, L., Abdelaziz, A.: Sliding-mode control of power converters: AC/DC converters & DC/AC inverters. Int. J. Control 91(11), 2573–2587 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  33. Sunila, M., Sankaranarayanan, V., Sundereswaran, K.: Optimised sliding mode control for MIMO uncertain non-linear system with mismatched disturbances. Electron. Lett. 54(5), 290–291 (2018)

    Article  Google Scholar 

  34. Singh, S., Janardhanan, S.: Sliding mode control-based linear functional observers for discrete-time stochastic systems. Int. J. Syst. Sci. 48(2), 1–8 (2017)

    MathSciNet  MATH  Google Scholar 

  35. Zheng, B., Yu, X., Xue, Y.: Quantized feedback sliding-mode control: an event-triggered approach. Automatica 91(5), 126–135 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  36. Liu, J.K., Wang, X.H.: Advanced Sliding Mode Control for Mechanical Systems: Design, Analysis and MATLAB Simulation. Springer, Berlin (2012)

    MATH  Google Scholar 

  37. Mobayen, S.: Design of novel adaptive sliding mode controller for perturbed chameleon hidden chaotic flow. Nonlinear Dyn. 92, 1539–1553 (2018)

    Article  MATH  Google Scholar 

  38. Liu, L., Han, Z., Li, W.: Global sliding mode control and application in chaotic systems. Nonlinear Dyn. 56, 193–198 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  39. Mobayen, S.: An adaptive fast terminal sliding mode control combined with global sliding mode scheme for tracking control of uncertain nonlinear third-order systems. Nonlinear Dyn. 82(1), 1–12 (2015)

    MathSciNet  MATH  Google Scholar 

  40. L’Afflitto, A., Anderson, R.B., Mohammadi, K.: An introduction to nonlinear robust control for unmanned quadrotor aircraft: how to design control algorithms for quadrotors using sliding mode control and adaptive control techniques. IEEE Control Syst. Mag. 38(3), 102–121 (2018)

    Article  MathSciNet  Google Scholar 

  41. Bouabdallah, S., Siegwart, R.: Backstepping and sliding-mode techniques applied to an indoor micro quadrotor. In: Proceedings of IEEE International Conference on Robotics and Automation, pp. 2247–2252 (2005)

  42. Shaik, M.K., Whidborne, J.F.: Robust sliding mode control of a quadrotor. In: Proceedings of IEEE International Conference on Control, pp. 1–20 (2016)

  43. Du, H., Yu, X., Chen, M.Z.Q., Li, S.: Chattering-free discrete-time sliding mode control. Automatica 68, 87–91 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  44. Rezkallah, M., Hamadi, A., Chandra, A., Singh, B.: Design and implementation of active power control with improved P&O method for Wind-PV-Battery based standalone generation system. IEEE Trans. Ind. Electron. 65(7), 5590–5600 (2018)

    Article  Google Scholar 

  45. Derbel, N., Ghommam, J., Zhu, Q.: Applications of Sliding Mode Control. Springer, Singapore (2017)

    Book  Google Scholar 

  46. Ma, C., Chen, M., Lam, J., Cheung, K.: A novel body frame based approach to aerospacecraft attitude tracking. ISA Trans. 70, 228–237 (2017)

    Article  Google Scholar 

  47. Shi, S., Xu, S., Zhang, B., Ma, Q., Zhang, Z.: Global second-order sliding mode control for nonlinear uncertain systems. Int. J. Robust Nonlinear Control 29, 224–237 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  48. Guo, J., Lu, R., Yao, D., Zhou, Q.: Implementation of the load frequency control by two approaches: variable gain super-twisting algorithm and super-twisting-like algorithm. Nonlinear Dyn. 93, 1073–1086 (2018)

    Article  MATH  Google Scholar 

  49. Espinoza, E., Espinoza, E., Lozano, R.: Second order sliding mode controllers for altitude control of a quadrotor UAS. Neurocomputing 233(C), 61–71 (2017)

    Google Scholar 

  50. Mojallizadeh, M., Badamchizadeh, M.: Second-order fuzzy sliding-mode control of photovoltaic power generation systems. Sol. Energy 149, 332–340 (2017)

    Article  Google Scholar 

  51. Derafa, L., Benallegue, A., Fridman, L.: Super twisting control algorithm for the attitude tracking of a four rotors UAV. J. Frankl. Inst. Eng. Appl. Math. 349(2), 685–699 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  52. Zheng, E.H., Xiong, J.J., Luo, J.L.: Second order sliding mode control for a quadrotor UAV. ISA Trans. 53(4), 1350–1356 (2014)

    Article  Google Scholar 

  53. Filiberto, M., Espinoza, E.S., González-Hernández, I., Sergio, S., Rogelio, L.: Robust trajectory tracking for unmanned aircraft systems using a nonsingular terminal modified super-twisting sliding mode controller. J. Intell. Robot. Syst. 93(1–2), 55–72 (2019)

    Google Scholar 

  54. Xiong, J.J., Zhang, G.B.: Global fast dynamic terminal sliding mode control for a quadrotor UAV. ISA Trans. 66, 233–240 (2017)

    Article  Google Scholar 

  55. Mo, H., Farid, G.: Nonlinear and adaptive intelligent control techniques for quadrotor UAV—a survey. Asian J. Control 21(3), 1–20 (2019)

    MathSciNet  MATH  Google Scholar 

  56. Mohsen, V., Mahdi, K.: Adaptive fractional order sliding mode control for a quadrotor with a varying load. Aerosp. Sci. Technol. 86, 737–747 (2019)

    Article  Google Scholar 

  57. Mofid, O., Mobayen, S.: Adaptive sliding mode control for finite-time stability of quad-rotor UAVs with parametric uncertainties. ISA Trans. 72, 1–14 (2018)

    Article  Google Scholar 

  58. Hua, C., Wang, K., Chen, J., You, X.: Tracking differentiator and extended state observer-based nonsingular fast terminal sliding mode attitude control for a quadrotor. Nonlinear Dyn. 94(1), 343–354 (2018)

    Article  Google Scholar 

  59. Ha, Q., Nguyen, Q., Rye, D., Durrant-Whyte, H.: Fuzzy sliding-mode controllers with applications. IEEE Trans. Ind. Electron. 48(1), 38–46 (2001)

    Article  Google Scholar 

  60. Tang, Y., Zhang, H., Gong, J.: Adaptive-fuzzy sliding-mode control for the attitude system of a quadrotor. In: Chinese Automation Congress, pp. 1075–1079 (2015)

  61. Abdelhameed, M.: Enhancement of sliding mode controller by fuzzy logic with application to robotic manipulators. Mechatronics 15(4), 439–458 (2005)

    Article  Google Scholar 

  62. Niu, Y., Wang, X.: A novel adaptive fuzzy sliding-mode controller for uncertain chaotic systems. Nonlinear Dyn. 73(3), 1201–1209 (2013)

    Article  MathSciNet  Google Scholar 

  63. Yang, Y., Yan, Y.: Attitude regulation for unmanned quadrotors using adaptive fuzzy gain-scheduling sliding mode control. Aerosp. Sci. Technol. 54, 208–217 (2016)

    Article  Google Scholar 

  64. Wang, J., Wang, X., Wang, J.: Trajectory tracking controller design for a quadrotor aircraft based on fuzzy sliding-mode control. In: Proceedings of the 36th Chinese Control Conference, pp. 1354–1358 (2017)

  65. Raharja, N.M., Wahyunggoro, O., Cahyadi, A.I.: Altitude control for quadrotor with mamdani fuzzy model. In: Proceedings of IEEE International Conference on Science in Information Technology, pp. 309–314 (2015)

  66. Salehfard, S., Abdollahi, T., Xiong, C., Ai, Y.: An optimized fuzzy-Padé controller applied to attitude stabilization of a quadrotor. Int. J. Control Autom. Syst. 16(3), 1425–1434 (2018)

    Article  Google Scholar 

  67. Du, H., Zhu, W., Wen, G., Wu, D.: Finite-time formation control for a group of quadrotor aircraft. Aerosp. Sci. Technol. 69, 609–616 (2017)

    Article  Google Scholar 

  68. Du, H., Qian, C., Yang, S., Li, S.: Recursive design of finite-time convergent observers for a class of time-varying nonlinear systems. Automatica 49(2), 601–609 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  69. Du, H., Li, S.: Attitude synchronization for flexible spacecraft with communication delays. IEEE Trans. Autom. Control 61(11), 3625–3630 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  70. Deng, C., Yang, G.H.: Distributed adaptive fault-tolerant control approach to cooperative output regulation for linear multi-agent systems. Automatica 103, 62–68 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  71. Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice-Hall, Upper Saddle River (1991)

    MATH  Google Scholar 

  72. Deng, C., Yang, G.: Distributed adaptive fault-tolerant containment control for a class of multi-agent systems with non-identical matching non-linear functions. IET Contr. Theory Appl. 10(3), 273–281 (2016)

    Article  MathSciNet  Google Scholar 

  73. Lee, D., Kim, H.J., Sastry, S.: Feedback linearization vs. adaptive sliding mode control for a quadrotor helicopter. Int. J. Control Autom. Syst. 7(3), 419–428 (2009)

    Article  Google Scholar 

  74. Zhang, Y., Chen, Z., Zhang, X., Sun, Q., Sun, M.: A novel control scheme for quadrotor UAV based upon active disturbance rejection control. Aerosp. Sci. Technol. 79, 601–609 (2018)

    Article  Google Scholar 

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Acknowledgements

This project is supported by National Natural Science Foundation of China (Grant Nos. 51475084, 51875093, 61603081 and U1708257) and Fundamental Research Funds for the Central Universities of China (Grant No. N160306004). The authors would also like to thank the reviewers and the editors a lot for their precious comments and professional suggestions that helped to improve the paper significantly.

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Zhang, J., Ren, Z., Deng, C. et al. Adaptive fuzzy global sliding mode control for trajectory tracking of quadrotor UAVs. Nonlinear Dyn 97, 609–627 (2019). https://doi.org/10.1007/s11071-019-05002-9

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