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Integral Sliding Mode based Control for Quadrotors with Disturbances: Simulations and Experiments

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  • Control Theory and Applications
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Abstract

This work proposes a compound control which combines backstepping control and integral sliding mode (ISM) idea. The backstepping framework is adopted to guarantee nominal performance of the closed-loop system, while the use of ISM is to eliminate the adverse effect of perturbations such that nominal performance is recovered. To avoid the chattering problem of ISM control, novel multivariable super-twisting algorithm is introduced to attenuate this phenomenon. Furthermore, the proposed control law is applied to tackle trajectory tracking problem of quadrotors subjected to parameter uncertainties and external perturbations. To avoid the singularity of rotation dynamics, quaternion-based control is applied in attitude controller design. A rigorous proof for stability of the closed-loop system is derived by the Lyapunov theory. Finally, several comparative simulations and experimental results demonstrate the effectiveness and superiority of the proposed method.

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References

  1. Q. Quan, Introduction to Multicopter Design and Control, Springer, Singapore, 2017.

    Book  Google Scholar 

  2. R. Mahony, V. Kumar, and P. Corke, “Multirotor aerial vehicles: modeling, estimation, and control of quadrotor,” IEEE Robot. Autom. Mag., vol. 19, no. 3, pp. 20–32, September 2012.

    Article  Google Scholar 

  3. H. Lee and H. J. Kim, “Trajectory tracking control of multirotors from modelling to experiments: a survey,” Int. J. Control Autom. Syst., vol. 15, no. 1, pp. 281–292, 2017.

    Article  Google Scholar 

  4. S. Omari, M. D. Hua, G. Ducard, and G. Hamel, “Hardware and software architecture for nonlinear control of multirotor helicopters,” IEEE/ASME Trans. Mechatronics, vol. 18, no. 6, pp. 1724–1736, December 2013.

    Article  Google Scholar 

  5. R. Garcia, F. R. Rubio, and M. G. Ortega, “Robust PID control of the quadrotor helicopte,” Proc. of 2nd IFAC Conf. Adv. PID Control, pp. 229–234, October 2012.

  6. S. Bouabdallah, A. Noth, and R. Siegwart, “PID vs LQ control techniques applied to an indoor micro quadrotor,” Proc. of IEEE/RSJ Int. Conf. Intell. Robots Syst., pp. 2451–2456, September 2004.

  7. G. V. Raffo, M. G. Ortega, and F. R. Rubio, “An underactuated H ∞ control strategy for a QuadRotor helicopter,” Proc. Eur. Control Conf., pp. 3845–3850, 2009.

  8. A. Das, K. Subbarao, and F. Lewis, “Dynamic inversion with zero-dynamics stabilisation for quadrotor control,” IET Contr. Theory Appl., vol. 3, no. 3, pp. 303–314, 2009.

    Article  MathSciNet  Google Scholar 

  9. T. Madani and A. Benallegue, “Backstepping control for a quadrotor helicopter,” Proc. of IEEE/RSJ Int. Conf. Intell. Robots Syst, pp. 3255–3260, October 2006.

  10. Z. Zuo, “Trajectory tracking control design with command-filtered compensation for a quadrotor,” Int. J. Robust Nonlinear Control, vol. 4, no. 11, pp. 2343–2355, 2010.

    MathSciNet  Google Scholar 

  11. W. Jasim, D. B. Gu, and F. R. Rubio, “Integral backstepping controller for quadrotor path tracking,” Proc. Int. Conf. Adv. Robot., 2015.

    Google Scholar 

  12. M. Basri, “Trajectory tracking control of autonomous quadrotor helicopter using robust neural adaptive backstepping approach,” J Aerospace Eng., vol. 21, no. 2, 2018.

  13. Y. Zou and Z. Y. Meng, “Immersion and invariance-based adaptive controller for quadrotor systems,” IEEE Trans. Syst., Man, Cybern.: Syst., 2018. DOI: https://doi.org/10.1109/TSMC.2018.2790929

  14. R. Wang and J. K. Liu, “Trajectory tracking control of a 6-DOF quadrotor UAV with input saturation via backstepping,” J. Franklin Inst., vol. 355, no. 7, pp. 3288–3309, 2018.

    Article  MathSciNet  MATH  Google Scholar 

  15. S. Bertrand, N. Guénard, T. Hamel, H. Piet-Lahanier, and L. Eck, “A hierarchical controller for miniature VTOL UAVs: Design and stability analysis using singular perturbation theory,” Control Eng. Pract., vol. 19, no. 10, pp. 1099–1108, 2011.

    Article  Google Scholar 

  16. K. Alexis, G. Nikolakopoulos, and A. Tzes, “Switching model predictive attitude control for a quadrotor helicopter subject to atmospheric disturbances,” Control Eng. Pract., vol. 19, no. 10, pp. 1195–1207, 2011.

    Article  Google Scholar 

  17. B. Zhao, B. Xian, Y. Zhang, and X. Zhang, “Switching model predictive attitude control for a quadrotor helicopter subject to atmospheric disturbances,” Int. J. Robust Nonlinear Control, vol. 25, no. 18, pp. 3714–3731, 2016.

    Article  Google Scholar 

  18. S. Islam, P. X. Liu, and A E. Saddik, “Nonlinear robust adaptive sliding mode control design for miniature unmanned multirotor aerial vehicle,” Int. J. Control Autom. Syst., vol. 15, no. 10, pp. 1–8, 2017.

    Google Scholar 

  19. H. K. Khalil, Noninear Systems, Prentice-Hall, New Jersey, 1996.

    Google Scholar 

  20. G. Antonelli, E. Cataldi, F. Arrichiello, P. R. Giodano, S. Chiaverini, and A, Franchi, “Adaptive trajectory tracking for quadrotor MAVs in presence of parameter uncertainties and external disturbances,” IEEE Trans. Control Syst. Technol., vol. 26, no. 1, pp. 248–254, January 2018.

    Article  Google Scholar 

  21. T. Madani and A. Benallegue, “Backstepping sliding mode control applied to a miniature quadrotor flying robot,” Proc. Ind. Electron. 2006-32nd Annual Conf., pp. 700–705, 2006.

  22. X. Xie, D. Yue, H. Zhang, and Y. Xue, “Fault estimation observer design for discrete-time takagi-sugeno fuzzy systems based on homogenous polynomially parameter-dependent Lyapunov functions,” IEEE Trans. Cybern., vol. 47, no. 9, pp. 2504–2513, 2017.

    Article  Google Scholar 

  23. Y. Huang and W. C. Xue, “Backstepping sliding mode control applied to a miniature quadrotor flying robot,” ISA Trans., vol. 53, no. 4, pp. 963–976, 2014.

    Article  MathSciNet  Google Scholar 

  24. A. Aboudonia, A. El-Badawy, and R. Rashad, “Active anti-disturbance control of a quadrotor unmanned aerial vehicle using the command-filtering backstepping approach,” Nonlinear Dyn., vol. 90, no. 1, pp. 1–17, October 2017.

    Article  MATH  Google Scholar 

  25. W. H. Chen, J. Yang, L. Guo, and S. H. Li, “Disturbance-observer-based control and related methods-An overview,” IEEE Trans. Ind. Electron., vol. 63, no. 2, pp. 1083–1095, 2016.

    Article  Google Scholar 

  26. X. L. Shao, J. Liu, H. L. Cao, C, Shen, and H. Wang, “Robust dynamic surface trajectory tracking control for a quadrotor UAV via extended state observer,” Int. J. Robust Nonlinear Control, vol. 28, no. 7, pp. 2700–2719, May 2018.

    Article  MathSciNet  MATH  Google Scholar 

  27. W. J. Cao and J. X. Xu, “Nonlinear integral-type sliding surface for both matched and unmatched uncertain systems,” IEEE Trans. Autom. Control, vol. 49, no. 8, pp. 1355–1360, 2004.

    Article  MathSciNet  MATH  Google Scholar 

  28. F. Casta and L. Fridman, “Analysis and design of integral sliding manifolds for systems with unmatched perturbations,” IEEE Trans. Autom. Control, vol. 51, no. 5, pp. 853–858, 2006.

    Article  MathSciNet  MATH  Google Scholar 

  29. M. Rubagotti, A. Estrada, F. Castanos, A. Ferrara, and L. Fridman, etc., “Integral sliding mode control for nonlinear systems with matched and unmatched perturbations,” IEEE Trans. Autom. Control, vol. 56, no. 11, pp. 2699–2704, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  30. A. Levant, “A multivariable super-twisting sliding mode approach,” Automatica, vol. 50, no. 3, pp. 984–988, 2014.

    Article  MathSciNet  MATH  Google Scholar 

  31. B. L. Tian, L. H. Liu, H. C. Lu, Z. Zio, Q. Zong, and Y. Zhang, “Multivariable Finite Time Attitude Control for Quadrotor UAV: Theory and Experimentation,” IEEE Trans. Ind. Electron., vol. 65, no. 3, pp. 2567–2577, March 2018.

    Article  Google Scholar 

  32. C. G. Mayhew, R. G. Sanfelice, and A. R. Teel, “Quaternion-based hybrid control for robust global attitude tracking,” IEEE Trans. Autom. Control, vol. 56, no. 11, pp. 2555–2566, November 2011.

    Article  MathSciNet  MATH  Google Scholar 

  33. J. Gadewadikar, F. Lewis, K. Subbarao, and B. M. Chen, “Structured H-infinity command and control-loop design for unmanned helicopters,” J. Guid. Control Dyn., vol. 31, no. 4, pp. 1093–1102, 2008.

    Article  Google Scholar 

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Authors and Affiliations

  1. Beijing Key Laboratory of UAV Autonomous Control, Beijing Institute of Technology, Beijing, 10081, China

    Tao Jiang, Tao Song & Defu Lin

Authors
  1. Tao Jiang
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  2. Tao Song
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  3. Defu Lin
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Corresponding author

Correspondence to Tao Jiang.

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Recommended by Associate Editor Juhoon Back under the direction of Editor Chan Gook Park.

Tao Jiang received the B.S. degree from Beijing Institute of Technology, Beijing, China, in 2014. He is currently working toward a Ph.D. degree in the Institute of UAV Autonomous Control, Beijing Institute of Technology, Beijing, China. His main research interests include robust and nonlinear control of unmanned aircraft vehicles, and development of robotic control systems.

Tao Song is the associate professor in the Institute of UAV Autonomous Control, Beijing Institute of Technology, Beijing, China. He focuses on flight system identification in the frequency domain. He finished his Post-doctoral research in the Institute of Flight System Dynamic, Technical University of Munich in April, 2016. He holds a doctor degree from school of aerospace engineering, Beijing Institute of Technology.

Defu Lin is the professor of flight vehicle design in Beijing Institute of Technology. He focuses on overall design of fixed-wing and rotor-wing flight vehicles. He is the head of the Institute of UAV Autonomous Control and the director of Beijing key laboratory of UAV Autonomous Control. He got his doctor degree in school of aerospace engineering, Beijing Institute of Technology in 2004.

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Jiang, T., Song, T. & Lin, D. Integral Sliding Mode based Control for Quadrotors with Disturbances: Simulations and Experiments. Int. J. Control Autom. Syst. 17, 1987–1998 (2019). https://doi.org/10.1007/s12555-018-0500-4

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  • DOI: https://doi.org/10.1007/s12555-018-0500-4

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