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Disturbance Observer-based LQR Tracking Control for Unmanned Autonomous Helicopter Slung-load System

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  • Control Theory and Applications
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Abstract

This work investigates the optimal tracking control for unmanned autonomous helicopter (UAH) slung-load system under external disturbance. Firstly, the linearized UAH slung-load system model is obtained by using the small perturbation linearization method, in which parameter uncertainty and disturbance are considered. Secondly, the control objective is described via a reference model, and the tracking controller is designed for the UAH slung-load system by using the reference model control approach, disturbance observer based-control (DOBC) scheme, and LQR control method. Thirdly, under the proposed tracking controller, the stability of the closed-loop system is analyzed on the basis of Lyapunov stability theory and linear matrix inequality (LMI) technique. Finally, some simulations and comparisons are presented to illustrate the proposed control method.

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References

  1. M. A. M. Basri, A. R. Husain, and K. A. Danapalasingam, “Robust chattering free backstepping sliding mode control strategy for autonomous quadrotor helicopter,” International Journal of Mechanical and Mechatronics Engineering, vol. 14, no. 3, pp. 36–44, 2014.

    Google Scholar 

  2. D. Fusato, G. Guglieri, and R. Celi, “Flight dynamics of an articulated rotor helicopter with an external slung-load,” Journal of the American Helicopter Society, vol. 46, no. 1, pp. 3–14, 2001.

    Article  Google Scholar 

  3. T. Oktay and C. Sultan, “Modeling and control of a helicopter slung-load system,” Aerospace science and technology, vol. 29, no. 1, pp. 206–222, 2013.

    Article  Google Scholar 

  4. J. J. Potter, C. J. Adams, and W. Singhose, “A planar experimental remote-controlled helicopter with a suspended load,” IEEE/ASME Transactions on Mechatronics, vol. 20, no. 5, pp. 2496–2503, 2015.

    Article  Google Scholar 

  5. S. El-Ferik, A. H. Syed, H. M. Omar, and M. A. Deriche, “Nonlinear forward path tracking controller for helicopter with slung-load,” Aerospace Science and Technology, vol. 69, pp. 602–608, 2017.

    Article  Google Scholar 

  6. Y. Ren, K. Li, and H. Ye, “Modeling and anti-swing control for a helicopter slung-load system,” Applied Mathematics and Computation, vol. 372, 124990, 2020.

    Article  MathSciNet  Google Scholar 

  7. Y. Cao, W. Nie, Z. Wang, and S. Wan, “Dynamic modeling of helicopter-slung-load system under the flexible sling hypothesis,” Aerospace Science and Technology, vol. 99, 105770, 2020.

    Article  Google Scholar 

  8. C. Adams, J. Potter, and W. Singhose, “Input-shaping and model-following control of a helicopter carrying a suspended load,” Journal of Guidance Control and Dynamics, vol. 38, no. 1, pp. 94–105, 2015.

    Article  Google Scholar 

  9. K. Thanapalan, “Nonlinear controller design for a helicopter with an external slung-load system,” Systems Science and Control Engineering, vol. 5, no. 1, pp. 97–107, 2017.

    Article  Google Scholar 

  10. C. David, C. Rita, and S. Carlos, “A trajectory tracking control law for a quadrotor with slung-load,” Automatica, vol. 106, pp. 384–389, 2019.

    Article  MathSciNet  Google Scholar 

  11. L. Liu, M. Chen, and T. Li, “Composite anti-disturbance reference model L2-L control for helicopter slung-load,” Jounal of Intelligent and Robotic Systems, vol. 102, no. 15, 2021.

  12. L. Liu, W.-H. Chen, and X. Lu, “Aperiodically intermittent H synchronization for a class of reaction diffusion neural networks,” Neurocomputing, vol. 222, pp. 105–115, 2017.

    Article  Google Scholar 

  13. S. Dong, W. Ren, Z-G. Wu, and H. Su “H output consensus for Markov jump multiagent systems with uncertainties,” IEEE Transactios on Cybernetics, vol. 50, no. 5, pp. 2264–2273, 2020.

    Article  Google Scholar 

  14. M. Chen, S. Ge, and B. How, “Robust adaptive neural network control for a class of uncertain MIMO nonlinear systems with input nonlinearities,” IEEE Transactions on Neural Networks, vol. 21, no. 5, pp. 796–812, 2010.

    Article  Google Scholar 

  15. W. H. Chen, “Disturbance observer-based control for nonlinear systems,” IEEE/ASME Transactions on Mechatronics, vol. 9, no. 4, pp. 706–710, 2004.

    Article  Google Scholar 

  16. W. H. Chen, J. Yang, and S. Li, “Disturbance observer-based control and related methods-an overview,” IEEE Transactions on Industrial Electronics, vol. 63, no. 2, pp. 1083–1095, 2016.

    Article  MathSciNet  Google Scholar 

  17. S. Qi, H. Wang, H.-N. Wu, and L. Guo, “Composite antidisturbance control for nonlinear systems via nonlinear disturbance observer and dissipative control,” International Journal of Robust and Nonlinear Control, vol. 29, no. 12, pp. 4056–4068, 2019.

    MathSciNet  MATH  Google Scholar 

  18. M. Chen, S. Xiong, and Q. Wu, “Tracking flight control of quadrotor based on disturbance observer,” IEEE Transactions on Systems, Man, and Cybernetics, vol. 51, no. 3, pp. 1414–1423, 2021.

    Article  Google Scholar 

  19. X. Wei, Z. Wu, and H. Karimi, “Disturbance observer-based disturbance attenuation control for a class of stochastic systems,” Automatica, vol. 63, no. 63, pp. 21–25, 2016.

    Article  MathSciNet  Google Scholar 

  20. T. Li, T. Wang, J. Zhai, and S. Fei, “Event-triggered observer-based robust H control for networked control systems with unknown disturbance,” International Journal of Robust and Nonlinear Control, vol. 30, pp. 2671–2688, 2020.

    Article  MathSciNet  Google Scholar 

  21. W. Ha and J. Back, “A disturbance observer-based robust tracking controller for uncertain robot manipulators,” International Journal of Control, Automation, and Systems, vol. 16, no. 2, pp. 417–425, 2018.

    Article  Google Scholar 

  22. J. Xu and Y. Niu, “Disturbance-observer-based LQR control of singularly perturbed systems via recursive decoupling methods,” International Journal of Systems Science, vol. 50, no. 4, pp. 764–776, 2019.

    Article  MathSciNet  Google Scholar 

  23. Z. Ding, “Output regulation of uncertain nonlinear systems with nonlinear exosystems,” IEEE Transactions on Automatic Control, vol. 51, no. 3, pp. 498–503, 2006.

    Article  MathSciNet  Google Scholar 

  24. Y. Ren, M. Chen, and Q. Wu, “Disturbance observer-based boundary control for a suspension cable system moving in the horizontal plane,” Transactions of the Institute of Measurement and Control, vol. 41, no. 2, pp. 340–349, 2018.

    Article  Google Scholar 

  25. M. Chen, Y. Ren, and J. Liu, “Antidisturbance control for a suspension cable system of helicopter subject to input non-linearities,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 12, pp. 2292–2304, 2017.

    Article  Google Scholar 

  26. K. Chen, “Robust optimal adaptive sliding mode control with the disturbance observer for a manipulator robot system,” International Journal of Control, Automation, and Systems, vol. 16, no. 4, pp. 1701–1715, 2018.

    Article  Google Scholar 

  27. H. Ma, M. Chen, and Q. Wu, “Inverse optimal control for unmanned aerial helicopters with disturbances,” Optimal Control Applications and Methods, vol. 40, no. 1, pp. 152–171, 2019.

    Article  MathSciNet  Google Scholar 

  28. X. Wang, X. Chen, and L. Wen, “The LQR baseline with adaptive augmentation rejection of unmatched input disturbance,” International Journal of Control, Automation, and Systems, vol. 15, no. 3, pp. 1302–1313, 2017.

    Article  Google Scholar 

  29. R. Sepulchre, M. Jankovic, and P. Kokotovic, Constructive Nonlinear Control, Springer, London, UK, 2012.

    MATH  Google Scholar 

  30. H. Liu, G. Lu, and Y. Zhong, “Robust LQR attitude control of a 3-DOF laboratory helicopter for aggressive maneuvers,” IEEE Transactions on Industrial Electronics, vol. 60, no. 10, pp. 4627–4636, 2013.

    Article  Google Scholar 

  31. P. Xia, H. Shi, H. Wen, Q. Bu, Y. Hu, and Y. Yang, “Robust LMI-LQR control for dual active bridge DC-DC converters with high parameter uncertainties,” IEEE Transactions on Transportation Electrification, vol. 6, no. 1, pp. 131–145, 2020.

    Article  Google Scholar 

  32. Y. Alothman, W. Jasim, and D. Gu, “Quadrotor lifting-transporting cable-suspended payloads control,” Proc. of 21st International Conference on Automation and Computing (ICAC), pp. 1–6, 2015.

  33. W. Sun, H. Gao, and O. Kaynak, “Finite frequency H control for vehicle active suspension systems,” IEEE Transactions on Control Systems and Technology, vol. 19, no. 2, pp. 416–422, 2011.

    Article  Google Scholar 

  34. A. Isidori, L. Marconi, and A. Serrani, “Robust nonlinear motion control of a helicopter,” IEEE Transactions on Automatic Control, vol. 48, no. 3, pp. 413–426, 2003.

    Article  MathSciNet  Google Scholar 

  35. I. Raptis and K. Valavanis, Linear and nonlinear control of small-scale unmanned helicopters, Intelligent Systems, Control and Automation: Science and Engineering. Springer, Netherlands, 2011.

    Book  Google Scholar 

  36. Y. Li, H. Sun, G. Zong, and L. Hou, “Anti-disturbance control for time-varying delay Markovian jump nonlinear systems with multiple disturbances,” International Journal of Systems Science, vol. 48, no. 15, pp. 3186–3200, 2017.

    Article  MathSciNet  Google Scholar 

  37. G. Duan and H. Yu, LMIs in Control Systems Analysis, Design and Applications, CRC Press, 2013.

  38. J. Guo, G. Tao, and Y. Liu, “A multivariable MRAC scheme with application to a nonlinear aircraft model,” Automatica, vol. 47, no. 4, pp. 804–812, 2011.

    Article  MathSciNet  Google Scholar 

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Funding

This work was supported in part by the National Natural Science Foundation of China under Grant (U2013201, 62073164); in part by the Key R & D projects (Social Development) in Jiangsu Province of China under Grant BE2020704; in part by the Aeronautical Science Foundation of China under Grant 20200007052001.

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Correspondence to Mou Chen.

Additional information

Lijun Liu received his M.S. degree at the College of Mathematics and Information Science, Guangxi University, Nanning in 2017. He is currently pursuing a Ph.D. degree in control theory and control engineering from the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing. His Current research interests include include nonlinear system control and flight control.

Mou Chen is currently a Full Professor with the College of Automation Engineering, Nanjing University of Aeronautics and Astronautics. He was an Academic Visitor with the Department of Aeronautical and Automotive Engineering, Lough-borough University, U.K., from 2007 to 2008. From 2008 to 2009, he was a Research Fellow with the Department of Electrical and Computer Engineering, National University of Singapore. He was a Senior Academic Visitor with the School of Electrical and Electronic Engineering, University of Adelaide, Australia, in 2014. His research interests include nonlinear system control, intelligent control, and flight control.

Tao Li received his Ph.D. degree in engineering from Southeast University in 2008 and was a postdoctoral research fellow at the School of Instrument Science and Engineering of Southeast University during year 2008 and 2011, China. He has been a visiting scholar at Control System Center of Manchester University from year 2016 to 2017, UK. He is currently an associate professor at School of Automation Engineering, Nanjing University of Aeronautics and Astronautics in China. His current research interests include neural networks, time-delay systems, networked control systems, etc.

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Liu, L., Chen, M. & Li, T. Disturbance Observer-based LQR Tracking Control for Unmanned Autonomous Helicopter Slung-load System. Int. J. Control Autom. Syst. 20, 1166–1178 (2022). https://doi.org/10.1007/s12555-020-0514-6

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