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Dynamics and anti-disturbance control for tethered aircraft system

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Abstract

Tethered aircraft system has been widely investigated because of its extensive application in hose-drogue autonomous aerial refueling, aerial towed decoy, and towed aerial recovery drogue, etc. Yet, due to the system nonlinearity, unknown airflow disturbances and unmeasurable tether tension, the anti-disturbance control of the tethered aircraft system is still a difficulty, which has not been well solved in the existing literature. In this paper, by introducing the elasticity and length variation of the tether, the system model composed of the multi-link tether model and the 6-degree-of-freedom dynamics of the tether aircraft is accurately established, and the reachable domain of the tethered aircraft is carefully analyzed. Then, the system nonlinearity is handled by applying a new coordinate transformation, and the lumped disturbances are estimated by extended state observers. Finally, an extended state observer-based adaptive dynamic surface control approach is employed to guarantee the accurate tracking of the tethered aircraft under airflow disturbances. In comparison with PID method and active disturbance rejection control method, simulation results demonstrate that the proposed control method has better tracking ability under airflow disturbances, specially gust.

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References

  1. Cochran, J.E., Innocenti, M., No, T.S., Thukral, A.: Dynamics and control of maneuverable towed flight vehicles. J. Guid. Control. Dyn. 15(5), 1245–1252 (1992)

    Google Scholar 

  2. Bourmistrov, A.S., Hill, R.D., Riseborough, P.: Nonlinear control law for aerial towed target. J. Guid. Control. Dyn. 18(6), 1232–1238 (1995)

    Google Scholar 

  3. Sun, Y., Duan, H., Xian, N.: Fractional-order controllers optimized via heterogeneous comprehensive learning pigeon-inspired optimization for autonomous aerial refueling hose-drogue system. Aerosp. Sci. Technol. 81, 1–13 (2018)

    Google Scholar 

  4. Dai, X., Wei, Z., Quan, Q., Cai, K.: Hose-drum-unit modeling and control for probe-and-drogue autonomous aerial refueling. IEEE Trans. Aerosp. Electron. Syst. 56(4), 2779–2791 (2020)

    Google Scholar 

  5. Wu, Cihang, Hui, Jiapeng, Yan, Jianguo, Guo, Yiming, Xiao, Bing: Dynamic modeling and faster finite-time attitude stabilization of receiver aircraft for aerial refueling. Nonlinear Dynamics 104(6), 467–481 (2021). https://doi.org/10.1007/s11071-021-06288-4

    Article  Google Scholar 

  6. Ma, D., Wang, S., Yang, M., Dong, Y.: Dynamic simulation of aerial towed decoy system based on tension recurrence algorithm. Chin. J. Aeronaut. 29(6), 1484–1495 (2016)

    Google Scholar 

  7. Ma, T., Wei, Z., Chen, H., Wang, X.: Simulation of the dynamic retrieval process of a towed target system under towing airplane’s wake and atmospheric turbulence. Proc. Inst. Mech. Eng. Part G-J. Aerosp. Eng. 234(2), 095441002091,629 (2020)

    Google Scholar 

  8. Su, Z., Li, C., Zhen, Z.: Anti-disturbance constrained control of the air recovery carrier via an integral barrier lyapunov function. Aerosp. Sci. Technol. 106, 106,157 (2020)

    Google Scholar 

  9. Su, Z., Xie, M., Li, C.: Rise based active vibration control for the flexible refueling hose. Aerosp. Sci. Technol. 92, 387–404 (2019)

    Google Scholar 

  10. Yu, B.S., Xu, S.D., Jin, D.P.: Chaos in a tethered satellite system induced by atmospheric drag and earth’s oblateness. Nonlinear Dyn. 101(2), 1233–1244 (2020)

    Google Scholar 

  11. Aslanov, V.S.: Prospects of a tether system deployed at the l1 libration point. Nonlinear Dyn. 106(3), 2021–2033 (2021)

    Google Scholar 

  12. Dai, X., Quan, Q., Ren, J., Xi, Z., Cai, K.Y.: Terminal iterative learning control for autonomous aerial refueling under aerodynamic disturbances. J. Guid. Control. Dyn. 41(7), 1577–1584 (2018)

    Google Scholar 

  13. Ledkov, A., Aslanov, V.: Evolution of space tethered system’s orbit during space debris towing taking into account the atmosphere influence. Nonlinear Dyn. 96(3), 2211–2223 (2019)

    Google Scholar 

  14. Quisenberry, J., Arena, A.: Discrete cable modeling and dynamic analysis. In: AIAA Aerospace Sciences Meeting and Exhibit (2006)

  15. Liu, Z., Liu, J., He, W.: Modeling and vibration control of a flexible aerial refueling hose with variable lengths and input constraint. Automatica 77, 302–310 (2017)

    MathSciNet  MATH  Google Scholar 

  16. Williams, P., Lapthorne, P., Trivailo, P.: Circularly-towed lumped mass cable model validation from experimental data. In: AIAA Modeling and Simulation Technologies Conference and Exhibit (2006)

  17. Kamman, R.J.W.: Modeling and simulation of hose-paradrogue aerial refueling systems. J. Guid. Control. Dyn. 33(1), 53–63 (2010)

    Google Scholar 

  18. Su, Z., Li, C., Liu, Y.: Anti-disturbance dynamic surface trajectory stabilization for the towed aerial recovery drogue under unknown airflow disturbances. Mech. Syst. Signal Process. 150, 107,342 (2021)

    Google Scholar 

  19. Williams, P.: Deployment/retrieval optimization for flexible tethered satellite systems. Nonlinear Dyn. 52(1–2), 159–179 (2008)

    MATH  Google Scholar 

  20. Jung, W., Mazzoleni, A.P., Chung, J.: Nonlinear dynamic analysis of a three-body tethered satellite system with deployment/retrieval. Nonlinear Dyn. 82(3), 1127–1144 (2015)

    MathSciNet  MATH  Google Scholar 

  21. Chen, C.C., Chen, Y.T.: Control design of nonlinear spacecraft system based on feedback linearization approach. IEEE Access 8, 116,626-116,641 (2020)

    Google Scholar 

  22. Waswa, P.M., Redkar, S.: Control of nonlinear spacecraft attitude motion via state augmentation, lyapunov-floquet transformation and normal forms. Adv. Space Res. 64(3), 668–686 (2019)

    Google Scholar 

  23. Liu, Y., Huang, L., Xiao, D., Guo, Y.: Global adaptive control for uncertain nonaffine nonlinear hysteretic systems. ISA Trans. 58, 255–261 (2015)

    Google Scholar 

  24. Zhou, W., Liao, C., Zheng, L., Liu, M.: Adaptive fuzzy output feedback control for a class of nonaffine nonlinear systems with unknown dead-zone input. Nonlinear Dyn. 79(4), 1–13 (2014)

    MathSciNet  Google Scholar 

  25. Wang, Y., Chen, M., Wu, Q., Zhang, J.: Fuzzy adaptive non-affine attitude tracking control for a generic hypersonic flight vehicle. Aerosp. Sci. Technol. 80, 56–66 (2018)

    Google Scholar 

  26. Su, Z., Wang, H., Yao, P., Huang, Y., Qin, Y.: Back-stepping based anti-disturbance flight controller with preview methodology for autonomous aerial refueling. Aerosp. Sci. Technol. 61, 95–108 (2017)

    Google Scholar 

  27. Wei, C., Luo, J., Guo, Z., Yin, Z., Yuan, J.: Active vibration control of underactuated free-floating spacecraft via a performance enhanced way. Acta Astronaut. 157, 477–488 (2019)

    Google Scholar 

  28. Liu, Y.: Adaptive tracking control for a class of uncertain pure-feedback systems. Int. J. Robust Nonlinear Control 26(5), 1143–1154 (2016)

    MathSciNet  MATH  Google Scholar 

  29. Liu, Y., Huang, L., Xiao, D.: Adaptive dynamic surface control for uncertain nonaffine nonlinear systems. Int. J. Robust Nonlinear Control 27(4), 535–546 (2017)

    MathSciNet  MATH  Google Scholar 

  30. Shu, Y., Tong, Y., Yu, C.: Robust neural tracking control for switched nonaffine stochastic nonlinear systems with unknown control directions and backlash-like hysteresis. J. Franklin Inst. 357(5), 2791–2812 (2020)

    MathSciNet  MATH  Google Scholar 

  31. Chen, M., Tao, G., Jiang, B.: Dynamic surface control using neural networks for a class of uncertain nonlinear systems with input saturation. IEEE Trans. Neural Netw. Learn. Syst. 26(9), 2086–2097 (2015)

    MathSciNet  Google Scholar 

  32. Chen, M., Wang, H., Liu, X., Hayat, T., Alsaadi, F.E.: Adaptive finite-time dynamic surface tracking control of nonaffine nonlinear systems with dead zone. Neurocomputing 366, 66–73 (2019)

    Google Scholar 

  33. Song, Jiacheng, Yan, Maode, Ju, Yongfeng, Yang, Panpan: Nonlinear gain feedback adaptive DSC for a class of uncertain nonlinear systems with asymptotic output tracking. Nonlinear Dyn. 98(7), 2195–2210 (2019). https://doi.org/10.1007/s11071-019-05317-7

    Article  MATH  Google Scholar 

  34. Chen, W., Yang, J., Guo, L., Li, S.: Disturbance-observer-based control and related methods–an overview. IEEE Trans. Ind. Electron. 63(2), 1083–1095 (2016)

    Google Scholar 

  35. Zhi, Y., Liu, L., Guan, B., Wang, B., Cheng, Z., Fan, H.: Distributed robust adaptive formation control of fixed-wing uavs with unknown uncertainties and disturbances. Aerosp. Sci. Technol. 126, 107,600 (2022)

    Google Scholar 

  36. Zhou, S., Shen, C., Xia, Y., Chen, Z., Zhu, S.: Adaptive robust control design for underwater multi-dof hydraulic manipulator. Ocean Eng. 248, 110,822 (2022)

    Google Scholar 

  37. Fuhui, G., Pingli, L.: Fast self-adapting high-order sliding mode control for a class of uncertain nonlinear systems. J. Syst. Eng. Electron. 32(3), 690–699 (2021)

    Google Scholar 

  38. Qiu, J., Sun, K., Wang, T., Gao, H.: Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. 27(11), 2152–2162 (2019)

    Google Scholar 

  39. Ran, M., Wang, Q., Dong, C., Xie, L.: Active disturbance rejection control for uncertain time-delay nonlinear systems. Automatica 112, 108,692 (2020)

    MathSciNet  MATH  Google Scholar 

  40. Liu, J., Sun, M., Chen, Z., Sun, Q.: Output feedback control for aircraft at high angle of attack based upon fixed-time extended state observer. Aerosp. Sci. Technol. 95, 105,468 (2019)

    Google Scholar 

  41. Castillo, A., Santos, T.L.M., Garcia, P., Normey-Rico, J.E.: Predictive eso-based control with guaranteed stability for uncertain mimo constrained systems. ISA Trans. 112, 161–167 (2021)

    Google Scholar 

  42. Tang, P., Lin, D., Zheng, D., Fan, S., Ye, J.: Observer based finite-time fault tolerant quadrotor attitude control with actuator faults. Aerosp. Sci. Technol. 104, 105,968 (2020)

  43. Shao, X., Liu, N., Liu, J., Wang, H.: Model-assisted extended state observer and dynamic surface control-based trajectory tracking for quadrotors via output-feedback mechanism. Int. J. Robust Nonlinear Control 28(6), 2404–2423 (2018)

    MathSciNet  MATH  Google Scholar 

  44. Shen, Z., Wang, Q., Yang, G., Zhang, M.: Anti-disturbance backstepping control for air-breathing hypersonic vehicles based on extended state observer. ISA Trans. 92, 84–93 (2019)

    Google Scholar 

  45. Bo, L., Hu, Q., Ma, G.: Extended state observer based robust attitude control of spacecraft with input saturation. Aerosp. Sci. Technol. 50, 173–182 (2016)

    Google Scholar 

  46. Liu, Y., Tong, S.: Barrier lyapunov functions for nussbaum gain adaptive control of full state constrained nonlinear systems. Automatica 76, 143–152 (2017)

    MathSciNet  MATH  Google Scholar 

  47. Gage, S.: Creating a unified graphical wind turbulence model from multiple specifications. In: Aiaa Modeling and Simulation Technologies Conference and Exhibit (2013)

  48. Dogan, A., Venkataramanan, S., Blake, W.: Modeling of aerodynamic coupling between aircraft in close proximity. J. Aircr. 42(4), 941–955 (2005)

    Google Scholar 

  49. Kuk, T., Ro, K.: Design, test and evaluation of an actively stabilised drogue refuelling system. Aeronaut. J. 117(1197), 1103–1118 (2013)

    Google Scholar 

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Funding

This research is sponsored by the National Natural Science Foundation of China under Grant Numbers 91848205 and 61725303.

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Authors and Affiliations

  1. Research Center of Intelligent Robotics, School of Astronautics, Northwestern Polytechnical University, Xi’an, China

    Mengshi Song & Panfeng Huang 

  2. National Key Laboratory of Aerospace Flight Dynamics, Northwestern Polytechnical University, Xi’an, China

    Mengshi Song & Panfeng Huang 

Authors
  1. Mengshi Song
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  2. Panfeng Huang 
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Correspondence to Panfeng Huang .

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A Appendix

A Appendix

$$\begin{aligned}&{{\varvec{A}}_2} = {{\varvec{M}}^{ - 1}}\left( {\frac{{{{\varvec{S}}_{\mathrm{I},\mathrm{h}}}{{\varvec{S}}_{\mathrm{d},\mathrm{I}}}{{{\varvec{F'}}}_\mathrm{d}}}}{{0.5{m_1} + {m_\mathrm{d}}}} + \frac{{{{\varvec{S}}_{\mathrm{I},\mathrm{h}}}{{\varvec{S}}_{\mathrm{1},\mathrm{I}}}{{\varvec{t}}_{n,n}}}}{{0.5{m_1} + {m_\mathrm{d}}}}} \right) .\\&{\varvec{M}} = \left[ {\begin{array}{*{20}{c}} 1&{}0&{}0\\ 0&{}{{l_\mathrm{h}}}&{}0\\ 0&{}0&{}{ - {l_\mathrm{h}}\cos {\xi _\mathrm{h}}} \end{array}} \right] .\\&{{\varvec{B}}_2} = \left[ {\begin{array}{*{20}{c}} {{l_\mathrm{h}}{\dot{\phi }} _\mathrm{h}^2{{\cos }^2}{\xi _\mathrm{h}} + {l_\mathrm{h}}{\dot{\xi }} _\mathrm{h}^2 + g\sin {\phi _\mathrm{h}}\cos {\xi _\mathrm{h}}}\\ {\frac{{ - 2{{\dot{l}}_\mathrm{h}}{{{\dot{\xi }} }_\mathrm{h}} - {l_\mathrm{h}}{\dot{\phi }} _\mathrm{h}^2\sin {\xi _\mathrm{h}}\cos {\xi _\mathrm{h}} - g\sin {\phi _\mathrm{h}}\sin {\xi _\mathrm{h}}}}{{{l_\mathrm{h}}}}}\\ {\frac{{\left( {2{l_\mathrm{h}}{{{\dot{\xi }} }_\mathrm{h}}\sin {\xi _\mathrm{h}} - 2{{\dot{l}}_\mathrm{h}}\cos {\xi _\mathrm{h}}} \right) {{{\dot{\phi }} }_\mathrm{h}} + g\cos {\phi _\mathrm{h}}}}{{{l_\mathrm{h}}\cos {\xi _\mathrm{h}}}}} \end{array}} \right] .\\&{{\varvec{C}}_2} = {{\varvec{M}}^{ - 1}}\left( {\frac{{{{\varvec{S}}_{\mathrm{I},\mathrm{h}}}{{\varvec{S}}_{\mathrm{d},\mathrm{I}}}{{\varvec{\varDelta }}_{\mathrm{fd}}}}}{{0.5{m_1} + {m_\mathrm{d}}}}+ \frac{{{{\varvec{S}}_{\mathrm{I},\mathrm{h}}}{{\varvec{S}}_{\mathrm{1},\mathrm{I}}}{{\varvec{\varDelta }}_{1,n}}}}{{0.5{m_1} + {m_\mathrm{d}}}} + \frac{{0.5{{\varvec{S}}_{\mathrm{I},\mathrm{h}}}{{\varvec{D}}_1}}}{{0.5{m_1} + {m_\mathrm{d}}}}} \right) . \\&{{\varvec{A}}_3} = \left[ {\begin{array}{*{20}{c}} 1&{}0&{}0\\ 0&{}{\frac{1}{{\cos \vartheta }}}&{}0\\ 0&{}0&{}1 \end{array}} \right] . \\&{{\varvec{C}}_3} = \left[ {\begin{array}{*{20}{c}} 0\\ {\frac{{\sin \gamma }}{{\cos \vartheta }}{\omega _y} + \frac{{\cos \gamma - 1}}{{\cos \vartheta }}{\omega _z}}\\ {\left( {\cos \gamma - 1} \right) {\omega _y} - \sin \gamma {\omega _z}} \end{array}} \right] .\\&{{\varvec{A}}_4} = \left[ {\begin{array}{*{20}{c}} 1&{}0&{}0\\ 0&{}{\frac{1}{2}\rho {{\left\| {{{\varvec{v}}_{\mathrm{0}}}} \right\| }^2}SL\frac{{{m_{z,1}}}}{{{I_z}}}}&{}0\\ 0&{}0&{}{\frac{1}{2}\rho {{\left\| {{{\varvec{v}}_{\mathrm{0}}}} \right\| }^2}SL\frac{{{m_{y,1}}}}{{{I_y}}}} \end{array}} \right] .\\&{{\varvec{B}}_4} = \left[ {\begin{array}{*{20}{c}} 0\\ {\frac{{{\omega _x}{\omega _y}({I_x} - {I_y})}}{{{I_z}}}}\\ {\frac{{{\omega _x}{\omega _z}({I_z} - {I_x})}}{{{I_y}}}} \end{array}} \right] + \frac{1}{2}\rho {\left\| {{{\varvec{v}}_0}} \right\| ^2}SL\left[ {\begin{array}{*{20}{c}} 0\\ {\frac{{{m_{z,2}}\psi }}{{{I_z}}}}\\ {\frac{{{m_{y,2}}\vartheta }}{{{I_y}}}} \end{array}} \right] .\\&{{\varvec{C}}_4} = \left[ {\begin{array}{*{20}{c}} 0\\ {\frac{{{\varDelta _{\mathrm{md},z}} + {M_{\mathrm{t},z}}}}{{{I_z}}}}\\ {\frac{{{\varDelta _{\mathrm{md},y}} + {M_{\mathrm{t},y}}}}{{{I_y}}}} \end{array}} \right] .\\&{{\varvec{\varDelta }}_\mathrm{md}} = \left[ {\begin{array}{*{20}{c}} {{\varDelta _{\mathrm{md},x}}}\\ {{\varDelta _{\mathrm{md},y}}}\\ {{\varDelta _{\mathrm{md},z}}} \end{array}} \right] . \end{aligned}$$

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Song, M., Huang , P. Dynamics and anti-disturbance control for tethered aircraft system. Nonlinear Dyn 110, 2383–2399 (2022). https://doi.org/10.1007/s11071-022-07742-7

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