Skip to main content
SpringerLink
Log in

Robust Finite-time Attitude Tracking Control of Rigid Spacecraft Under Actuator Saturation

  • Regular Papers
  • Control Theory and Applications
  • Published:
International Journal of Control, Automation and Systems Aims and scope Submit manuscript

Abstract

This paper investigates the robust finite-time attitude tracking control problem for rigid spacecraft considering the modeling uncertainty, external disturbance and actuator saturation. An auxiliary system is proposed to directly compensate for the saturated control input. First, the basic controller is formulated based on the fast nonsingular terminal sliding mode surface (FNTSMS), the fast-TSM-type reaching law and the auxiliary system in the presence of upper bounded external disturbance. Then, when facing system uncertainty which consists of both modeling uncertainty and external disturbance and has upper bounded first derivative, the extended state observer (ESO) is associated with the first controller to improve the robustness of control system. Furthermore, to handle more general system uncertainty which is upper bounded by a polynomial function of the closed-loop system states, a continuous adaptive controller is designed to compensate for the total system uncertainty on line. The proposed controllers are able to deal with system uncertainty, input singularity and actuator saturation, while simultaneously providing fast finite-time convergence speed for the control system. And the problems of complex parameters selection process and repeated differentiations of nonlinear functions can be avoided. Rigorous stability analyses are given via the Lyapunov stability theory and digital simulations are conducted to illustrate the effectiveness of the proposed controllers.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. W. C. Luo, Y. C. Chu, and K. V. Ling, “H-infinity inverse optimal attitude-tracking control of rigid spacecraft,” Journal of Guidance Control & Dynamics, vol. 28, no. 3, pp. 481–494, 2005.

    Article  Google Scholar 

  2. J. R. Forbes, “Passivity-based attitude control on the special orthogonal group of rigid-body rotations,” Journal of Guidance Control & Dynamics, vol. 36, no. 6, pp. 1596–1605, 2013. [click]

    Article  Google Scholar 

  3. S. Sheng and C. Sun, “An adaptive attitude tracking control approach for an unmanned helicopter with parametric uncertainties and measurement noises,” International Journal of Control, Automation and Systems, vol. 14, no. 1, pp. 217–228, 2016. [click]

    Article  MathSciNet  Google Scholar 

  4. R. Kristiansen, P. J. Nicklasson, and J. T. Gravdahl, “Satellite attitude tracking by quaternion-based backstepping,” IEEE Transactions on Control Systems Technology, vol. 17, no. 1, pp. 227–232, 2009. [click]

    Article  Google Scholar 

  5. Y. J. Liu and S. Tong, “Optimal control-based adaptive NN design for a class of nonlinear discrete-time block triangular systems,” IEEE Transactions on Cybernetics, vol. 46, no. 11, pp. 2670–2680, 2016. [click]

    Article  Google Scholar 

  6. J. K. Lee, Y. H. Choi, and B. P. Jin, “Sliding mode tracking control of mobile robots with approach angle in Cartesian coordinates,” International Journal of Control, Automation and Systems, vol. 13, no. 3, pp. 718–724, 2015. [click]

    Article  Google Scholar 

  7. Y. J. Liu and S. Tong, “Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems,” Automatica, vol. 76, pp. 143–152, 2017.

    Article  MathSciNet  MATH  Google Scholar 

  8. S. T. Venkataraman and S. Gulati, “Control of nonlinear systems using terminal sliding modes,” American Control Conference, vol. 115, no. 3, pp. 891–893, 2009.

    MATH  Google Scholar 

  9. Y. Tang, “Terminal sliding mode control for rigid robots,” Automatica, vol. 34, no. 1, pp. 51–56, 1998.

    Article  MathSciNet  MATH  Google Scholar 

  10. E. Jin and Z. Sun, “Robust controllers design with finite time convergence for rigid spacecraft attitude tracking control,” Aerospace Science & Technology, vol. 12, no. 4, pp. 324–330, 2008.

    Article  MATH  Google Scholar 

  11. S. Yu, X. Yu, B. Shirinzadeh, and Z. Man, “Continuous finite time control for robotic manipulators with terminal sliding mode,” Automatica, vol. 41, no. 11, pp. 1957–1964, 2005. [click]

    Article  MathSciNet  MATH  Google Scholar 

  12. K. Lu and Y. Xia, “Finite-time fault-tolerant control for rigid spacecraft with actuator saturations,” IET Control Theory & Applications, vol. 7, no. 11, pp. 1529–1539, 2013. [click]

    Article  MathSciNet  Google Scholar 

  13. P. M. Tiwari, S. Janardhanan, and M. U. Nabi, “A finitetime convergent continuous time sliding mode controller for spacecraft attitude control,” International Workshop on Variable Structure Systems, pp. 399–403, 2010.

    Google Scholar 

  14. S. Wu, G. Radice, Y. Gao, and Z. Sun, “Quaternion-based finite time control for spacecraft attitude tracking,” Acta Astronautica, vol. 69, no. 1-2, pp. 48–58, 2011. [click]

    Article  Google Scholar 

  15. Y. Guo, S. M. Song, and X. H. Li, “Quaternion-based finite-time control for attitude tracking of the spacecraft without unwinding,” International Journal of Control, Automation and Systems, vol. 13, no. 6, pp. 1351–1359, 2015. [click]

    Article  Google Scholar 

  16. C. Pukdeboon and P. Siricharuanun, “Nonsingular terminal sliding mode based finite-time control for spacecraft attitude tracking,” International Journal of Control, Automation and Systems, vol. 12, no. 3, pp. 530–540, 2014. [click]

    Article  Google Scholar 

  17. Q. Hu, B. Li, and J. Qi, “Disturbance observer based finitetime attitude control for rigid spacecraft under input saturation,” Aerospace Science & Technology, vol. 39, pp. 13–21, 2014.

    Article  Google Scholar 

  18. K. Lu, Y. Xia, and M. Fu, “Controller design for rigid spacecraft attitude tracking with actuator saturation,” Information Sciences, vol. 220, no. 220, pp. 343–366, 2013.

    Article  MathSciNet  MATH  Google Scholar 

  19. Z. Zhu, Y. Xia, and M. Fu, “Attitude stabilization of rigid spacecraft with finite-time convergence,” International Journal of Robust & Nonlinear Control, vol. 21, no. 6, pp. 686–702, 2011.

    Article  MathSciNet  MATH  Google Scholar 

  20. Z. Song, H. Li, and K. Sun, “Finite-time control for nonlinear spacecraft attitude based on terminal sliding mode technique,” ISA Transactions, vol. 53, no. 1, pp. 117–124, 2014.

    Article  Google Scholar 

  21. K. Lu and Y. Xia, “Adaptive attitude tracking control for rigid spacecraft with finite-time convergence,” Automatica, vol. 49, no. 12, pp. 3591–3599, 2013. [click]

    Article  MathSciNet  MATH  Google Scholar 

  22. A. H. J. D. Ruiter, “Adaptive spacecraft attitude control with actuator saturation,” Journal of Guidance Control & Dynamics, vol. 33, no. 5, pp. 1692–1696, 2012. [click]

    Article  Google Scholar 

  23. Y. J. Liu, S. Tong, D. J. Li and Y. Gao, “Fuzzy adaptive control with state observer for a Class of nonlinear discretetime systems with input constraint,” IEEE Transactions on Fuzzy Systems, vol. 24, no. 5, pp. 1147–1158, 2015. [click]

    Article  Google Scholar 

  24. L. Wang, T. Chai, and L. Zhai, “Neural-network-based terminal sliding mode control of robotic manipulators including actuator dynamics,” IEEE Transactions on Industrial Electronics, vol. 56, no. 9, pp. 3296–3304, 2009. [click]

    Article  Google Scholar 

  25. A. M. Zou, K. D. Kumar, Z. G. Hou, and X. Liu, “Finitetime attitude tracking control for spacecraft using terminal sliding mode and Chebyshev neural network,” IEEE Transactions on Systems Man & Cybernetics, Part B, Cybernetics, vol. 41, no. 4, pp. 950–963, 2011.

    Article  Google Scholar 

  26. Y. J. Liu, S. Tong, C. L. Chen and D. J. Li, “Neural controller design based adaptive control for nonlinear MIMO systems with unknown hysteresis inputs,” IEEE Transactions on Cybernetics, vol. 46, no. 1, pp. 9–19, 2016.

    Article  Google Scholar 

  27. C. L. Chen, G. X. Wen, Y. J. Liu, and Z. Liu, “Observerbased adaptive backstepping consensus tracking control for high order nonlinear semi-strict-feedback multiagent systems,” IEEE Transactions on Cybernetics, vol. 46, no. 7, pp. 1591–1601, 2016.

    Article  Google Scholar 

  28. C. L. P. Chen, Y. J. Liu, and G. X. Wen, “Fuzzy neural network based adaptive control for a class of uncertain nonlinear stochastic systems,” IEEE Transactions on Cybernetics, vol. 44, no. 5, pp. 583–593, 2014. [click]

    Article  Google Scholar 

  29. G. X. Wen, C. L. P. Chen, Y. J. Liu, and Z. Liu, “Neuralnetwork-based adaptive leader-following consensus control for second-order non-linear multi-agent systems,” IET Control Theory and Applications, vol. 9, no. 13, pp. 1927–1934, 2015. [click]

    Article  MathSciNet  Google Scholar 

  30. J. D. Boskovic, S. M. Li, and R. K. Mehra, “Robust tracking control design for spacecraft under control input saturation,” Journal of Guidance Control & Dynamics, vol. 27, no. 4, pp. 627–633, 2004. [click]

    Article  Google Scholar 

  31. R. J. Wallsgrove and M. R. Akella, “Globally stabilizing saturated attitude control in the presence of bounded unknown disturbances,” Journal of Guidance Control & Dynamics, vol. 28, no. 5, pp. 957–963, 2005. [click]

    Article  Google Scholar 

  32. M. R. Akella, A. Valdivia, and G. R. Kotamraju, “Velocityfree attitude controllers subject to actuator magnitude and rate saturations,” Journal of Guidance Control & Dynamics, vol. 28, no. 4, pp. 659–666, 2005. [click]

    Article  Google Scholar 

  33. D. Bustan, N. Pariz, and S. K. Sani, “Robust fault-tolerant tracking control design for spacecraft under control input saturation,” ISA Transactions, vol. 53, no. 4, pp. 1073–1080, 2014. [click]

    Article  Google Scholar 

  34. A. M. Zou, K. D. Kumar, and A. H. J. D. Ruiter, “Robust attitude tracking control of spacecraft under control input magnitude and rate saturations,” International Journal of Robust & Nonlinear Control, no. 26, pp. 799–815, 2016.

    Article  MathSciNet  MATH  Google Scholar 

  35. J. Hu and H. Zhang, “A simple saturated control framework for spacecraft with bounded disturbances,” International Journal of Robust & Nonlinear Control, vol. 26, no. 3, pp. 367–384, 2015.

    MathSciNet  MATH  Google Scholar 

  36. Haibo Du and Shihua Li. “Finite-time attitude stabilization for a spacecraft using homogeneous method,” Journal of Guidance Control & Dynamics, vol. 35, no. 3, pp. 740–748, 2012. [click]

    Article  Google Scholar 

  37. Q. Hu, J. Zhang, and M. I. Friswell, “Finite-time coordinated attitude control for spacecraft formation flying under input saturation,” Journal of Dynamic Systems Measurement & Control, vol. 137, no. 6, 2015.

    Google Scholar 

  38. B. Xiao, Q. Hu, and M. I. Friswell, “Active fault-tolerant attitude control for flexible spacecraft with loss of actuator effectiveness,” International Journal of Adaptive Control & Signal Processing, vol. 27, no. 11, pp. 925–943, 2013. [click]

    Article  MathSciNet  MATH  Google Scholar 

  39. J. Ma, P. Li, L. Geng, and Z. Zheng, “Adaptive finite-time attitude tracking control of an uncertain spacecraft with input saturation,” IEEE Conference on Control Application (CAA), Part of 2015 IEEE Multi-Conference on Systems and Control, Sydney, Australia, pp. 930–935, 2015.

    Chapter  Google Scholar 

  40. M. D. Shuster, “A survey of attitude representations,” The journal of the Astronautical Sciences, vol. 41, no. 4, pp. 439–517, 1993.

    MathSciNet  Google Scholar 

  41. D. J. Zhao and D. G. Yang, “Model-free control of quadrotor vehicle via finite-time convergent extended state observer,” International Journal of Control, Automation and Systems, vol. 14, no. 1, pp. 242–254, 2016. [click]

    Article  Google Scholar 

  42. W. C. Cai, X. H. Liao, and Y. D. Song, “Indirect robust adaptive fault-tolerant control for attitude tracking of spacecraft,” Journal of Guidance Control & Dynamics, vol. 31, no. 5, pp. 1456–1463, 2008. [click]

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Center for Control Theory and Guidance Technology, Harbin Institute of Technology, Harbin, 150001, China

    Hai-Tao Chen & Shen-Min Song

  2. Beijing Institute of Control Engineering, Beijing, 100190, China

    Zhi-Bin Zhu

Authors
  1. Hai-Tao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shen-Min Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhi-Bin Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shen-Min Song.

Additional information

Recommended by Associate Editor Ohmin Kwon under the direction of Editor Jessie (Ju H.) Park. This paper was supported by the National Natural Science Foundation of China (61174037) and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (61021002).

Hai-Tao Chen received his B.S. and M.S. degrees in School of Automation from USTB. Currently, he is a Ph.D. student in the School of Astronautics at Harbin Institute of Technology. His main research interests include spacecraft attitude control, sliding mode control and adaptive control.

Shen-Min Song received his Ph.D. degree in Control Theory and Application from Harbin Institute of Technology in 1996. He carried out postdoctoral research at Tokyo University from 2000 to 2002. He is currently a professor in the School of Astronautics at Harbin Institute of Technology. His main research interests include spacecraft guidance and control, intelligent control, and nonlinear theory and application.

Zhi-Bin Zhu received his Ph.D. degree in Control Science and Engineering from Harbin Institute of Technology in 2009. He is currently a senior engineer at Beijing Institute of Control Engineering. His main research interests include nonlinear control, spacecraft guidance and control, space robot on-orbit control.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, HT., Song, SM. & Zhu, ZB. Robust Finite-time Attitude Tracking Control of Rigid Spacecraft Under Actuator Saturation. Int. J. Control Autom. Syst. 16, 1–15 (2018). https://doi.org/10.1007/s12555-016-0768-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-016-0768-1

Keywords

Search

Navigation