Skip to main content
SpringerLink
Log in

Nonsingular Terminal Sliding Mode Control-based Prescribed Performance Guidance Law with Impact Angle Constraints

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

Abstract

Conventional guidance law designs can only guarantee steady-state performance. However, transient performance is also the key performance index in practical guidance applications. In this paper, a novel terminal guidance law is presented for missile intercepting maneuvering target with impact angle constraints, which can strictly guarantee the prescribed steady-state and transient performances of interception. By utilizing the prescribed performance control technique, the prescribed performance tracking control problem is transformed into an equivalent unconstrained form such that the tracking error can be limit to the prescribed performance bound. Then, on the basis of transferred the tracking error, a novel nonsingular terminal sliding mode control-based guidance law is proposed with impact angle constraint, and the extended state observer is incorporated to online estimate the external disturbances and unknown target maneuver. The closed-loop system stability and the convergence characteristic are rigorously proved. Finally, extensive contrast simulations are conducted to demonstrate the efficiency and superiority of the proposed guidance law for different engagement scenarios.

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. H. B. Zhou, S. M. Song, and J. H. Song, “Design of sliding mode guidance law with dynamic delay and impact angle constraint,” International Journal of Control, Automation, and Systems, vol. 15, no. 1, pp. 239–247, January 2017.

    Article  Google Scholar 

  2. V. Rajasekhar and A. G. Sreenatha, “Fuzzy logic implementation of proportional navigation guidance,” Acta Astronautica, vol. 46, no. 1, pp. 17–24, January 2000.

    Article  Google Scholar 

  3. X. Hu, S. X. Yang, F. F. Xiong, and G. Q. Zhang, “Stability of spinning missile with homing proportional guidance law,” Aerospace Science and Technology, vol. 71, pp. 546–555, December 2017.

    Article  Google Scholar 

  4. K. S. Erer and O. Merttopçuoğlu, “Indirect impact-angle-control against stationary targets using biased pure proportional navigation,” Journal of Guidance, Control, and Dynamics, vol. 35, no. 2, pp. 700–704, August 2012.

    Article  Google Scholar 

  5. J. W. Zhu, D. L. Su, Y. Xie, and H. F. Sun, “Impact time and angle control guidance independent of time-to-go prediction,” Aerospace Science and Technology, vol. 86, pp. 818–825, March 2019.

    Article  Google Scholar 

  6. C. L. Lin, Y. P. Lin, and K. M. Chen, “On the design of fuzzified trajectory shaping guidance law,” ISA Transactions, vol. 48, no. 2, pp. 148–155, April 2009.

    Article  MathSciNet  Google Scholar 

  7. G. Weiss and I. Rusnak, “All-aspect three-dimensional guidance law based on feedback linearization,” Journal of Guidance, Control, and Dynamics, vol. 38, no. 12, pp. 2421–2428, December 2015.

    Article  Google Scholar 

  8. B. S. Chen, Y. Y. Chen, and C. L. Lin, “Nonlinear fuzzy H∞ guidance law with saturation of actuators against maneuvering targets,” IEEE Transactions on Control Systems Technology, vol. 10, no. 6, pp. 769–779, December 2002.

    Article  Google Scholar 

  9. K. Z. Meng, D. Zhou, and R. L. Du, “L2 gain-based guidance law with acceleration saturation,” Proc. of the 54th Annual Conf. Society of Instrument and Control Engineers of Japan, pp. 800–805, July 2015.

  10. J. W. Zhu and S. X. Zhang, “Adaptive optimal gliding guidance independent of QEGC,” Aerospace Science and Technology, vol. 71, pp. 373–381, December 2017.

    Article  Google Scholar 

  11. G. Y. Li, Z. G. Yu, and Z. X. Wang, “Three-dimensional adaptive sliding mode guidance law for missile with autopilot lag and actuator fault,” International Journal of Control, Automation, and Systems, vol. 17, no. 6, pp. 1369–1377, May 2019.

    Article  Google Scholar 

  12. N. Harl and S. N. Balakrishnan, “Impact time and angle guidance with sliding mode control,” IEEE Transactions on Control Systems Technology, vol. 20, no. 6, 1436–1449, December 2012.

    Article  Google Scholar 

  13. Y. Zhao, Y. Z. Sheng, and X. D. Liu, “Sliding mode control-based guidance law with impact angle constraint,” Chinese Journal of Aeronautics, vol. 27, no. 1, pp. 145–152, 2014.

    Article  Google Scholar 

  14. O. Mofid, M. Momeni, S. Mobayen, and A. Fekih, “A disturbance-observer-based sliding mode control for the robust synchronization of uncertain delayed chaotic systems: Application to data security,” IEEE Access, vol. 9, pp. 16546–16555, January 2021.

    Article  Google Scholar 

  15. Y. N. Yang and Y. Yan, “Neural network approximation-based nonsingular terminal sliding mode control for trajectory tracking of robotic airships,” Aerospace Science and Technology, vol. 54, pp. 192–197, April 2016.

    Article  Google Scholar 

  16. O. Mofid and S. Mobayen, “Sliding mode disturbance observer control based on adaptive synchronization in a class of fractional-order chaotic systems,” International Journal of Adaptive Control and Signal Processing, vol. 33, no. 3, pp. 462–474, December 2018.

    MathSciNet  MATH  Google Scholar 

  17. Z. H. Zhao, C. T. Li, J. Yang, and S. H. Li, “Output feedback continuous terminal sliding mode guidance law for missile-target interception with autopilot dynamics,” Aerospace Science and Technology, vol. 86, pp. 256–267, March 2019.

    Article  Google Scholar 

  18. J. H. Song, S. M. Song, Y. Guo, and H. B. Zhou, “Nonlinear disturbance observer-based fast terminal sliding mode guidance law with impact angle constraints,” International Journal of Innovative Computing Information and Control, vol. 11, no. 3, pp. 787–802, January 2015.

    Google Scholar 

  19. S. R. Kumar, S. Rao, and D. Ghose, “Sliding-mode guidance and control for all-aspect interceptors with terminal angle constraints,” Journal of Guidance, Control, and Dynamics, vol. 35, no. 4, pp. 1230–1246, July 2012.

    Article  Google Scholar 

  20. B. C. Zhou and W. H. Wang, “An improved nonsingular fast terminal sliding mode guidance law with impact angle constraints,” Proc. of the 8th International Conference on Intelligent Control and Information Processing, pp. 8–15, November 2017.

  21. S. R. Kumar, S. Rao, and D. Ghose, “Nonsingular terminal sliding mode control with terminal angle constraints for non-manuievering targets,” Proc. of the 12th IEEE Workshop on Variable Structure Systems, pp. 291–296, January 2012.

  22. S. R. Kumar, S. Rao, and D. Ghose, “Nonsingular terminal sliding mode guidance with impact angle constraints,” Journal of Guidance, Control, and Dynamics, vol. 37, no. 4, pp. 1114–1130, July 2014.

    Article  Google Scholar 

  23. J. L. Zhao and J. Zhou, “Strictly convergent nonsingular terminal sliding mode guidance law with impact angle constraints,” Optik, vol. 127, no. 22, pp. 10971–10980, November 2016.

    Article  Google Scholar 

  24. C. P. Bechlioulis and G. A. Rovithakis, “Adaptive control with guaranteed transient and steady state tracking error bounds for strict feedback systems,” Automatica, vol. 45, no. 2, pp. 532–538, February 2009.

    Article  MathSciNet  Google Scholar 

  25. C. P. Bechlioulis and G. A. Rovithakis, “Robust adaptive control of feedback linearizable MIMO nonlinear systems with prescribed performance,” IEEE Transactions on Automatic Control, vol. 53, no. 9, pp. 2090–2099, November 2008.

    Article  MathSciNet  Google Scholar 

  26. A. K. Kostarigka, Z. Doulgeri, and G. A. Rovithakis, “Prescribed performance tracking for flexible joint robots with unknown dynamics and variable elasticity,” Automatica, vol. 49, no. 5, pp. 1137–1147, May 2013.

    Article  MathSciNet  Google Scholar 

  27. M. Wang and A. L. Yang, “Dynamic learning from adaptive neural control of robot manipulators with prescribed performance,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 47, no. 8, pp. 2244–2255, January 2017.

    Article  Google Scholar 

  28. J. Na, Q. Chen, X. M. Ren, and Y. Guo, “Adaptive prescribed performance motion control of servo mechanisms with friction compensation,” IEEE Transactions on Industrial Electronics, vol. 61, no. 1, pp. 486–494, January 2014.

    Article  Google Scholar 

  29. Q. Y. Yang and M. Chen, “Adaptive neural prescribed performance tracking control for near space vehicles with input nonlinearity,” Neurocomputing, vol. 174, pp. 780–789, October 2015.

    Article  Google Scholar 

  30. Y. B. Huang, J. Na, X. Wu, X. Q. Liu, and Y. Guo, “Adaptive control of nonlinear uncertain active suspension systems with prescribed performance,” ISA Transactions, vol. 54, pp. 145–155, January 2015.

    Article  Google Scholar 

  31. J. Na, Y. B. Huang, X. Wu, G. B. Gao, G. Herrmann, and J. Z. Jiang, “Active adaptive estimation and control for vehicle suspensions with prescribed performance,” IEEE Transactions on Control Systems Technology, vol. 26, no. 6, pp. 2063–2077, November 2018.

    Article  Google Scholar 

  32. C. Ming, R. S. Sun, and B. Zhu, “Nonlinear fault-tolerant control with prescribed performance for air-breathing supersonic missiles,” Journal of Spacecraft and Rockets, vol. 54, no. 5, pp. 1092–1099, August 2017.

    Article  Google Scholar 

  33. S. F. Xiong, W. H. Wang, X. D. Liu, S. Wang, and Z. Q. Chen, “Guidance law against maneuvering targets with intercept angle constraint,” ISA Transactions, vol. 53, no. 4, pp. 1332–1342, July 2014.

    Article  Google Scholar 

  34. J. Q. Han, “From PID to active disturbance rejection control,” IEEE Transactions on Industrial Electronics, vol. 56, no. 3, pp. 900–906, March 2009.

    Article  Google Scholar 

  35. Z. Zhu, D. Xu, J. M. Liu, and Y. Q. Xia, “Missile guidance law based on extended state observer,” IEEE Transactions on Industrial Electronics, vol. 60, no. 12, pp. 5882–5891, December 2013.

    Article  Google Scholar 

  36. M. R. Mokhtari, A. C. Braham, and B. Cherki, “Extended state observer-based control for coaxial-rotor UAV,” ISA Transactions, vol. 61, pp. 1–14, March 2016.

    Article  Google Scholar 

  37. J. X. Liu, S. Vazquez, L. Wu, A. Marquez, H. J. Gao, and L. G. Franquelo, “Extended state observer-based sliding-mode control for three-phase power converters,” IEEE Transactions on Industrial Electronics, vol. 64, no. 1, pp. 22–31, September 2016.

    Article  Google Scholar 

  38. S. E. Talole, J. P. Kolhe, and S. B. Phadke, “Extended-state-observer-based control of flexible-joint system with experimental validation,” IEEE Transactions on Industrial Electronics, vol. 57, no. 4, pp. 1411–1419, May 2010.

    Article  Google Scholar 

  39. S. M. He, D. F. Lin, and J. Wang, “Chattering-free adaptive fast convergent terminal sliding mode controllers for position tracking of robotic manipulators,” Proc. of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, vol. 230, no. 4, pp. 514–526, March 2015.

    Google Scholar 

  40. J. Q. Han and R. Zhang, “Error analysis of the second order ESO,” Journal of system Science and Mathematical Science, vol. 19, no. 4, pp. 465–471, October 1999.

    MathSciNet  MATH  Google Scholar 

  41. J. H. Song, S. M. Song, and H. B. Zhou, “Adaptive nonsingular fast terminal sliding mode guidance law with impact angle constraints,” International Journal of Control, Automation, and Systems, vol. 14, no. 1, pp. 99–114, February 2016.

    Article  Google Scholar 

Download references

Funding

This project was supported by National Natural Science Foundation of China (52002185). The authors are grateful for the projects supported by the National Natural Science Foundation of China (Grant No. 52002185).

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing, 210094, China

    Chao Ming & Xiaoming Wang

Authors
  1. Chao Ming
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Xiaoming Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chao Ming.

Additional information

Chao Ming received his Ph.D. degree in the School of Energy and Power Engineering from Nanjing University of Science and Technology in 2017. He is currently a lecturer at the School of Mechanical Engineering, Nanjing University of Science and Technology. His research interests include the guidance and control design of aircraft.

Xiaoming Wang is currently a professor at the School of Mechanical Engineering, Nanjing University of Science and Technology. His research interests include the system technology of the intelligent ammunition.

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ming, C., Wang, X. Nonsingular Terminal Sliding Mode Control-based Prescribed Performance Guidance Law with Impact Angle Constraints. Int. J. Control Autom. Syst. 20, 715–726 (2022). https://doi.org/10.1007/s12555-020-0806-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12555-020-0806-x

Keywords

Search

Navigation