Advertisement

Nonlinear Dynamics

, Volume 81, Issue 1–2, pp 881–892 | Cite as

Robust terminal angle constraint guidance law with autopilot lag for intercepting maneuvering targets

  • Shaoming He
  • Defu Lin
  • Jiang Wang
Original Paper

Abstract

In this paper, a robust continuous guidance law with terminal angle constraint for intercepting maneuvering targets in the presence of autopilot lag is proposed and its finite-time stability is proved. First, assuming that the missile autopilot is sufficiently fast, a composite fast nonsingular terminal sliding mode guidance (CFNTSMG) law is presented. The proposed guidance law is obtained through a combination of fast nonsingular terminal sliding mode control theory and generalized disturbance observer (GDOB). The presented guidance law requires no priori information on target maneuver, which is estimated and compensated online by GDOB. Moreover, no discontinuous term exists in CFNTSMG law and therefore chattering is eliminated effectively. Next, viewing the missile autopilot as an uncertain second-order system, an integrated guidance and control dynamics is formulated and the systematic step-by-step backstepping technique is used to derive a new robust guidance law, which not only holds the advantages of CFNTSMG law, but also is insensitive to autopilot lag. At each backstepping step, novel continuous virtual/real control laws using finite-time control approach are designed and tracking differentiator is used to overcome the ‘explosion of complexity’ problem encountered with traditional backstepping method. Theoretical analysis and numerical simulations demonstrate the effectiveness of the proposed method.

Keywords

Fast nonsingular terminal sliding mode control Generalized disturbance observer  Tracking differentiator Missile guidance  Terminal angle constraint Autopilot lag   Finite-time convergence 

Notes

Acknowledgments

This work was supported by the Natural Science Foundation of China (Grant No. 61172182). Finally, the authors are deeply grateful to the editor and the associate editor for the time and effort spent in handling the paper and to the anonymous reviewers for their valuable comments and constructive suggestions with regard to the revision of the paper.

References

  1. 1.
    Nesline, F.W., Zarchan, P.: A new look at classical vs modern homing missile guidance. J. Guid. Control Dyn. 4(1), 78–85 (1981)CrossRefGoogle Scholar
  2. 2.
    Palumbo, N.F., Blauwkamp, R.A., Lloyd, J.M.: Basic principles of homing guidance. Johns Hopkins APL Tech. Dig. 29(1), 25–41 (2010)Google Scholar
  3. 3.
    Zarchan, P.: Tactical and Strategic Missile Guidance. American Institute of Aeronautics and Astronautics Publications, New York (1998)Google Scholar
  4. 4.
    Garnell, P.: Guided Weapon Control Systems, 2nd edn. Pergamon, Oxford (1980)Google Scholar
  5. 5.
    Zhou, D., Sun, S., Teo, K.L.: Guidance laws with finite time convergence. J. Guid. Control Dyn. 32(6), 1838–1846 (2009)CrossRefGoogle Scholar
  6. 6.
    Taub, I., Shima, T.: Intercept angle missile guidance under time varying acceleration bounds. J. Guid. Control Dyn. 36(3), 686–699 (2013)CrossRefGoogle Scholar
  7. 7.
    Kumar, S.R., Rao, S., Ghose, D.: Sliding-mode guidance and control for all-aspect interceptors with terminal angle constraints. J. Guid. Control Dyn. 35(4), 1230–1246 (2012)CrossRefGoogle Scholar
  8. 8.
    Kim, M., Grider, K.V.: Terminal guidance for impact attitude angle constrained flight trajectories. IEEE Trans. Aerosp. Electron. Syst. 9(6), 852–859 (1973)CrossRefGoogle Scholar
  9. 9.
    Lee, Y.I., Kim, S.H., Tahk, M.J.: Analytic solutions of optimal angularly constrained guidance for first-order lag system. Proc. Inst. Mech. Eng. G. J. Aerosp. Eng. 227(5), 827–837 (2013)CrossRefGoogle Scholar
  10. 10.
    Ohlmeyer, E.J., Phillips, C.A.: Generalized vector explicit guidance. J. Guid. Control Dyn. 29(2), 261–268 (2006)CrossRefGoogle Scholar
  11. 11.
    Ryoo, C.K., Cho, H., Tahk, M.J.: Time-to-go weighted optimal guidance with impact angle constraints. IEEE Trans. Control Syst. Technol. 14(3), 483–492 (2006)CrossRefGoogle Scholar
  12. 12.
    Wang, H., Lin, D.H., Chen, Z.X., Wang, J.: Optimal guidance of extended trajectory shaping. Chin. J. Aeronaut. 27(5), 1259–1272 (2014)CrossRefGoogle Scholar
  13. 13.
    Lee, C.H., Lee, J.I., Tahk, M.J.: Sinusoidal function weighted optimal guidance laws. Proc. Inst. Mech. Eng. G. J. Aerosp. Eng. 229(3), 534–542 (2015)Google Scholar
  14. 14.
    Yamasaki, T., Balakrishnan, S.N., Takano, H., Yamaguchi, I.: Second order sliding mode-based intercept guidance with uncertainty and disturbance compensation. In: Proceedings of AIAA Guidance, Navigation, and Control Conference, August 19–22, Boston, MA (2013)Google Scholar
  15. 15.
    Harl, N., Balakrishnan, S.N.: Impact time and angle guidance with sliding mode control. IEEE Trans. Control Syst. Technol. 20(6), 1436–1449 (2012)CrossRefGoogle Scholar
  16. 16.
    Zhao, Y., Sheng, Y.Z., Liu, X.D.: Sliding mode control based guidance law with impact angle constraint. Chin. J. Aeronaut. 27(1), 145–152 (2014)CrossRefGoogle Scholar
  17. 17.
    Shima, T.: Intercept-angle guidance. J. Guid. Control Dyn. 34(2), 484–492 (2011)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Bhat, S.P., Bernstein, D.S.: Continuous finite-time stabilization of the translational and rotational double integrators. IEEE Trans. Autom. Control 43(5), 678–682 (1998)MATHMathSciNetCrossRefGoogle Scholar
  19. 19.
    Cheng, Y., Du, H., He, Y., Jia, R.: Finite-time tracking control for a class of high-order nonlinear systems and its applications to DC–DC buck converters. Nonlinear Dyn. 76(2), 1133–1140 (2014)MATHMathSciNetCrossRefGoogle Scholar
  20. 20.
    Shtessel, Y.B., Shkolnikov, I.A., Levant, A.: Guidance and control of missile interceptor using second-order sliding modes. IEEE Trans. Aerosp. Electron. Syst. 45(1), 110–124 (2009)CrossRefGoogle Scholar
  21. 21.
    Man, Z., Yu, X.: Terminal sliding mode control of MIMO linear systems. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 44(11), 1065–1070 (1997)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Zhang, Y.X., Sun, M.W., Chen, Z.Q.: Finite-time convergent guidance law with impact angle constraint based on sliding mode control. Nonlinear Dyn. 70(1), 619–625 (2012)MathSciNetCrossRefGoogle Scholar
  23. 23.
    He, S., Lin, D.: A robust impact angle constraint guidance law with seeker’s field-of-view limit. Trans. Inst. Meas. Control 37(3), 317–328 (2015)CrossRefGoogle Scholar
  24. 24.
    Feng, Y., Yu, X., Man, Z.: Non-singular terminal sliding mode control of rigid manipulators. Automatica 28(11), 2159–2167 (2002)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Kumar, S.R., Rao, S., Ghose, D.: Nonsingular terminal sliding mode guidance with impact angle constraints. J. Guid. Control Dyn. 37(4), 1114–1130 (2014)CrossRefGoogle Scholar
  26. 26.
    Chwa, D.Y., Choi, J.Y.: Adaptive nonlinear guidance law considering control loop dynamics. IEEE Trans. Aerosp. Electron. Syst. 39(4), 1134–1143 (2003)CrossRefGoogle Scholar
  27. 27.
    Sun, S., Zhou, D., Hou, W.T.: A guidance law with finite time convergence accounting for autopilot lag. Aerosp. Sci. Technol. 25(1), 132–137 (2013)CrossRefGoogle Scholar
  28. 28.
    Zhou, D., Qu, P., Sun, S.: A guidance law with terminal impact angle constraint accounting for missile autopilot. J. Dyn. Syst. Meas. Control Trans. ASME 135(5), 1–10 (2013)CrossRefGoogle Scholar
  29. 29.
    Li, G.L., Yan, H., Ji, H.B.: A guidance law with finite time convergence considering autopilot dynamics and uncertainties. Int. J. Control Autom. Syst. 12(5), 1011–1017 (2014)CrossRefGoogle Scholar
  30. 30.
    Yu, S., Yu, X., Shirinzadeh, B., Man, Z.: Continuous finite-time control for robotic manipulators with terminal sliding mode. Automatica 41(11), 1957–1964 (2005)MATHMathSciNetCrossRefGoogle Scholar
  31. 31.
    Ginoya, D., Shendge, P., Phadke, S.: Sliding mode control for mismatched uncertain systems using an extended disturbance observer. IEEE Trans. Ind. Electron. 61(4), 1983–1992 (2014)CrossRefGoogle Scholar
  32. 32.
    Zou, A.M., Kumar, K.D., Hou, Z.G.: Distributed consensus control for multi-agent systems using terminal sliding mode and Chebyshev neural networks. Int. J. Robust Nonlinear Control 23(3), 334–357 (2013)MATHMathSciNetCrossRefGoogle Scholar
  33. 33.
    Lu, K., Xia, Y.: Adaptive attitude tracking control for rigid spacecraft with finite-time convergence. Automatica 49(12), 3591–3599 (2013)MathSciNetCrossRefGoogle Scholar
  34. 34.
    Han, J.Q.: Active Disturbance Rejection Control Technique—The Technique for Estimating and Compensating the Uncertainties. National Defence Industry Press, Beijing (2008)Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.School of Aerospace EngineeringBeijing Institute of TechnologyBeijingPeople’s Republic of China

Personalised recommendations