Skip to main content
SpringerLink
Log in

An Expanded Two-Dimensional Proportional–Derivative Command to Line-of-Sight Guidance Law

  • Published:
Gyroscopy and Navigation Aims and scope Submit manuscript

Abstract

This paper deals with an expanded two-dimensional (2D) proportional-derivative (PD) command to line-of-sight (CLOS) guidance law which fights the spiral type trajectory of an anti-tank guided missile (ATGM) in the plane perpendicular to the line-of-sight (LOS) or the so called picture plane, in order to improve the transition process performance while putting the missile onto the LOS. The guidance law acts as a classical PD control law within a small predetermined area around the LOS while at missile deviations pointing a position outside this area the control law includes additional nonlinear components connected with the derivatives of the missile position vector in the plane perpendicular to the LOS. The global asymptotic stability of the guidance loop is established by a specific positive definite Lyapunov function. The effectiveness of the proposed approach is illustrated by simulation results. The guidance law enables to decrease the near-field boundary of the missile operational range.

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. Blakelock, J.H., Automatic control of aircraft and missiles, Wiley-Interscience, 1991, chap. 8, 8-3, 8-4, pp. 273−284.

    Google Scholar 

  2. Neupokoev, F.K., Shooting by anti-aircraft missiles, Voennoe izdatelstvo, Moskow, 1991, (in Russian) Chap. 2, §2.2, pp. 76−82.

    Google Scholar 

  3. Siouris, G.M., Missile Guidance and Control Systems, Springer-Verlag New York, 2004, chap. 4, 4.2.2, pp. 162–174.

    Google Scholar 

  4. Shneydor, N.A., Missile Guidance and Pursuit: Kinematics, Dynamics and Control, Horwood Publishing, 1998, chap. 2, pp. 11−46.

    Book  Google Scholar 

  5. Ha, I.-J., Chong, S., “Design of a CLOS Guidance Law via Feedback Linearization,” IEEE Trans. Aerosp. Electron. Syst., vol. 28, issue 1, 1992, pp. 51–63. doi 10.1109/7.135432

    Google Scholar 

  6. Penev, B.G., “Variant of a system for automatic control of antitank guided missile in polar coordinates,” Proceedings of Conference “Weapons and military equipment of the year 2000”, Conference of the Military Scientific and Technological Institute of the Ministry of Defense, 18−20 December 1995, Sofia, Vol. 1 “Weapons, ammunition and surveillance devices”, 1995, pp. 54−56. (in Bulgarian) Available on URL: https://doi.org/e-university.tusofia.bg/e-publ/search-det.php?id=2556

    Google Scholar 

  7. Penev, B.G., Lashnev, A.T., Iliev, I.Ya., “Control of the vector of normal acceleration of anti-tank guided missile in pseudo-polar coordinates,” Proceedings of Jubilee Conference ”120 years of the April Uprising” of the Higher Air Force School, Dolna Mitropoliya, 22–23 May 1996, vol. 1 “Aviation and Aerospace”, 1996, pp. 336–342. (in Bulgarian) Available on URL: https://doi.org/e-university.tu-sofia.bg/e-publ/search-det.php?id=2587

    Google Scholar 

  8. Pastrick, H.L., Seltzer, S.M., Warren, M.E., “Guidance Laws for Short-Range Tactical Missiles,” Journal of Guidance, Control, and Dynamics, vol. 4, no. 2, 1981, pp. 98–108. doi 10.2514/3.56060

    Google Scholar 

  9. Guerchet, P., Estival, J.L., “Line of Sight Guidance Law by Predictive Functional Control for High Velocity Short-Range Tactical Missile,” Proceedings of the European Control Conference 1991, July 2–5, 1991, Grenoble, France, vol. 2, pp. 1759–1764.

    Google Scholar 

  10. Huang, J., Lin, C.-F., “A modified CLOS guidance law via right inversion,” IEEE Trans. Aerosp. Electron. Syst., vol. 31, 1995, pp. 491–495. doi 10.1109/7.366334

    Google Scholar 

  11. Lin, C.-M., Hsu, C.-F., “Guidance Law Design by Adaptive Fuzzy Sliding-Mode Control,” Journal of Guidance, Control, and Dynamics, vol. 25, no. 2, 2002, pp. 248–256. doi 10.2514/2.4905

  12. Menon, P. K. A., Duke, E. L., “Time-optimal aircraft pursuit evasion with a weapon envelope constraint,” Journal of Guidance, Control, and Dynamics, Vol. 15, no. 2, March 1992, pp. 448–456. doi 10.2514/3.20856

    Google Scholar 

  13. Nobahari, H., Pourtakdoust, S.H., “Optimal Fuzzy CLOS Guidance Law Design Using Ant Colony Optimization,” Lecture Notes in Computer Science, vol. 3777 LNCS, 2005, pp. 95–106. doi 10.1007/11571155_10

    Google Scholar 

  14. Nobahari, H., Pourtakdoust, S.H., “An optimal-fuzzy two-phase CLOS guidance law design using ant colony optimization,” Aeronautical Journal, vol. 111, issue 1124, 2007, pp. 621–636.

    Google Scholar 

  15. Yamasaki, T., Balakrishnan, S.N., Takano, h., “Modified Command to Line-of-Sight Intercept Guidance for Aircraft Defense,” Journal of Guidance, Control, and Dynamics, vol. 36, no. 3, 2013, pp. 898–902. doi 10.2514/1.58566

    Google Scholar 

  16. Ratnoo, A., Shima, T., “Line of Sight Guidance for Defending an Aircraft,” AIAA Guidance, Navigation, and Control Conference, 02 August 2010–05 August 2010, Toronto, Ontario, Canada, 2010. doi 10.2514/6.2010-7877

    Book  Google Scholar 

  17. Tsalik, R., Shima, T., “Inscribed Angle Guidance,” Journal of Guidance, Control, and Dynamics, vol. 38, no. 1, January 2015, pp. 30–40. doi 10.2514/1.G000468

    Book  Google Scholar 

  18. Cho, N., Kim, Y., Park, S., “Three-Dimensional Nonlinear Differential Geometric Path-Following Guidance Law,” Journal of Guidance, Control, and Dynamics, vol. 38, no. 12, December 2015, pp. 2366–2385. doi 10.2514/1.G001060

    Google Scholar 

  19. Elhalwagy, Y.Z., Tarbouchi, M., “Fuzzy logic sliding mode control for command guidance law design,” ISA Transactions, vol. 43, 2004, pp. 231–242.

    Google Scholar 

  20. Elhalwagy, Y.Z., “Guidance Law Design Using Intelligent Non-Linear Controller,” 13th International Conference on AEROSPACE SCIENCES & AVIATION TECHNOLOGY (ASAT-13), May 26–28, 2009, Military Technical College, Kobry Elkobbah, Cairo, Egypt, 2009, Paper: ASAT-13-CT-32.

    Google Scholar 

  21. Sadeghinasab, E., Koofigar, H.R., Ataei, M., “Design of robust command to line-of-sight guidance law: A Fuzzy adaptive approach,” Journal of Engineering Science and Technology, Vol. 11, No. 11, 2016, pp. 1528–1542.

    Google Scholar 

  22. Alrawi, A.A.A., Graovac, S., Ahmad, R.B., Rahman, M.M., “Modified guidance law based on a sliding mode controller for a missile guidance system,” Tehnički vjesnik, vol. 23, no. 3, 2016, pp. 639–646. doi 10.17559/TV-20130625173047

    Google Scholar 

  23. Zaidi. H., Wu, P., Bellahcene, A., “Missile Guidance Law Design via Backstepping Technique,” International Journal of Engineering and Applied Sciences, vol. 3, issue 4, 2016, pp. 85–90.

    Google Scholar 

  24. Yanushevsky, R.T., “Generalized Missile Guidance Laws against Maneuvering Targets,” Proceedings of 25th Congress of the International Council of the Aeronautical Sciences, Hamburg, Germany, 3−8 September 2006, vol. 5, 2006, pp. 3043–3050.

    Google Scholar 

  25. Balakrishnan, S.N., Stansbery, D.T., Evers, J.H., Cloutier, J.R., “Analytical guidance laws and integrated guidance/autopilot for homing missiles,” Proceedings of IEEE International Conference on Control and Applications, vol. 1, 1993, pp. 27–32.

    Google Scholar 

  26. Balakrishnan, S.N., “Analytical missile guidance laws with a time-varying transformation,” Journal of Guidance, Control, and Dynamics, Vol. 19, No. 2, March 1996, pp. 496–499. doi 10.2514/3.21646

    Book  MATH  Google Scholar 

  27. Liu, X., Huang, W., Du, L., Lan, P., Sun, Y., “Three-Dimensional integrated guidance and control for BTT aircraft constrained by terminal flight angles,” Proceedings of the 2015 27th Chinese Control and Decision Conference, CCDC 2015, May 23–25, 2015, Qingdao Haiqing Hotel, Qingdao, China, Session SatA04: Nonlinear Systems (I). doi 10.1109/CCDC.2015.716167510. 1109/CCDC.2015.7161675

    Book  Google Scholar 

  28. Levy, M., Shima, T., Gutman, S., “Linear Quadratic Integrated Versus Separated Autopilot-Guidance Design,” Journal of Guidance, Control, and Dynamics, vol. 36, no. 6, 2013, pp. 1722–1730. doi 10.2514/1.61363

    Google Scholar 

  29. White, B., Zbikowski, R., Tsourdos, A., “Direct Intercept Guidance using Differential Geometry Concepts,” AIAA Guidance, Navigation, and Control Conference and Exhibit, Guidance, Navigation, and Control and Colocated Conferences, 2005. doi 10.2514/6.2005-5969

    Google Scholar 

  30. White, B, Zbikowski, R., Tsourdos, A., “Direct Intercept Guidance using Differential Geometry Concepts,” IEEE Transactions on Aerospace and Electronic Systems, vol. 43, issue 3, July 2007, pp. 899−919. doi 10.1109/TAES.2007.4383582

    Google Scholar 

  31. Li, D., Poh, E.K., “Nonlinear integrated steering and control of flight vehicles,” Guidance, Navigation, and Control Conference and Exhibit, 1998. doi 10.2514/6.1998-4210

    Book  Google Scholar 

  32. Balakrishnan, S.N., Tsourdos, A., and White, B.A., Advances in Missile Guidance, Control, and Estimation, CRC Press, 2016, chap. 14.

    Google Scholar 

  33. Khruslov, V.N., Feofilov, S.V., Goryachev, O.V., Lavit, I.M., and Indyukhin, A.F., “Missile Control in the Polar Coordinate System Using a Scalar Radius,” Gyroscopy and Navigation, vol. 6, no. 1, 2015, pp. 66–72. doi 10.1134/S207510871501006X

    Book  Google Scholar 

  34. Davies, D. R., “Line of sight missile guidance”, U.S. Patent 4750688, Issued June 14, 1988.

    Google Scholar 

  35. Shipunov, A.G., Morozov, V.I., Petrushin, V.V., “Method of Control Signal Forming for Double-Channel Rocket Rotating Around Longitudinal Axis,” Russian Federation Patent RU 2511610 C1, Issued 10.04.2014 Bull. 10.

  36. Gusev, A.V., Morozov, V.I., Nedosekin, I.A., Minakov, V.M., Tarasov, V. I., “Method of beam control over rolling missile and beam-controlled rolling missile”, Russian Federation Patent RU 2460966 C1, Issued March 14, 2011.

    Google Scholar 

  37. Mandić, S., Stojković, S., Milenković, D., Milošević, M., “Aerodynamic Compensation of the Modified Guided Anti-Tank Missile Configuration,” Scientific Technical Review, vol. 64, no. 1, 2014, pp. 3–12.

    Google Scholar 

  38. Pavic, M., Mandic, S., Cuk, D., Pavkovic, B., “A new type of flight simulator for manual command to lineof-sight guided missile,” Optik-International Journal for Light and Electron Optics, vol. 125, issue 21, November 2014, pp. 6579–6585. doi 10.1016/j.ijleo.2014.06.163

    Google Scholar 

  39. Pontryagin, L. S., and Lohwater, A. J., Ordinary Differential Equations, Addison-Wesley Publishing Company, 1962, chap. 2, § 7, Examples.

    Google Scholar 

  40. Besekerskiy, V.A., Popov, E.P., Theory of automatic control systems, Professiya, Moscow, 2003, (in Russian), chap. 17, § 17.2.

    Google Scholar 

  41. Khalil, H.K., Nonlinear systems, 2nd ed., Prentice Hall, 1996, chap. 3.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Optoelectronics and Laser Engineering, Technical University—Sofia, Branch Plovdiv, 61 Sanct Petersburg Blvd., Plovdiv, 4000, Bulgaria

    Borislav G. Penev

Authors
  1. Borislav G. Penev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Borislav G. Penev.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Penev, B.G. An Expanded Two-Dimensional Proportional–Derivative Command to Line-of-Sight Guidance Law. Gyroscopy Navig. 9, 344–351 (2018). https://doi.org/10.1134/S2075108718040132

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S2075108718040132

Search

Navigation