Mathematical model control loop guidance system of radio beam riding

Аuthors

Burenko E. A.

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

e-mail: super.evgeny-burenko2012@yandex.ru

Abstract

The purpose of this article is to review the theoretical principles and practical methods for constructing a mathematical model of the control loop of a radio beam riding guidance system using modern computer simulation programs Mathcad and MATLAB – Simulink. The principles of constructing mathematical models of the control loop for a radio beam riding guidance system of a guided missile when aiming at a target by the method of combination (target covering) using modern computer simulation programs Mathcad and MATLAB – Simulink are considered. The construction of a model in the Mathcad environment using the method of numerical solution of a system of differential equations describing the control loop (modeling as a solution to the Cauchy problem), as well as the construction of a simulation model in the MATLAB environment – Simulink based on the mathematical apparatus of functional links, is considered. The modeling of the processes of missile guidance to an air target performing a maneuver with a given normal overload has been carried out. The trajectory of the control point, missile and target, obtained as a result of modeling, as well as the main phase variables of the model characterizing the process of aiming the missile at the target, are presented. The capabilities of the corresponding computer programs in modeling guidance systems are shown. The practical value of the work also lies in the possibility of using the developed mathematical models in the educational process for students to master the principles of construction and operation of guidance systems, as well as to develop the skills of mathematical modeling of the corresponding systems.

Keywords:

radio control system, guidance, beam riding guidance, radio beam riding, beam riding guidance system, control loop, guidance loop, guided missile, Cauchy problem, mathematical modeling, simulation modeling, computer modeling

References

1. Sokolovskii G.A. Proektirovanie upravlyaemykh raket klassa “vozdukh – vozdukh” (Design of guided air-to-air missiles) in 2 parts. Moscow, Izd-vo GosMKB “Vympel”, 2005, 1168 p.

2. Kanashchenkov A.I., Merkulov V.I. Aviatsionnye sistemy radioupravleniya. Sistemy komandnogo radioupravleniya. Avtonomnye i kombinirovannye sistemy navedeniya (Aviation radio control systems. Command radio control systems. Autonomous and Combined Guidance Systems), Moscow, Radiotekhnika, 2004, vol. 3, 320 p.

3. Veitsel' V.A., Volkovskii A.S., Volkovskii S.A. et al. Radiosistemy upravleniya (Radio control systems), Moscow, Drofa, 2005, 416 p.

4. Veitsel' V.A. Radiosistemy i kompleksy upravleniya (Radio Systems and Control Complexes), Moscow, Vuzovskaya kniga, 2016, 574 p.

5. Bykov A.V., Nesterov S.V. Modelirovanie radiosistem upravleniya (Modeling of radio control systems), Volgograd, Izd-vo VolGU, 2013, 247 p.

6. Mazepa R.B., Dogaev A.V. Modelirovanie i otsenka effektivnosti radiosistem upravleniya (Modeling and efficiency assessment of radio control systems). Moscow, Goryachaya liniya – Telekom, 2019, 182 p.

7. Tolpegin O.A., Kashin V.M., Novikov V.G. Matematicheskie modeli sistem navedeniya raket (Mathematical models of missile guidance systems), Saint Petersburg, Baltiiskii gosudarstvennyi tekhnicheskii universitet, 2016, 154 p.

8. Bukhalev V.A. Osnovy avtomatiki i teorii upravleniya (Fundamentals of automation and control theory), Moscow, VVIA im. professora N.E. Zhukovskogo, 2006, 406 p.

9. Litvinova D.V. Informatsionno-izmeritel'nye i upravlyayushchie sistemy, 2020, vol. 18, no. 4, pp. 43 – 48. DOI: 10.18127/j20700814-202004-05

10. Kristalinskii V.R., Konstantinov G.V. Sistemy komp'yuternoi matematiki i ikh prilozheniya, 2020, no. 21, pp. 52 – 58.

11. Bykov A.V., Kharitonov V.V. Osnovy matematicheskogo modelirovaniya radioelektronnykh ustroistv (Fundamentals of mathematical modeling of radio-electronic devices), Volgograd, Izd-vo VolGU, 2012, 232 p.

12. Borisov Yu.P., Tsvetnov V.V. Matematicheskoe modelirovanie radiotekhnicheskikh sistem i ustroistv (Mathematical modeling of radio engineering systems and devices), Moscow, Radio i svyaz', 1985, 176 p.

13. Kulikovskii A.A. Spravochnik po radioelektronike (Handbook of radio electronics), Moscow, Izd-vo “Energiya”, 1970, vol. 3, 816 p.

14. Davydov Yu.T., Danich Yu.S., Zhukovskii A.P. et al. Radiopriemnye ustroistva (Radio receiving devices), Moscow, Vysshaya shkola, 1989, 342 p.

15. Amosov A.A., Dubinskii Yu.A., Kopchenova N.V. Vychislitel'nye metody dlya inzhenerov (Computational Methods for Engineers), Moscow, Vysshaya shkola, 1994, 544 p.

16. Burenko E.A. Mezhdunarodnyi nauchno-issledovatel'skii zhurnal, 2021, no. 7 (109), Ch. 1, pp. 48 – 68. DOI: 10.23670/IRJ.2021.109.7.008

17. Burenko E.A. Mezhdunarodnyi nauchno-issledovatel'skii zhurnal, 2021, no. 5 (107), Ch. 1, pp. 40 – 60. DOI: 10.23670/IRJ.2021.107.5.007

18. Semyashkina M.A., Koshkin D.V. XXXVII studencheskaya mezhdunarodnaya nauchno-prakticheskaya konferentsiya “Nauchnoe soobshchestvo studentov: Mezhdistsiplinarnye issledovaniya”: sbornik statei. Novosibirsk, Sibirskaya akademicheskaya kniga, 2018, no. 2 (37), pp. 73 – 78.

19. Morozov A.Yu., Reviznikov D.L. Trudy MAI, 2016, no. 89. URL: https://trudymai.ru/eng/published.php?ID=73407

20. Fadin D.A. Trudy MAI, 2015, no. 80. URL: https://trudymai.ru/eng/published.php?ID=57021

21. Kalyagin M.Yu., Voloshin D.A., Mazaev A.S. Trudy MAI, 2020, no. 112. URL: https://trudymai.ru/eng/published.php?ID=116625. DOI: 10.34759/trd-2020-112-20

22. Gus'kov A.A., Spirin A.A., Norinskaya I.V. Trudy MAI, 2020, no. 111. URL: https://trudymai.ru/eng/published.php?ID=115157. DOI: 10.34759/trd-2020-111-14

23. George M. Siouris. Missile Guidance and Control Systems. New York, Springer, 2004. 681 p.

24. Tatarchenko A.E. Upravlyaemye snaryady i rakety (Guided projectiles and missiles), Moscow, Izd-vo DOSAAF, 1962, 88 p.

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