Parametric synthesis of the brake pressure control system


Аuthors

Goncharova V. I.

Saint Petersburg State University of Aerospace Instrumentation, 67, Bolshaya Morskaya str., Saint Petersburg, 190000, Russia

e-mail: goncharova_31kaf@bk.ru

Abstract

Automatic control systems (ACS) with distributed parameters are a fairly large and widely used class of systems. The difficulty in researching and constructing mathematical models of such systems lies mainly in their features, namely, that they require taking into account two or more parameters. Hence the name - ACS with distributed parameters. This fact implies the description of a block with distributed parameters by a partial differential equation. Many well-known methods of parametric synthesis, including the generalized Galerkin method, involve the use of ordinary differential equations, which makes it urgent to implement the transition from partial differential equations to ordinary differential equations. The paper implements the transition from hyperbolic partial differential equations to ordinary differential equations using the method of separation of variables (Fourier method), which was first applied to automatic control systems with distributed parameters. Also, the algorithm of parametric synthesis, the well-known generalized Galerkin method, is extended to automatic control systems with distributed parameters, in particular to ACS pressure in the braking system. It is noted in the work that earlier automatic control systems with distributed parameters were synthesized as systems with a delay. A comparison of the operation of the systems is carried out in the case when the control unit is considered as a link of "pure delay", and in the case when the control unit is considered as a link with distributed parameters. In the course of solving the synthesis problem, the parameters of the desired program motion, the discrepancy, and the equation of system dynamics are determined based on the known structure of the synthesized ACS. From the obtained values of the variable parameters of the regulator and the transients of the system, it follows that using the modified generalized Galerkin method (orthogonal projection method), the mathematical model of the block with distributed parameters makes it possible to build a more accurate mathematical model of the control system.

Keywords:

automatic control system, ACS with distributed parameters, method of separation of variables (Fourier), partial differential equations

References

  1. Shishlakov V.F., Goncharova V.I. Parametric synthesis of a nonlinear pulsed automatic control system with distributed parameters. Radiotekhnika. 2024. Vol. 88, No. 8. P. 54-70. (In Russ.). DOI: 10.18127/j00338486-202408-06 
  2. Ostroukh A.V., Pronin C.B., Volosova A.V. et al. Parametric Synthesis of Quantum Circuits for Training Perceptron Neural Networks. Intelligent Technologies and Electronic Devices in Vehicle and Road Transport Complex (TIRVED), November 2022. DOI: 10.1109/TIRVED56496.2022.9965536
  3. Iskhakov A.R., Akbashev V.R. Structural Synthesis of the Computer Vision and Its Parametric Identification with Statistical Estimation of Variational Parameters. Journal of Computational and Engineering Mathematics. 2023. Vol. 10, No. 1.
  4. Goncharova V.I., Shishlakov V.F. Parametric synthesis of linear automatic control systems with distributed parameters. Izvestiya Vuzov. Priborostroenie. 2024. Vol. 67, No. 3. P. 230-240. (In Russ.). DOI: 10.17586/0021-3454-2024-67-3-230-240
  5. Goncharova V.I. Parametric synthesis of a nonlinear automatic control system with distributed parameters. Trudy MAI. 2024. No. 134. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=178476
  6. Nikitin A.V., Shishlakov V.F. Parametricheskii sintez nelineinykh sistem avtomaticheskogo upravleniya: monografiya (Parametric synthesis of nonlinear automatic control systems): monograph. Saint Petersburg: SPbGUAP Publ., 2003. 358 p.
  7. Shishlakov V.F. Synthesis of nonlinear pulsed control systems in the time domain. Izvestiya Vuzov. Priborostroenie. 2003. No. 12. P. 25-30. (In Russ.)
  8. Zaitseva A.A., Belyavtsev M.V., Zaitsev E.A. et al. Synthesis of an algorithm for controlling helicopter engines in conditions of structural and parametric uncertainty. Elektrotekhnicheskie i informatsionnye kompleksy i sistemy. 2024. Vol. 20, No. 2. P. 123-128. (In Russ.). DOI: 10.17122/1999-5458-2024-20-2-123-128 
  9. Gamynin N.S. Gidravlicheskii privod sistemy upravleniya (Hydraulic drive of the control system). Moscow: Mashinostroenie Publ., 1972. 376 p.
  10. Gamynin N.S. Gidravlicheskii sledyashchii privod (Hydraulic tracking drive). Moscow: Mashinostroenie Publ., 1968. 466 p.
  11. Charnyi I.A. Neustanovivsheesya dvizhenie real'noi zhidkosti v trubakh (Unsteady movement of a real liquid in pipes). Moscow: Gostekhizdat Publ., 1951. 224 p.
  12. Goncharova V.I. Programma dlya realizatsii perekhoda ot differentsial'nykh giperbolicheskikh uravnenii v chastnykh proizvodnykh k obyknovennym differentsial'nym uravneniyam. Svidetel'stvo o gosudarstvennoi registratsii programmy dlya EVM № 2023681118 RF (Program for the implementation of the transition from partial differential hyperbolic equations to ordinary differential equations. Certificate of state registration of a computer program No. 2023681118 Russian Federation), 10.10.2023 
  13. Fletcher K. Chislennye metody na osnove metoda Galerkina (Numerical methods based on the Galerkin method). Moscow: Mir Publ., 1988. 352 p.
  14. Zhukhin N.O., Legkaya V.I. Solving the problem of parametric synthesis for self-propelled guns with the speed of a long-component freight train. Byulleten' rezul'tatov nauchnykh issledovanii. 2023. No. 1. P. 170-182. (In Russ.). DOI: 10.20295/2223-9987-2023-1-170-182
  15. Vatutin M.A., Klyuchnikov A.I. A technique for increasing the stability of a nonlinear link with a delay for an auto-oscillatory accelerometer. Trudy MAI. 2022. No. 127. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=170355. DOI: 10.34759/trd-2022-127-22
  16. Uryupin I.V. Modeling and evaluation of connectivity of aviation and railway transport systems of passenger transportation of the Russian Federation. Trudy MAI. 2024. No. 134. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=178479
  17. Ankilov A.V., Vel'misov P.A., Semenov A.S. Reshenie lineinykh zadach matematicheskoi fiziki na osnove metodov vzveshennykh nevyazok (Solving linear problems of mathematical physics based on methods of weighted residuals). Ul'yanovsk: UlGTU Publ., 2010. 179 p. 
  18. Ermakov P.G. Statistical data processing of on-board navigation systems of an unmanned helicopter-type aircraft during landing. Trudy MAI. 2024. No. 138. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=182679
  19. Ermakov P.G., Evdokimenkov V.N., Gogolev A.A. Determination of the angle of inclination of an unequipped landing pad of an unmanned helicopter aircraft based on information from a digital terrain map. Trudy MAI. 2023. No. 132. (In Russ.). URL: https://trudymai.ru/eng/published.php?ID=176860. DOI: 10.34759/trd-2023-132-23 
  20. Elsukov V.S., Lachin V.I., Pavlov V.V. Synthesis of control systems with alternating compensating feedback in conditions of limited uncertainty. Izvestiya vysshikh uchebnykh zavedenii. Elektromekhanika. 2020. Vol. 63, No. 5. P. 40-45. (In Russ.). DOI: 10.17213/0136-3360-2020-5-40-45
  21. Kornyushin YU.P. Synthesis of robust regulators for nonlinear tracking systems. Naukoemkie tekhnologii. 2020. Vol. 21, No. 6. P. 63-69. (In Russ.). DOI: 10.18127//j19998465-202006-10
  22. Mikhailenko L.A., Rusin D.S., Ustimenko V.V., Chubar' A.V. Parametric synthesis of the regulator by a metaheuristic algorithm in the SimInTech environment. Kosmicheskie apparaty i tekhnologii. 2020. Vol. 4, No. 3 (33). P. 171-177. (In Russ.). DOI: 10.26732/j.st.2020.3.05
  23. Fel'ker M.N., Bakhtereva K.D. Development of an automatic control system for the flotation process of potassium chloride. Vestnik Yuzhno-Ural'skogo gosudarstvennogo universiteta. Seriya: Komp'yuternye tekhnologii, upravlenie, radioelektronika. 2021. Vol. 21, No. 1. P. 147-158. (In Russ.). DOI: 10.14529/ctcr210113
  24. Parshukov A.N. Technology for improving robust quality of control for one-dimensional linear discrete control systems with structural-parametric uncertainty. Tomsk State University Journal of Control and Computer Science. 2024. No. 67. P. 12-21. (In Russ.). DOI: 10.17223/19988605/67/2
  25. Eremin E.L., Smirnova S.A., Shelenok E.A. Structural-parametric synthesis of a hybrid periodic system of combined control of a multimode object under conditions of uncertainty. Mekhatronika, avtomatizatsiya, upravlenie. 2024. Vol. 25, No. 9. P. 447-457. (In Russ.). DOI: 10.17587/mau.25.447-457
  26. Malev N.A. Synthesis of a parametrically invariant tracking electric drive using the method of restoring model parameters. Izvestiya vysshikh uchebnykh zavedenii. Problemy energetiki. 2023. Vol. 25, No. 2. P. 40-57. (In Russ.). DOI: 10.30724/1998-9903-2023-25-2-40-57


Download

mai.ru — informational site MAI

Copyright © 2000-2025 by MAI

 Вход