• Yevgen Aleksandrov Харківський національний автомобільно-дорожній університет, Ukraine https://orcid.org/0000-0001-7525-6383
  • Tetyana Aleksandrova Національний технічний університет «Харківський політехнічний інститут», Ukraine https://orcid.org/0000-0001-9596-0669
  • Alexander Grigoriev Національний технічний університет «Харківський політехнічний інститут», Ukraine https://orcid.org/0000-0002-0155-1694
  • Yaroslav Morhun Національний технічний університет «Харківський політехнічний інститут», Ukraine https://orcid.org/0000-0002-7399-4937




The existing publications that investigate vehicle course stability optimization were analyzed. A mathematical model, which describes the disturbed movement of a car with a tank, was compiled. This model allows to consider the liquid free surface oscillations and determine their effect on the car course stability during constant motion or emergency braking. There was described the main information regarding the car that was used to perform mathematical calculations. An algorithm was developed for deriving the characteristic equation for a complex system of differential equations describing dynamic changes in the movement parameters of a car, oscillations of partial layers of liquid in a tank and the operation of an electromagnetic drive of the control valve and an electronic PID controller for a two-circuit system for ensuring course stability. Based on the developed mathematical model, the influence of forced oscillations of the fluid on the stability area of the system built in the plane of variable parameters of the controller is investigated. It is shown that low-frequency oscillations of the free surface of a liquid lead to a significant reduction in the stability area, which indicates the need to consider such oscillations when solving problems of analysis and synthesis of this system. It was found that for a car with a tank, where low-frequency transverse oscillations of the liquid occur, which are accompanied by a redistribution of mass and disturb the movement, an increase of the speed unambiguously leads to a deterioration in directional stability. That enables exclusion of speed from the number of variable parameters and significantly simplify the problem being solved. The calculations for cases with different loading levels were performed. It was found out that the level of liquid in the tank, considering its relationship with the speed, has an ambiguous effect on the car course stability, and it is unacceptable to limit the research calculations to the case with 50 % load. Instead of this, it is necessary to find a line that bends from above the stability boundaries that correspond to many liquid levels.

Keywords: fluid vibrations; exchange rate stability system; area of stability; tank; PID-controller; parameters.

Author Biographies

Yevgen Aleksandrov, Харківський національний автомобільно-дорожній університет

доктор технічних наук, професор, Харківський національний автомобільно-дорожній університет, професор кафедри автомобілів ім. А. Б. Гредескула; м. Харків, Україна; ORCID: https://orcid.org/0000-0001-7525-6383; e-mail: aleksandrov.ye.ye@gmail.com.

Tetyana Aleksandrova, Національний технічний університет «Харківський політехнічний інститут»

доктор технічних наук, професор, Національний технічний університет «Харківський політехнічний інститут», професор кафедри системного аналізу та інформаційно-аналітичних технологій; м. Харків, Україна; ORCID: https://orcid.org/0000-0001-9596-0669; e-mail: aleksandrova.t.ye@gmail.com.

Alexander Grigoriev, Національний технічний університет «Харківський політехнічний інститут»

доктор технічних наук, професор, Національний технічний університет «Харківський політехнічний інститут», професор кафедри вищої математики; м. Харків, Україна; ORCID: https://orcid.org/0000-0002-0155-1694; e-mail: kpi.mmtt@gmail.com.

Yaroslav Morhun, Національний технічний університет «Харківський політехнічний інститут»

Національний технічний університет «Харківський політехнічний інститут», аспірант, м. Харків, Україна; ORCID: https://orcid.org/0000-0002-7399-4937; e-mail: yarki95@gmail.com.


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How to Cite

Aleksandrov, Y., Aleksandrova, T., Grigoriev, A., & Morhun, Y. (2021). ABOUT THE INFLUENCE OF VIBRATIONS OF THE CONVEYED LIQUID ON THE AREA OF STABILITY OF A CLOSED SYSTEM AUTOMATIC VEHICLE COURSE CONTROL. Bulletin of National Technical University "KhPI". Series: System Analysis, Control and Information Technologies, (1 (5), 29–41. https://doi.org/10.20998/2079-0023.2021.01.05