Control of a reservoir partially filled with liquid based on Gauss's principle of least constraint (deceleration task)


  • O. V. Konstantinov Institute of Mathematics of NAS of Ukraine, 01601, Kyiv, Tereshchenkivska str., 3



The task of constructing control for the motion of a given reservoir - a liquid with a free surface mechanical system is provided in the presence of constant perturbations - the oscillations of the free surface of the liquid. To construct the control, the principle of the least coaxing of Gauss was used, which allows to minimize the control load and implement the given laws of the software movement. The control calculation was carried out on the basis of a simplified linear model with two degrees of freedom, which allowed the control function to be obtained in analytical form for various software laws (including nonlinear) movement of the reservoir and free surface of the liquid. The tank partially filled with a liquid, which initially moves evenly at a given speed, must be completely stopped at a given time. The control, constructed for the implementation of linear software laws of motion, can be used only to provide "comfortable" movements of the reservoir, that is, in the absence of large disturbances of the free surface of the liquid. In order to ensure the movement of the reservoir in the presence of highly intense loads, it is necessary to introduce nonlinear software motion laws for obtaining and using a nonlinear control law.

Key words: Gauss’s principle, program movement.

Pages of the article in the issue: 86-89

Language of the article: Ukrainian


HALIULLIN, A. (1987) Postroenie system programnogo dvigenija. Moskva: Nauka.

LIMARCHENKO, O., YASINSKII, V. (1997) Nelinejnaya dynamika konstrukcij s gidkostij. Kiev: NTTU KPI.


How to Cite

Konstantinov, O. V. (2019). Control of a reservoir partially filled with liquid based on Gauss’s principle of least constraint (deceleration task). Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 86–89.



Differential equations, mathematical physics and mechanics