Geodesic
Zubov's optimum damping method in the control problem of one gyroscope system
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 2, pp. 278-284

Voir la notice de l'article provenant de la source Math-Net.Ru

The article considers the control problem of the aircraft cabin simulator with a four-axis gimbal gyroscopic system. The difficulty of the control problem of standard three-axis gimbal gyroscopic system is the presence of the phenomena ‘`gimbal lock’’ when the two axes of the system become collinear or close to collinear. One of the applied solutions to avoid "gimbal lock’’ is to use of the fourth additional gimbal. Such fore-axis gimbal systems are presented in the works of various autors. However, the problem of an optimal control of four-axis gimbal gyroscopic system is still under the question. Sufficient conditions for the solvability of the control problem are obtained on the base of the one-to-one interconnection between the movement of the cabin, the angular velocities of the cabin axes and the necessary deviations of gimbals rotation angles. This result is presented in lemmas. According this obtained sufficient conditions, the algorithm for constructing a control of the gimbal system in terms of optimal damping process of movement, according to Zubov’s method, is proposed.
Keywords: dumping, optimal control, gyroscope, rotation control. 
@article{VSPUI_2022_18_2_a7,
     author = {A. P. Zhabko and N. A. Zhabko and P. V. Yakovlev},
     title = {Zubov's optimum damping method in the control problem of one gyroscope system},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {278--284},
     publisher = {mathdoc},
     volume = {18},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a7/}
}
TY  - JOUR
AU  - A. P. Zhabko
AU  - N. A. Zhabko
AU  - P. V. Yakovlev
TI  - Zubov's optimum damping method in the control problem of one gyroscope system
JO  - Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
PY  - 2022
SP  - 278
EP  - 284
VL  - 18
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a7/
LA  - ru
ID  - VSPUI_2022_18_2_a7
ER  - 
%0 Journal Article
%A A. P. Zhabko
%A N. A. Zhabko
%A P. V. Yakovlev
%T Zubov's optimum damping method in the control problem of one gyroscope system
%J Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ
%D 2022
%P 278-284
%V 18
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a7/
%G ru
%F VSPUI_2022_18_2_a7
A. P. Zhabko; N. A. Zhabko; P. V. Yakovlev. Zubov's optimum damping method in the control problem of one gyroscope system. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, Tome 18 (2022) no. 2, pp. 278-284. http://geodesic.mathdoc.fr/item/VSPUI_2022_18_2_a7/