Zubov's optimum damping method in the control problem of one gyroscope system

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.