V. ZUBOV’S OPTIMUM DAMPING METHOD IN THE CONTROL PROBLEM OF ONE GYROSCOPE SYSTEM

IF 0.3 Q4 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya Pub Date : 2022-01-01 DOI:10.21638/11701/spbu10.2022.208

A. P. Zhabko, Natalya A. Zhabko, P. Yakovlev

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Abstract

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.

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一类陀螺仪系统控制问题中的zubov最优阻尼法

研究了采用四轴框架陀螺仪系统的飞机座舱模拟器控制问题。标准三轴框架陀螺仪系统控制问题的难点在于系统两轴共线或接近共线时存在“框架锁”现象。避免“万向节锁定”的解决方案之一是使用第四个额外的万向节。这种前轴框架系统在许多作者的著作中都有介绍。然而，四轴框架陀螺仪系统的最优控制问题仍然是一个有待解决的问题。在座舱运动、座舱轴角速度和万向架转动角度的必要偏差一一对应的基础上，得到了控制问题可解的充分条件。这个结果用引理表示。根据得到的充分条件，根据Zubov方法，构造了基于运动最优阻尼过程的云台系统控制算法。

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来源期刊

Vestnik Sankt-Peterburgskogo Universiteta Seriya 10 Prikladnaya Matematika Informatika Protsessy Upravleniya MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

1.30

自引率

50.00%

发文量

期刊介绍： The journal is the prime outlet for the findings of scientists from the Faculty of applied mathematics and control processes of St. Petersburg State University. It publishes original contributions in all areas of applied mathematics, computer science and control. Vestnik St. Petersburg University: Applied Mathematics. Computer Science. Control Processes features articles that cover the major areas of applied mathematics, computer science and control.