摘要
船用惯性导航或平台罗经等导航系统中 ,常常用高精度二自由度陀螺稳定平台 .这些系统在启动时 ,由于陀螺的定轴性和船的摇摆 ,陀螺框架会激烈地撞击止档 ,从而影响陀螺的精度 .为此 ,在系统中施加反馈回路把主轴限制在零位附近 .这些回路称为约束回路 .陀螺启动过程中 ,陀螺的惯性矩是变化的 ,而且由于陀螺特性 ,每一个陀螺的两条约束回路是相互耦合的 .所以 ,二自由度陀螺的约束回路是一个相互耦合的时变控制系统 .本文从二自由度陀螺的技术方程出发推导了系统的状态空间模型 ,用李亚普诺夫直接法分析约束回路的稳定性问题 ,并用变量梯度法找到了李亚普诺夫函数 ,从而得出了回路的稳定性条件 .由于陀螺的启动时间比约束回路的时间常数大得多 ,因而仿真结果和实验室试验结果都说明 ,只要根据时变参数不断修改稳定条件 ,就可以使系统稳定 ,从而解决了一种特殊时变系统的稳定性问题 .
In shipboard inertial navigation systems or stabilized gyrocompasses, Two_Degree_of_Freedom(TDF) gyros of high precision are often used to stabilize the platform. During starting process of the system, the gyro gimbals will bump against the stop bins because of gyro's property and ship swinging, which will seriously ruin gyro's accuracy. Feedback loops are applied to restraining the gimbals within the two stop bins, wherefore the loops are called restraint loops. When the gyro is turned on, it's momentum H varies and restraint loops are coupled due to gyro's property. Therefore, the two restraint loops of a TF gyro compose a coupled, time_varying control system. In the paper, the state model of the system was derived based on the technical functions of a TDF gyro. The stability of the restraint loops was analyzed via Lyapunov direct method. From variable gradient method, the Lyapunov function V was found, whereby the stability conditions of the system were obtained. Since the starting process of a TDF gyro is much longer than the time constant of the restraint loops for the time_varying system, it can be stabilized as long as the stability conditions are satisfied step by step, which is just the conclusion from the computer simulations and the lab tests as well.
出处
《哈尔滨工程大学学报》
EI
CAS
CSCD
2000年第3期7-11,共5页
Journal of Harbin Engineering University
关键词
陀螺约束回路
稳定性
李亚普诺夫法
分析
two_degree of freedom gyro
Lyapunov stability criterion
varaible gradient method
