Resonance type gyro stability analysis method

Abstract

The present invention discloses a resonance type gyro stability analysis method, which comprises the following three basic steps: (1) establishing the dynamic model of a resonance type gyro; (2) drawing the stability parameter region distribution map of the resonance type gyro; and (3) determining the stability parameter range of the resonance type gyro. According to the present invention, the coefficient of the resonance type gyro dynamic model is the rapid varying function of the time, and the vibration caused by the parameter change is named the parameter excitation characteristic equation; according to the stability analysis method of the resonance type gyro, the stability parameter region distribution map of the resonance type gyro is obtained by using the small parameter method based on the dynamic model, the two Lyapunov functions of the resonance type gyro dynamic model are established, and the stability of the gyro dynamic model is adopted as the conversion condition so as to achieve the parameter value range of the stable working of the gyro; and the method overcomes the influence of the parameter excitation on the stable working of the gyro, achieves the steady state output of the resonance type gyro, extends the application scope, and can further be used for the stability analysis of other resonance type sensors.

Description

technical field [0001] The invention belongs to the technical field of inertia, relates to a resonant gyroscope, in particular to a stability analysis method of a direct frequency output resonant gyroscope, which is suitable for medium and low-precision low-cost navigation systems and positioning and orientation systems. Background technique [0002] The resonant gyroscope uses the principle of resonance as the detection mechanism of the gyroscope. This gyroscope directly detects the change of the resonant frequency of the resonator to detect the angular velocity, and the frequency output characteristic is a parameter excitation dynamic characteristic, which is characterized as a variable coefficient parameter excitation linear differential equation. [0003] Based on the existing analysis, the stability interval of linear differential equations excited by variable coefficient parameters is a series of discrete intervals, and the distribution of intervals presents strong non...

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Problems solved by technology

The third type of method is to apply the Lyapunov stability theory. The limitation of this method is that it is required to find an appropriate Lyapunov function

For regular systems it is possible to use the Hamilton function, but for other systems the Lyapunov function may not be found

Using this method, one can qualitatively determine the stability of the system over a large range, but cannot quantitatively determine the response of the system

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