Influence of drive loop noise on detection loop

Through the analysis of the whole measurement and control system of gyroscope, we can know that the influence of the gyroscope driving loop on the detection loop is mainly concentrated in two aspects. One is to drive the output of the PLL in the loop, and the phase signal of the output of the PLL will affect the detection loop as the reference of phase-sensitive demodulation in the detection loop; The second is the amplitude of the drive displacement. According to the Coriolis effect, the amplitude of the drive displacement is a variable in the Coriolis force expression, and the noise superimposed on the amplitude of the drive displacement will directly affect the Coriolis force and eventually affect the output of the detection channel.

When discussing the influence of drive loop noise on the detection loop, this paper mainly considers the influence of the second factor, focusing on the noise superimposed on the drive displacement amplitude after the noise is driven by the silicon micromechanical gyroscope mode, that is, Nx(t) in Figure 1, which will directly affect the detection loop.

Firstly, the influence of noise sources Nefx(t) and Nmx(t) is studied, and the power spectral density diagram of Nefx(t) and Nmx(t) can be drawn, as shown in Figure 2.

Figure 2 Power spectral densities of Nefx(t) and Nmx(t)

It can be seen from Figure 2.1 that 1/ƒ noise plays a dominant role in the low frequency band, while white noise plays a dominant role in the high frequency band. The frequency ƒ0, which intersects the two noises, is called the transition frequency, usually within tens of Hertz. As can be seen from Figure 2.1, Nmx(t) is pure white noise, and the power spectral density of white noise is a straight line in the whole frequency band.

Next, the driving force noise Na(t) is analyzed, and its power spectral density can be obtained according to the formula shown in Figure 3.

Figure 3. Na(t) power spectral density

It can be seen from the figure that near the gyroscope drive resonant frequency of ƒx, the influence of 1/ƒ noise can be ignored and can be approximately regarded as white noise, and the noise energy is the superposition of mechanical thermal noise and electronic thermal noise amplified by the torturer.

The driving force noise Na(t) next drives the mode through the gyroscope, and the transfer function of the gyro-driven mode is:

By substituting the actual parameters of the gyroscope into the transfer function, the Bod diagram curve near the gyroscope driving resonant frequency is shown in Figure 4. As can be seen from the figure, signals near the resonant frequency are significantly amplified after passing through the gyroscope drive mode, while signals farther away from the resonant frequency are suppressed after passing through the drive mode, and signals at the resonant point show a phase shift of -Π/2. The gyroscope drive mode shows obvious band-pass characteristics, which can be approximated as an ideal bandpass filter, and the larger the Qx, the narrower the bandpass filter bandwidth, the larger the resonance peak, and the stronger the anti-interference ability.

Figure 4 MEMS gyroscope drive mode baud diagram

The power spectral density of the output Nx(t) after the noise is driven by the gyro mode is as follows:

The above formula is the bilateral power spectral density function of the total noise Nx(t) whose driving mode of the gyroscope affects the detection mode, and its schematic diagram is shown in Figure 5.

Figure 5 Nx(t) power spectral density

It can be seen from the diagram that when the noise frequency is at the driving resonance frequency, the response will peak. Since the gyroscope drive mode can be viewed as an ideal bandpass filter, and the noise can be approximately viewed as white noise before the input drive mode, Nx(t) can ultimately be viewed as a zero-mean narrow-band white noise.

Drive loop noise model simulation

Figure 6 Simulation model of drive loop noise

In the noise model, a white noise module is used to represent mechanical thermal noise, a white noise module plus an integral module is used to represent 1/ƒ noise, and a white noise module is superimposed on the basis of 1/ƒ noise to represent circuit noise. The parameters in Table 1 are replaced into the model for simulation. According to the analysis in the previous section, it mainly focuses on the output of the drive mode, that is, the noise on the drive amplitude. Then, the sampling time of the simulation model is set to 10-6s, the sampling number is set to 107, and the output drive_x in the model is sampled. The power spectral density was obtained by FFT transformation, as shown in Figure 7.

Figure 7 Power spectrum density of drive displacement noise simulation

As can be seen from Figure7, the noise on the drive amplitude has an obvious peak value at the drive resonance frequency, and the simulation results are consistent with the theoretical analysis.

Conclusion

In this paper, the noise model of the drive loop is established for the noise source in the measurement and control system, and then the noise model of the drive loop is analyzed through the power spectral density function, and the influence of the drive noise on the detection and control loop is emphatically discussed, and the expression of the noise superimposed on the drive displacement amplitude is obtained. Finally, the noise model of the drive loop is modeled, and the simulation results are consistent with the theoretical analysis.

Ericco is a professional research and development team for MEMS gyroscope, mainly for tactical and navigation grade MEMS gyroscope, such as the navigation grade ER-MG2-50/100, whose zero bias instability can reach 0.01-0.02°/hr. The tactical grade ER-MG2-069 has zero bias instability <0.1°/h.

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