全差分频率调制半球谐振陀螺装配误差辨识及补偿方法

doi:10.7527/S1000-6893.2025.32079

Abstract

Abstract:

To address the performance degradation of fully differential frequency-modulated Hemispherical Resonator Gyroscope （HRG） caused by assembly errors， this paper proposes a synchronous identification and compensation method for assembly errors based on nonlinear optimization from a signal processing perspective. First， a systematic correlation model between the assembly attitude errors and channel coupling errors under the time-division multiplexing control scheme is established， and the influence mechanisms of installation tilt and installation eccentricity on channel coupling errors are analyzed. On this basis， a dynamic output model of the HRG incorporating channel coupling errors is developed， revealing the coupling effect between the carrier rotation rate and the harmonic components of the gyroscope output. Finally， a synchronous identification and compensation method for assembly errors based on nonlinear optimization is proposed. Experimental results demonstrate that after compensating for assembly errors， the scale factor nonlinearity and circumferential drift stability of the gyroscope are reduced by 91.97% and 51.25%， respectively， reaching only 6.94×10^-7 and 0.398 （°）/h. This method significantly improves the gyroscope’s performance in both dynamic and static environments， providing theoretical support for the design and optimization of the high-precision HRG.

Key words: hemispherical resonator gyroscope, assembly errors, frequency-modulation, time-division multiplexing, error identification and compensation

CLC Number:

V241.5

Ruiqi WANG, Guoxing YI, Weinan XIE, Zhennan WEI, Shengwei DONG. Identification and compensation method for assembly errors in fully differential frequency-modulated hemispherical resonator gyroscope[J]. Acta Aeronautica et Astronautica Sinica, 2026, 47(5): 332079.

Figures/Tables 23

Fig.1

Fig.2

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Fig.4

Fig.5

Fig.6

Fig.7

Table 1

Structure and electrical parameters of HRG

参数	数值	参数	数值
R₁/mm	10.4	R₂/mm	11.13
f₀/Hz	7 500	θ_ω /（°）	17
∆f/Hz	0.001	m₀/g	2.5
τ/s	500	$∆$ （1/τ）	0
k	-0.554 0	a₀/V	5
V_dc /V	200	d/μm	25
φ/（"）	80	θ_φ /（°）	0
Δρ/μm	50 μm	θ_b /（°）	45

Table 1

Fig.8

Fig.9

Table 2

Table 3

Fig.10

Fig.11

Fig.12

Fig.13

Table 4

Table 5

Table 6

Fig.14

Fig.15

Table 7

Table 8

References 40

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转速/（（°）·s^-1）	增益误差/10^-4	辨识结果/10^-4	辨识误差/10^-7	相对误差/%
±200	9.90	9.894 154	5.85	0.059 0
±250	9.90	9.894 137	5.86	0.059 2
±300	9.90	9.894 154	5.85	0.059 0
±350	9.90	9.894 141	5.86	0.059 2
±400	9.90	9.894 105	5.89	0.059 5

转速/（（°）·s^-1）	失准角/（°）	辨识结果/（°）	辨识误差/10^-5 （°）	相对误差/%
±200	-0.031 0	-0.031 015 5	-1.55	0.050 0
±250	-0.031 0	-0.031 015 1	-1.51	0.048 8
±300	-0.031 0	-0.031 015 4	-1.54	0.049 7
±350	-0.031 0	-0.031 015 3	-1.53	0.049 2
±400	-0.031 0	-0.031 014 8	-1.48	0.047 9

转速/（（°）·s^-1）	补偿前辨识结果	补偿后辨识结果	误差减小率/%
±200	-0.002 334	-1.519×10^-5	99.349
±250	-0.002 341	7.559×10^-8	99.997
±300	-0.002 329	9.972×10^-6	99.572
±350	-0.002 335	6.910×10^-7	99.970
±400	-0.002 339	5.405×10^-6	99.769
平均值	-0.002 336	-6.236×10^-6	99.731

转速/（（°）·s^-1）	补偿前辨识结果/（°）	补偿后辨识结果/（°）	误差减小率/%
±200	0.037 50	8.975×10^-5	99.761
±250	0.037 59	1.606×10^-4	99.573
±300	0.037 18	-3.626×10^-4	99.025
±350	0.037 39	5.169×10^-6	99.986
±400	0.036 95	-4.338×10^-4	98.826
平均值	0.037 32	-1.082×10^-4	99.434

误差参数	本方法	文献［26］	文献［27］
增益误差	-0.002 336	-0.002 340	-0.002 334
失准角/（°）	0.037 32	0.037 34	0.037 29

Identification and compensation method for assembly errors in fully differential frequency-modulated hemispherical resonator gyroscope

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Figures/Tables 23

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陀螺编号	谐振频率/Hz	频率裂解/Hz	品质因数
1	7 060	9.04×10^-4	1.18×10⁷
2	8 168	1.85×10^-3	1.59×10⁷
3	7 072	4.43×10^-4	1.46×10⁷

陀螺编号	陀螺参数	补偿前	补偿后
1	增益误差	-0.001 95	1.20×10^-5
	失准角/（°）	0.014 5	-8.88×10^-6
	标度因数非线性/10^-6	7.100	0.847
	周向漂移稳定性/（（°）·h^-1）	0.262	0.138
2	增益误差	0.001 98	6.52×10^-7
	失准角/（°）	0.017 3	-3.20×10^-5
	标度因数非线性/10^-6	8.966	1.016
	周向漂移稳定性/（（°）·h^-1）	0.517	0.342
3	增益误差	0.002 84	-6.08×10^-6
	失准角/（°）	0.013 3	-3.66×10^-5
	标度因数非线性/10^-6	8.278	1.571
	周向漂移稳定性/（（°）·h^-1）	0.785	0.508