Abstract:The hemispherical resonator gyroscope (HRG) is currently the most accurate type of vibrating gyroscope. However, manufacturing defects inevitably cause uneven circumferential distribution of parameters such as mass, stiffness, quality factor, density, elastic modulus, and damping in the resonator, leading to frequency splitting and coupling errors between primary and secondary vibrations. Traditional frequency splitting compensation methods often reduce the quality factor and involve high costs and complex operations. In contrast, an electrostatic balance compensation scheme has been proposed, which applies electrostatic forces to different electrodes to adjust the resonator′s stiffness and compensate for frequency splitting. When combined with the NSGA-III multi-objective optimization algorithm, this approach optimizes the compensation parameters while considering the impact on resonator performance, power consumption, and the achievable frequency splitting compensation values. Validation results demonstrate that this method provides optimal compensation for frequency splitting in various resonators and frequency splits, achieving a 50.2% increase in compensation value. It also reduces required compensation voltages by 6.3% and 56.3%, maintaining an accuracy better than 0.5 mHz. After compensation, measurement errors decreased by an order of magnitude, with only a 2.3% reduction in natural frequency. This approach significantly enhances the dynamic performance of gyroscopes and offers valuable insight for optimal frequency splitting compensation in HRGs. It can also be applied to other types of gyroscopes, such as cup and ring gyroscopes.