Bias Modulation of Force-to-Rebalanced Micro Hemispherical Resonator Gyroscope Based on Mode-Rotation

Abstract

This paper presents a bias modulation method for the force-to-rebalanced (FTR) micro hemispherical resonator gyroscope ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> HRG) based on the mode-rotation, which is achieved by regulating the gyroscope’s drive and sense modes revolving at an assigned rate. The <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> HRG output under the mode-rotation includes the sinusoidally modulated bias and a rotation-induced DC bias. Accordingly, the alternating mode-rotation is proposed to chop the DC rate bias into square waves. By this approach, errors in the DC component from the scale factor drift are also modulated. The open-loop and closed-loop relationships between the rotation actuating force and the mode-rotation rate are investigated by theoretical analyses and numerical simulations. The lower and upper bounds of the rotation rate and the alternating frequency are discussed under the considerations of the error changing rate, the forcer capacity, the maximum voltage, the resonator momentum, and the measurement range. In addition, the controllers in the amplitude, quadrature, and inclination loops utilize the proportional-integral-resonance (PIR) regulating law to suppress the sinusoidal-varying errors introduced by the assigned rotation. The proposed bias modulation method was experimentally verified by a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> HRG with an FPGA platform. The results suggest the alternating mode-rotation improved the bias temperature coefficient by 12 times over the rotation-free FTR architecture. For a three-hour measurement at room temperature, the rate-integration of the mode alternately rotated FTR was within 50 degrees. In comparison, the rate-integration of the rotation-free FTR diverged over 600 degrees due to the bias drift. The presented bias modulation method can be utilized in axisymmetric gyroscopes, such as hemispherical, ring/disk, quad-mass gyroscopes, etc.