Electrostatic stiffness correction for quadrature error in decoupled dual-mass MEMS gyroscope

Abstract

This paper proposes an electrostatic stiffness correction method for the quadrature error (QUER) in a decoupled dual-mass gyroscope structure. The QUER is caused by the imperfections during the structure manufacturing process, and the two masses usually have different QUERs. The harm contribution to the Coriolis signal is analyzed and quantified. The generating forms of QUER motion in both masses are analyzed, the correction electrodes' working principle is introduced, and a single mass individual correction method is proposed. The QUER stiffness correction system is designed based on a PI controller, and the experiments are arranged to verify the theoretical analysis. The bias stability decreases from 2.06 to 0.64 deg ∕h after the QUER correction, and the parameters of scale factor such as nonlinearly, asymmetry, and repeatability, reduce from 143, 557, and 210 ppm to 84, 242, and 175 ppm, respectively.

Dual-Mass MEMS Gyroscope Structure, Design, and Electrostatic Compensation

“…The bias stability and scale factor temperature stability enhance from 89 /h and 662 ppm/ Cto17 /h and 231 ppm/ C, respectively, which achieves the correction goal. The quadrature error correction in dual-mass tuning fork MEMS gyro structure is investigated in literature [11], and this work also proves the quadrature stiffness are different in left and right masses. A quadrature error correction closed loop is proposed in the work, and utilizing the coupling stiffness correction method, the masses are corrected separately.…”

“…Most of the literature informs that the dominate signal component in output signal is quadrature error, which is generated in the structure manufacture process, and brings over several 100 S À1 equivalent input angular [9][10][11][12][13][14]. The original source of quadrature is the coupling stiffness, which is modulated by drive mode movement and generates quadrature error force.…”

“…The original source of quadrature is the coupling stiffness, which is modulated by drive mode movement and generates quadrature error force. The force has same frequency but has a 90 phase difference with Coriolis force and stimulates sense mode [11]. Most previous works utilize phase-sensitivity demodulation method to pick Coriolis signal from sense channel [9,13], which requires accurate phase information and longterm, full-temperature range stability.…”

“…However, the demodulation phase error and noise usually exist (sometimes more than 1 [9,12]), which bring undesirable bias. The coupling stiffness drift (the drive and sense modes' equivalent stiffness vary with temperature and generate the drift of coupling stiffness [6,11]) causes the quadrature error force drift, which is considered to be one of the most important reasons leading to bias long-term drift, and is proved by [11,14] experimental work.…”

“…The previous works provide several effective ways to reduce quadrature error and are concluded into three aspects after the structure is manufactured [9,11]: the quadrature signal compensation, the quadrature force correction and coupling stiffness correction. In work [9], the quadrature error is reduced by dc voltage based on synchronous demodulation and electrostatic quadrature compensation method, and the sigma-delta technology is employed in ADC and DAC.…”