Effects of Nonlinearity on the Angular Drift Error of an Electrostatic MEMS Rate Integrating Gyroscope

Abstract

Electrostatic MEMS coriolis vibratory gyroscopes (CVG) are essentially nonlinear because of the capacitive transducers employed for the excitation and detection of resonance vibration. This paper investigates the influence of nonlinearity on the precession angle dependent bias error of a MEMS rate integrating gyroscope (RIG) and proposes a novel correction to minimize this effect. A linear model of CVGs is commonly used in the dynamic analysis and control of MEMS RIGs. The linear model predicts a 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> harmonic angular drift error due mainly to non-proportional damping. However, experimental results from previous work demonstrate the existence of an additional 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> harmonic component in the precession rate, and in the resonant frequency and quadrature control. The analysis and removal of this high-order error term will further improve the accuracy of the RIG. Here, it is shown that high-order angularly modulated drift error is the result of nonlinear damping, and the stiffness nonlinearity is responsible for the 4 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">th</sup> harmonics present in the fluctuation of the operating frequency and in the control for quadrature nulling. It is understood that nonlinear damping may be introduced electrically by the energy sustain state feedback control that uses nonlinear capacitive measurements. Nonlinearity correction is proposed to the capacitive displacement detection that significantly reduces the high-order drift error. Simulation and experimental results are provided to validate the analysis. A DSP controlled MEMS RIG with nonlinearity correction exhibits an angular drift error of less than 0.2 deg/s.