Automatic Mode-Matching and Scale Factor
Adjustable Detection System for Force to Rebalance
Control of Cobweb-Like Gyroscopes
Mengmeng Cheng, Shuwen Guo*, Bo Fan, Quan Wan, Zuxiang Wen, Dacheng Xu
School of Electronic and Information Engineering, Soochow University, Suzhou, China
13862044796@163.com
Abstract—An automatic mode-matching circuit and scale
factor adjustable detection system for force to rebalance cobweb-
like disk resonator gyroscopes (DRG) are presented in this work.
The mode-matching circuit uses a phase detection system to
track and control phase difference between output signal of drive
mode and quadrature error to match the mode resonance
frequencies, which results in a significant performance
improvement. Besides, a new scale factor adjustment method is
proposed, which could be used in force to rebalance detection
system of cobweb-like DRG. The experimental results show that
the scale factor of gyroscope with closed loop controlled sense
mode improves from 7.9mV/°/s to 19.1mV/°/s, and the bias
instability improves from 11.19°/hr to 0.43°/hr.
Keywords—disk resonator gyroscopes; mode match; scale
factor adjustable
I. INTRODUCTION
The silicon micro-gyroscope plays an irreplaceable role in
the field of sensors, such as navigations, automobile and
military applications, because of its small size, light weight,
low cost and mass production. Generally, the gyroscope
operates at n=2 wineglass mode. The principle of gyroscope is
to realize the energy conversion between drive and sense
modes by Coriolis force, which is proportional to the angular
rate. So the angular rate can be obtained by measuring the
Coriolis force. Due to inevitable mismatching tolerance, there
is always a frequency split between the drive and sense modes,
which degrades energy conversion efficiency of Coriolis force
and effective quality factor. So far various methods have been
studied to reduce those frequency discordances. Some of them
tune the frequency through special manufacturing processes
[1]-[2], These methods fix the resonant frequency of gyroscope
once the manufacturing process is finished. Other methods are
trying to tune the frequency through negative electrostatic
effect. Reference [3] minimizes the frequency split by applying
tuning voltages manually, which is too laborious to achieve the
mode-matched condition. An automatic CMOS mode-
matching circuit is proposed in [4] by seeking the maximum
value of quadrature error automatically, while this method
needs a long time to find the maximum point. And in [5], the
neural network algorithm is applied to the automatic mode-
matching circuit, which can eliminate the frequency split more
accurately in a brief time because of its real time property.
However, such a method requires a large amount of data for
learning and training, which is not suitable for mass production.
Besides, the most common circuit to detect the angular rate at
present is the force to rebalance detection circuit, while most of
them focus on the bandwidth and stability of system [6]-[7].
There is little research on scale factor adjustment technique in
force to rebalance control loop.
In this work, a mode-matching circuit based on phase
difference detection technique [8] together with a dual carrier
modulation interface circuit are used to improve the signal to
noise ratio (SNR) of cobweb-like DRG. Besides, a new scale
factor adjustment method by introducing a decay factor in
force to rebalance control loop is proposed and demonstrated.
II. D
EVICE ARCHITECTURE
A schematic diagram of the proposed cobweb-like DRG is
depicted in Fig.1a.
Spoke
Beam
Lumped Mass
Anchor
(a) (b)
Tuni ng
electrodes
Fig. 1. (a) Schematic top view of cobweb-like DRG. (b) Elliptical flexural
modes of drive and sense modes of this gyroscope simulated by COMSOL.
The resonator consists of 10 concentric sixteen sided
cobweb rings connected through 8 alternating spokes to a
single central anchor, which is fixed tightly. The outer most
ring with 3900m diameter and central anchor whose diameter
is 1700m. Lumped mass pieces are hanged on odd layers of
rings and even layers of spokes from inner to outer to achieve
large proof mass [9]. The resonator is surrounded by 16
external electrodes for frequency tuning and quadrature
nulling , and capacitive gap is 7.5 μm. There are eight separate
polygon slots on each circle and the slots are inserted with
internal double electrodes to increase driving and sensing
Supported by the key projects of National Natural Science Foundation of
China under Grant No. 61434003.
978-1-5386-4707-3/18/$31.00 ©2018 IEEE