MEMS gyroscope with frequency regulation and electrostatic cancellation of the quadrature error
A MEMS gyroscope, wherein a suspended mass is mobile with respect to a supporting structure. The mobile mass is affected by quadrature error caused by a quadrature moment; a driving structure is coupled to the suspended mass for controlling the movement of the mobile mass in a driving direction at a driving frequency. Motion-sensing electrodes, coupled to the mobile mass, detect the movement of the mobile mass in the sensing direction and quadrature-compensation electrodes are coupled to the mobile mass to generate a compensation moment opposite to the quadrature moment. The gyroscope is configured to bias the quadrature-compensation electrodes with a compensation voltage so that the difference between the resonance frequency of the mobile mass and the driving frequency has a preset frequency-mismatch value.
1. A MEMS gyroscope, comprising:
a supporting structure;
a mobile mass mobile with respect to the supporting structure in a driving direction and in a sensing direction, the driving direction and the sensing direction being perpendicular to each other, the mobile mass being affected by a quadrature error caused by a quadrature moment;
a driving structure coupled to the mobile mass and configured to control movement of the mobile mass in the driving direction at a driving frequency, the mobile mass having a variable resonance frequency that differs from the driving frequency by a frequency mismatch;
motion-sensing electrodes coupled to the mobile mass and configured to detect movement of the mobile mass in the sensing direction; and
quadrature-compensation electrodes coupled to the mobile mass and configured to generate a compensation moment opposite to the quadrature moment; and
a compensation controller configured to bias the quadrature-compensation electrodes with at least one compensation voltage that drives the mobile mass at a preset frequency mismatch, wherein the quadrature-compensation electrodes comprise a first quadrature-compensation electrode and a second quadrature-compensation electrode, and the compensation controller is configured to bias the first and second quadrature-compensation electrodes at first and second compensation voltages V 1 , V 2 , respectively, where V 1 and V 2 are chosen for satisfying the equation:
Δ
f
0
=
1
2
π
ω
s
0
2
-
k
S
J
[
(
V
R
-
V
1
)
2
+
(
V
R
-
V
2
)
2
]
-
f
d
where:
Δf 0 is the preset frequency mismatch;
V R is a biasing voltage of the mobile mass;
ω S0 is a resonance frequency of the mobile mass;
k s /J is a parameter correlated to mechanical constants of the mobile mass; and
f d is the driving frequency.
2. The gyroscope of claim 1 , wherein the at least one compensation voltage is variable quadratically with the quadrature error.
3. The gyroscope of claim 1 , wherein the first and the second compensation voltage V 1 , V 2 satisfy the equation:
Q el +Q γ =0
wherein:
Q el is a compensation quadrature given by:
Q el =k Q [( V R −V 1 ) 2 −( V R −V 2 ) 2 ],
Q γ is the quadrature error,
k q is a proportionality constant linking the compensation quadrature Q el to the compensation moment M el .
4. The gyroscope of claim 1 , wherein the compensation controller includes a memory element configured to store values of the at least one compensation voltage.
5. A control method for controlling a MEMS gyroscope, comprising:
driving a mobile mass in a driving direction and at a driving frequency;
detecting a movement of the mobile mass in a sensing direction, perpendicular to the driving direction, wherein the mobile mass is affected by quadrature error caused by a quadrature moment in the sensing direction and having a variable resonance frequency, the difference between the resonance frequency and the driving frequency forming a frequency mismatch;
generating a compensation moment opposite to the quadrature moment via quadrature-compensation electrodes coupled to the mobile mass; and
biasing the quadrature-compensation electrodes with at least one compensation voltage that drives the mobile mass with a preset frequency mismatch, wherein biasing the quadrature-compensation electrodes comprises applying a first compensation voltage V 1 to a first quadrature-compensation electrode and applying a second compensation voltage V 2 to a second quadrature-compensation electrode and V 1 and V 2 satisfy the equation:
Δ
f
0
=
1
2
π
ω
s
0
2
-
k
S
J
[
(
V
R
-
V
1
)
2
+
(
V
R
-
V
2
)
2
]
-
f
d
where:
Δf 0 is the preset frequency mismatch;
V R is a biasing voltage of the mobile mass;
ω S0 is a resonance frequency of the mobile mass;
k s /J is a parameter correlated to an elastic constant of the mobile mass; and
f d is the driving frequency.
6. The method of claim 5 , wherein the at least one compensation voltage is variable quadratically with the quadrature error.
7. The method of claim 5 , wherein the first quadrature-compensation voltage V 1 and the second quadrature-compensation voltage V 2 satisfy the equation:
Q el +Q γ =0
where:
Q el is a compensation quadrature given by:
Q el =k Q [( V R −V 1 ) 2 −( V R −V 2 ) 2 ]
Q γ is the quadrature error;
k q is a proportionality constant that links the compensation quadrature Q el to the compensation moment M el .
8. A method for setting compensation parameters in a MEMS gyroscope, comprising:
driving a mobile mass of the MEMS gyroscope in a driving direction and at a driving frequency;
applying a plurality of pairs of values of compensation voltages V 1 , V 2 to a first quadrature-compensation electrode and a second quadrature-compensation electrode coupled to the mobile mass and detecting a corresponding plurality of frequency mismatch values Δf 0 between the driving frequency and a resonance frequency of the mobile mass;
detecting, from the plurality of frequency mismatch values, which of the pairs of values of the compensation voltages V 1 , V 2 are associated with a desired frequency mismatch value Δf 0d ;
detecting, from the pairs of values of the compensation voltages, which pair of values makes Q el +Q γ =0
wherein:
Q el is a compensation quadrature given by:
Q el =k Q [( V R −V 1 ) 2 −( V R −V 2 ) 2 ],
Q γ is quadrature error,
V R is a biasing voltage of the mobile mass, and
k q is a proportionality constant linking the compensation quadrature Q el to the compensation moment M el ; and
storing the pair of values of the compensation voltages V 1 , V 2 that makes Q el +Q γ =0.
9. The method of claim 8 , wherein detecting a corresponding plurality of values of frequency mismatch Δf 0 comprises solving equation:
Δ
f
0
=
1
2
π
ω
s
0
2
-
k
S
J
[
(
V
R
-
V
1
)
2
+
(
V
R
-
V
2
)
2
]
-
f
d
wherein:
Δf 0 is the preset frequency mismatch;
ω S0 is a resonance frequency of the mobile mass;
k s /J is a parameter correlated to an elastic constant of the mobile mass; and
f d is the driving frequency.
10. The method of claim 8 , further comprising:
measuring a driving frequency f d of the mobile mass in a driving direction through a driving measurement structure coupled to the mobile mass; and
measuring the sensing resonance frequency ω S0 and measuring the parameter k s /J by applying appropriate values of the compensation voltages V 1 , V 2 .
11. The method of claim 8 , wherein applying a plurality of pairs of compensation voltage values V 1 , V 2 and detecting a corresponding plurality of values of frequency mismatch Δf 0 comprises:
generating a table of frequency mismatch values Δf 0 .
12. An electronic system comprising:
a MEMS gyroscope including:
a supporting structure;
a mobile mass mobile with respect to the supporting structure in a driving direction and in a sensing direction, the driving direction and the sensing direction being perpendicular to each other, the mobile mass being affected by a quadrature error caused by a quadrature moment;
a driving structure coupled to the mobile mass and configured to control movement of the mobile mass in the driving direction at a driving frequency, the mobile mass having a variable resonance frequency that differs from the driving frequency by a frequency mismatch;
motion-sensing electrodes coupled to the mobile mass and configured to detect movement of the mobile mass in the sensing direction; and
quadrature-compensation electrodes coupled to the mobile mass and configured to generate a compensation moment opposite to the quadrature moment; and
a control unit that includes a compensation controller configured to bias the quadrature-compensation electrodes with at least one compensation voltage that drives the mobile mass at a preset frequency mismatch, wherein the quadrature-compensation electrodes comprise a first quadrature-compensation electrode and a second quadrature-compensation electrode, and the compensation controller is configured to bias the first and second quadrature-compensation electrodes at first and second compensation voltages V 1 , V 2 , respectively, where V 1 and V 2 are chosen for satisfying the equation:
Δ
f
0
=
1
2
π
ω
s
0
2
-
k
S
J
[
(
V
R
-
V
1
)
2
+
(
V
R
-
V
2
)
2
]
-
f
d
where:
Δf 0 is the preset frequency mismatch;
V R is a biasing voltage of the mobile mass;
ω S0 is a resonance frequency of the mobile mass;
k s /J is a parameter correlated to mechanical constants of the mobile mass; and
f d is the driving frequency.
13. The electronic system of claim 12 , wherein the at least one compensation voltage is variable quadratically with the quadrature error.
14. The electronic system of claim 12 , wherein the first and the second compensation voltage V 1 , V 2 satisfy the equation:
Q el +Q γ =0
wherein:
Q el is a compensation quadrature given by:
Q el =k Q [( V R −V 1 ) 2 −( V R −V 2 ) 2 ],
Q γ is the quadrature error,
k q is a proportionality constant linking the compensation quadrature Q el to the compensation moment M el .
15. The electronic system of claim 12 , wherein the compensation controller includes a memory element configured to store values of the at least one compensation voltage.