U.S. patent application number 09/927858 was filed with the patent office on 2003-02-20 for cloverleaf microgyroscope with electrostatic alignment and tuning.
Invention is credited to Challoner, A. Dorian, Gutierrez, Roman C., Tang, Tony K..
Application Number | 20030033850 09/927858 |
Document ID | / |
Family ID | 25455375 |
Filed Date | 2003-02-20 |
United States Patent
Application |
20030033850 |
Kind Code |
A1 |
Challoner, A. Dorian ; et
al. |
February 20, 2003 |
Cloverleaf microgyroscope with electrostatic alignment and
tuning
Abstract
A micro-gyroscope (10) having closed loop operation by a control
voltage (V.sub.ty), that is demodulated by an output signal of the
sense electrodes (S1, S2), providing Coriolis torque rebalance to
prevent displacement of the micro-gyroscope (10) on the output axis
(y-axis). The present invention provides independent alignment and
tuning of the micro-gyroscope by using separate sensors and
actuators to detect and adjust alignment and tuning. A quadrature
amplitude signal is used to detect misalignment, that is corrected
to zero by an electrostatic bias adjustment. A quadrature signal
noise level, or a transfer function test signal, is used to detect
residual mistuning, that is corrected to zero by a second
electrostatic bias adjustment.
Inventors: |
Challoner, A. Dorian;
(Manhattan Beach, CA) ; Gutierrez, Roman C.; (La
Crescenta, CA) ; Tang, Tony K.; (Glendale,
CA) |
Correspondence
Address: |
Angela M. Brunetti
Artz & Artz, P.C.
Suite 250
28333 Telegraph Road
Southfield
MI
48034
US
|
Family ID: |
25455375 |
Appl. No.: |
09/927858 |
Filed: |
August 9, 2001 |
Current U.S.
Class: |
73/1.77 ;
702/93 |
Current CPC
Class: |
G01C 19/56 20130101;
G01C 25/00 20130101; G01P 2015/084 20130101; G01P 2015/0842
20130101; G01C 19/5719 20130101 |
Class at
Publication: |
73/1.77 ;
702/93 |
International
Class: |
G01C 025/00 |
Goverment Interests
[0001] The invention described herein was made in the performance
of work under a NASA contract, and is subject to the provisions of
Public Law 96-517 (35 U.S.C. .sctn.202) in which the Contractor has
elected to retain title.
Claims
What is claimed is:
1. A method for aligning a micro-gyroscope having closed loop
control of drive, output and sense axes, said method comprising the
steps of: detecting misalignment of said micro-gyroscope; and
correcting misalignment to zero by an electrostatic bias
adjustment.
2. The method as claimed in claim 1 wherein said step of detecting
misalignment further comprises detecting misalignment by way of
quadrature signal amplitude obtained by demodulation of a signal of
said output axis using a signal in quadrature to rate signal for
said drive axis.
3. The method as claimed in claim 1 further comprising the step of
nulling an in-phase bias.
4. The method as claimed in claim 3 wherein said step of nulling an
in-phase bias further comprises nulling by electronically coupling
a torque component of said drive axis with said output axis.
5. A method for tuning a cloverleaf micro-gyroscope having closed
loop control of drive, output and sense axes, said method
comprising the steps of: detecting residual mistuning by way of a
signal; and correcting said residual mistuning to zero by way of
electrostatic bias adjustment.
6. The method as claimed in claim 5 wherein said step of detecting
residual mistuning further comprises detecting by way of a
quadrature signal noise level.
7. The method as claimed in claim 5 wherein said step of detecting
residual mistuning further comprises detecting by way of a transfer
function test signal.
8. A method for independently aligning and tuning a cloverleaf
micro-gyroscope having closed loop control of drive, output and
sense axes, said method comprising the steps of: detecting
misalignment of said micro-gyroscope by way of a quadrature signal
amplitude; correcting said misalignment to zero by way of an
electrostatic bias adjustment; detecting residual mistuning by way
of a signal; and correcting said residual mistuning by way of an
electrostatic bias adjustment.
9. The method as claimed in claim 8 wherein said step of detecting
a residual mistuning further comprises detecting a residual
mistuning by way of a quadrature signal noise level.
10. The method as claimed in claim 8 wherein said step of detecting
a residual mistuning further comprises detecting a residual
mistuning by way of a transfer function test signal.
11. The method as claimed in claim 8 further comprising the step of
nulling in-phase bias.
12. The method as claimed in claim 11 wherein said step of nulling
further comprises electronically coupling a torque component of
said drive axis with said output axis.
13. The method as claimed in claim 8 wherein said micro-gyroscope
closed loop control further comprises: using separate sensors and
actuators for said step of correcting said misalignment and said
step of correcting said residual mistuning.
14. The method as claimed in claim 8 wherein said step of
correcting said misalignment further comprises the step of
introducing an electrostatic cross-coupling spring, K.sup.e.sub.xy
for canceling said misalignment.
15. The method as claimed in claim 14 further comprising the step
of applying a bias voltage to a drive electrode on said drive axis
that is different from a bias voltage to another drive electrode on
said drive axis.
16. The method as claimed in claim 8 further comprising the step of
introducing a relative gain mismatch, .delta..sub.T.apprxeq.0, to
each drive electrode on said drive axis.
17. The method as claimed in claim 8 further comprising the step of
maximizing a stiffness matrix K.
18. The method as claimed in claim 8 wherein said step of
correcting said residual mistuning to zero further comprises
adjusting a total stiffness of said micro-gyroscope.
Description
TECHNICAL FIELD
[0002] The present invention relates to micro-machined
electromechanical systems, and more particularly to a MEMS
vibratory gyroscope having closed loop output.
BACKGROUND ART
[0003] Micro-gyroscopes are used in many applications including,
but not limited to, communications, control and navigation systems
for both space and land applications. These highly specialized
applications need high performance and cost effective
micro-gyroscopes.
[0004] There is known in the art a micro-machined electromechanical
vibratory gyroscope designed for micro-spacecraft applications. The
gyroscope is explained and described in a technical paper entitled
"Silicon Bulk Micro-machined Vibratory Gyroscope" presented in
June, 1996 at the Solid State Sensors and Actuator Workshop in
Hilton Head, S.C.
[0005] The prior art gyroscope has a resonator having a
"cloverleaf" structure consisting of a rim, four silicon leaves,
and four soft supports, or cantilevers, made from a single crystal
silicon. A metal post is rigidly attached to the center of the
resonator, in a plane perpendicular to the plane of the silicon
leaves, and to a quartz base plate with a pattern of electrodes
that coincides with the cloverleaf pattern of the silicon leaves.
The electrodes include two drive electrodes and two sense
electrodes.
[0006] The micro-gyroscope is electrostatically actuated and the
sense electrodes capacitively detect Coriolis induced motions of
the silicon leaves. The response of the gyroscope is inversely
proportional to the resonant frequency and a low resonant frequency
increases the responsivity of the device.
[0007] Micro-gyroscopes are subject to electrical interference that
degrades performance with regard to drift and scale factor
stability. Micro-gyroscopes often operate the drive and sense
signals at the same frequency to allow for simple electronic
circuits. However, the use of a common frequency for both functions
allows the relatively powerful drive signal to inadvertently
electrically couple to the relatively weak sense signal.
[0008] Residual mechanical imbalance of a cloverleaf
micro-gyroscope results in misalignment or coupling of drive motion
into the output axis. Presently, it is known to correct any
misalignment of the mechanical modal axes by electronically
rotating the sense and control axes into alignment with the
mechanical axes.
[0009] However, electronic alignment, in which the sense and
control axes are aligned with the mechanical modal axes results in
second harmonics and electronic tuning, as by AGC phase adjustment,
for example, has limited tuning range for high Q resonators and the
tuning will change with variations in damping or temperature. It is
known in the art that electrostatic tuning and AGC tuning operate
by nulling quadrature amplitude. However, the quadrature amplitude
signal more properly relates to misalignment so that when there is
no misalignment, there is no quadrature signal, even though there
may still be residual mistuning.
SUMMARY OF THE INVENTION
[0010] The present invention is a method for electrostatic
alignment and tuning of a cloverleaf micro-gyroscope having closed
loop operation. For closed loop output, a differential sense signal
(S1-S2) is compensated by a linear electronic filter and directly
fed back by differentially changing the voltages on two drive
electrodes (D1-D2) to rebalance Coriolis torque, suppress
quadrature motion and increase the damping of the sense axis
resonance. The resulting feedback signal is demodulated in phase
with the drive axis signal (S1+S2) to produce a measure of the
Coriolis force and, hence, the inertial rate input.
[0011] The micro-gyroscope and method of alignment and tuning of
the present invention detects residual mechanical imbalance of the
cloverleaf micro-gyroscope by quadrature signal amplitude and
corrects the alignment to zero by means of an electrostatic bias
adjustment rather than mechanical balancing. In-phase bias is also
nulled by electronically coupling a component of drive axis torque
into the output axis. Residual mistuning is detected by way of
quadrature signal noise level, or a transfer function test signal
and is corrected by means of an electrostatic bias adjustment. In
the present invention, the quadrature amplitude is used as an
indication of misalignment and quadrature noise level, or a test
signal level, is used as a tuning indicator for electrostatic
adjustment of tuning.
[0012] It is an object of the present invention to improve closed
loop micro-gyroscope performance. It is another object of the
present invention to improve the accuracy of micro-gyroscope
alignment and tuning.
[0013] It is a further object of the present invention to provide
electrostatic alignment and tuning for closed-loop operation of a
vibratory micro-gyroscope. It is still a farther object of the
present invention to use the quadrature amplitude as an indication
of misalignment. It is yet a further object of the present
invention to use quadrature noise level or a test signal level as a
tuning indicator. Yet a further object of the present invention is
to provide independent control of alignment and tuning for a closed
loop micro-gyroscope.
[0014] Other objects and features of the present invention will
become apparent when viewed in light of the detailed description of
the preferred embodiment when taken in conjunction with the
attached drawings and appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
[0015] FIG. 1 is an exploded view of a prior art vibratory
micro-gyroscope having four electrodes;
[0016] FIG. 2 is a block diagram of a prior art closed-loop
micro-gyroscope;
[0017] FIG. 3 is an example of a prior art circuit schematic for
closed loop sense/open loop drive operation;
[0018] FIG. 4 is an exemplary electrode arrangement for the method
of electrostatic alignment and tuning according to the present
invention, the electrode arrangement includes eight electrodes;
and
[0019] FIG. 5 is a flowchart of the method for electrostatic
alignment and tuning according to the present invention.
BEST MODE(S) FOR CARRYING OUT THE INVENTION
[0020] The method of the present invention is applicable to a
closed loop micro-gyroscope. In the preferred embodiment, the
closed loop micro-gyroscope is described in conjunction with FIGS.
1 through 3. For example purposes, and for simplicity, the closed
loop control of the preferred embodiment will be described in
accordance with a cloverleaf micro-gyroscope having four
electrodes.
[0021] FIG. 1 is an exploded view of the micro-gyroscope 10. The
cloverleaf micro-gyroscope 10 has a post 12 attached to a resonator
plate 14 having a cloverleaf shape with petals labeled 1, 2, 3, and
4. The cloverleaf resonator plate 14 is elastically suspended from
an outer frame 16.
[0022] A set of four electrodes 18, located under the resonator
plate 14, actuate the resonator plate and sense capacitance on the
resonator plate 14. Drive electrodes D1 and D2 actuate movement of
the resonator plate 14 and sense electrodes S1 and S2 sense
capacitance. A set of axes are labeled x, y and z to describe the
operation of the micro-gyroscope.
[0023] Rocking the post 12 about the x-axis actuates the
micro-gyroscope 10. The rocking motion is accomplished by applying
electrostatic forces to petals 1 and 4 by way of a voltage applied
to the drive electrodes, D1 and D2. For a steady inertial rate,
.OMEGA., along the z-axis or input axis, there will be a
displacement about the y-axis, or output axis, that can be sensed
by the differential output of the sensing electrodes, S1-S2 or
V.sub.thy. The displacement about the y-axis is due to the
influence of a rotation induced Coriolis force that needs to be
restrained by a counteracting force.
[0024] Referring now to FIG. 2, the wide-band closed-loop operation
of the micro-gyroscope will be described. The closed-loop control
circuit nulls displacement about the y-axis through linearized
electrostatic torques. The electrostatic torques are proportional
to control voltages. The two drive electrodes D1 and D2 produce
linearized electrostatic torques about the x and y axes that are
proportional to control voltages V.sub.tx and V.sub.ty. D1 and D2
are defined as:
D1=V.sub.o-V.sub.ty+V.sub.tx
[0025] and
D2=V.sub.o+V.sub.ty+V.sub.tx
[0026] where V.sub.o is a bias voltage.
[0027] The linearized torques are defined as:
T.sub.x=K.sub.TV.sub.tx
T.sub.y=K.sub.TV.sub.ty
[0028] where the torque constant is:
K.sub.T=[2r.sub.oC.sub.oV.sub.o][d.sub.o].sup.-1
[0029] r.sub.o=offset from x or y axis to control, or drive,
electrode center, C.sub.o is the capacitance of one control
electrode, V.sub.o is the bias voltage, and d.sub.o is electrode
gap which is the nominal separation between the electrode plane and
the resonator plane.
[0030] The control voltage V.sub.tx provides for automatic gain
control of the drive amplitude. The control voltage V.sub.ty
provides for Coriolis torque re-balance. The output axis (y-axis)
gain and phase compensation are selected based on computed or
measured transfer functions, G(s), from V.sub.ty to V.sub.thy. The
reference signal used to demodulate V.sub.ty is V.sub.thx which is
in phase with the drive axis rate signal, .omega..sub.x.
[0031] Referring still to FIG. 2, the closed loop operation of the
micro-gyroscope of the present invention measures the inertial
rate, .OMEGA., around the z-axis. Signals S1 and S2 are output from
pre-amplifiers 20 that are attached to the sense electrodes S1 and
S2.
[0032] The micro-gyroscope is set in motion by a drive loop 22 that
causes the post to oscillate around the x-axis. The post rocks and
has a rate of rotation about the x-axis. D1 and D2 apply voltages
in phase therefore, they push and pull the resonator plate (not
shown in FIG. 2) creating a torque, T.sub.x, on the x-axis.
[0033] When there is no inertial rate on the z-axis, there is no
differential motion on S1 and S2. In this case, V.sub.thy=S1-S2 =0.
S1 and S2 are in phase and indicate a rotation around the x-axis.
V.sub.thx=S1+S2 is amplitude and gain phase compensated in an
automatic gain control loop 22, 25, 27 to 25 drive V.sub.thx to
V.sub.tx. An amplitude reference level, V.sub.r, is compared with a
comparator 23 to the output of the amplitude detector 22 that
determines the amplitude of V.sub.thx. The resulting amplitude
error is gain and phase compensated 25 and applied as a gain to an
automatic gain control multiplier 27. A drive voltage V.sub.tx
proportional to V.sub.thx is thus determined that regulates the
amplitude of the vibration drive.
[0034] When an inertial rate is applied, it creates a difference
between S1 and S2 equal to V.sub.thy. In the prior art V.sub.thy
was merely sensed open loop as being proportional to the rate of
the micro-gyroscope. In the present invention V.sub.thy is gain and
phase compensated based on a computed, or measured, transfer
function G(s). The resulting closed loop output voltage V.sub.ty
generates an electrostatic torque T.sub.y to balance the Coriolis
torque, thereby nulling the motion on the output axis.
[0035] To obtain the microgyroscope output signal, V.sub.out,
proportional to an input rate .OMEGA., the rebalance torque voltage
V.sub.ty is demodulated with the drive reference signal V.sub.thx
by an output axis demodulator 29 and then processed through a
demodulator and filter circuit 26. The DC component of the output
signal of the demodulator, V.sub.out, is proportional to the
rotation rate .OMEGA..
[0036] In the above-described closed loop control, if the drive
axis creates a disturbance on the y-axis, it is also sensed using
the above described demodulation scheme for the output. The closed
loop operation prevents any rocking on the y-axis by feedback 24
applied by differentially feeding D1 and D2. D1 and D2 are
responsive to V.sub.ty as well as V.sub.tx.
[0037] V.sub.thx and V.sub.thy are defined by:
V.sub.thx=S1+S2
V.sub.thy=S1-S2
[0038] Both V.sub.thx and V.sub.thy are directly proportional to
the drive axis rate, i.e. V.sub.thx=K.sub..omega.)-.omega..sub.x
and output axis rate, .omega..sub.x=K.sub..omega..THETA..sub.x
where K.sub..omega.is defined by:
K.sub..omega.=[2r.sub.oC.sub.oV.sub.oR][d.sub.o].sup.-1
[0039] and R is the transimpedance from the preamplifiers 20.
[0040] The cloverleaves of the resonator plate and the substrate
beneath S1 and S2 electrodes are well grounded at the drive
frequency, capacitive drive feedthrough is reduced and stability
margins are improved.
[0041] FIG. 3 is an example of a schematic for closed loop
sense/open loop drive operation. However, the present invention is
applicable to either open loop or closed loop drive operation. It
should be noted that in the configuration shown in FIG. 3, the two
sense signals S1 and S2 are differenced, filtered and amplified.
The filter helps to remove residual second harmonics and adjusts
loop phase to provide stable closed loop operation. The following
amplifiers serve to combine the closed loop output feedback signal
with the open loop drive signal providing the correct signals to
electrodes D1 and D2. Rebalance of the Coriolis force and robust
damping of the output axis resonance is provided by this wideband
closed loop design.
[0042] The method of the present invention is best described herein
with reference to an eight-electrode micro-gyroscope 100 shown in
FIG. 4. The closed loop control is very similar to that described
in conjunction with FIGS. 1-3. However, in the micro-gyroscope
having eight electrodes, there are obviously four additional
electrodes, Q1, Q2, T1 and S3. D1 and D2 are used differentially
for closed loop control on the y-axis and in common mode for x-axis
control. S1 and S2 are dedicated to differential y-axis output
sensing. S3 senses the motion of the drive, or x-axis, and T1 is
used for tuning on x-axis. Q1 and Q2 are used to align the
micro-gyroscope.
[0043] The micro-gyroscope has an inertia matrix J, a stiffness
matrix, K and a damping matrix D which define the rotational motion
about the x and y axes. In operation, the micro-gyroscope is driven
about the x-axis in order to sense inertial rate about the z-axis
through Coriolis coupling of the driven motion to the sense, or y,
axis. As described above, in the preferred embodiment of the
present invention, the sense axis motion is nulled by a linear
feedback torque u.sub.y, where the torque is a measure of the
inertial rate .OMEGA..
[0044] It is also preferred that the micro-gyroscope have closely
tuned operation. Closely tuned operation has a drive frequency that
is selected close to the sense axis natural resonant frequency for
maximum mechanical gain. Symmetrical design and accurate
construction of the micro-gyroscope are important so that the two
rocking mode natural frequencies are similar. A self-resonant drive
about the x-axis, for example an AGC loop, will permit large drive
motion with small torque controls.
[0045] It is not presently known how to fabricate a micro-gyroscope
with atomic precision. Therefore, it is inevitable that asymmetry
and imbalance in the matricies J, D, and K will lead to false
Coriolis rate indications. The present invention independently
controls alignment and tuning of the micro-gyroscope. Control
torque, u.sub.y, about the y-axis will be detected with zero
inertial rate output.
[0046] The method 100 of the present invention is described with
reference to FIG. 5. Misalignment is detected 102 by the presence
of a quadrature signal amplitude on V.sub.out. The misalignment is
corrected 104 by an electrostatic bias adjustment to electrode Q1
or Q2.
[0047] Residual mistuning is detected 108 and corrected 110 by way
of an electrostatic bias adjustment to electrode T1. The detection
108 is accomplished by noting the presence of a quadrature signal
noise level or a transfer function test signal.
[0048] In the following description of the present invention, the
motion about the y-axis is regarded to be infinitesimal, i.e.
perfect feedback, and drive axis motion about the x-axis is
described as:
.theta..sub.s=.theta..sub.xosin(.omega..sub.ot)
[0049] where .omega..sub.o is the operating frequency of the drive
and I.sub.xo is the drive amplitude.
[0050] Small angle motion of a rocking mode gyroscope with inertia
and stiffness misalignment is governed by: 1 ( s 2 [ J xx J xy J yx
J yy ] + s [ D xx D xy D yx D yy ] + [ K xx K xy K yx K yy ] ) [ x
y ] = [ T x T y ]
[0051] where output axis torque
T.sub.y=T.sub.c+u.sub.y+.delta..sub.TT.sub- .d. The Coriolis torque
is T.sub.c=-J.sub.yy2k.OMEGA.s.theta..sub.x, k is the
micro-gyroscope angular gain, the wideband control is
u.sub.y=-G(s)(.theta..sub.y+.delta..sub.R.theta..sub.x) and the
drive torque T.sub.d=D.sub.xsI.sub.x is at a drive resonance of
.omega..sub.o=(K.sub.xx/J.sub.xx).sup.1/2.
[0052] Analysis of the small motion on the y-axis is described
hereinafter. The equation for y-axis motion has the form:
F(s).theta..sub.y+H(s).theta..sub.x=-G(s).theta..sub.y-G(s).delta..sub.R.t-
heta..sub.x+T.sub.c(s).theta..sub.x+L(s)).delta..sub.T.theta..sub.x
[0053] 2 y = - H ( s ) - G ( s ) R + L ( s ) T + T c ( s ) F ( s )
+ G ( s ) x
u.sub.y=-G(s).theta..sub.y-G(s).delta..sub.R.theta..sub.x
[0054] 3 u y = G ( s ) H ( s ) + L ( s ) T + T c ( s ) F ( s ) + G
( s ) x + G ( s ) [ G ( s ) R F ( s ) = G ( s ) - R ] x u y = - G (
s ) F ( s ) + G ( s ) [ - H ( s ) + L ( s ) T + T c ( s ) + R F ( s
) ] x
[0055] With properly compensated transimpedance buffers, electronic
amplification and biased electrostatic drive (i.e., FIG. 3), it is
possible to provide loop compensation G(s) approximately equal to
sK, so that u.sub.y can be expanded as: 4 u y = sK J yy s 2 + ( K +
D yy ) s + K yy [ ( J yx - R J yy ) s 2 + ( J yy 2 k + D yx - R D
yy - T D xx ) s + ( K yx - R K yy ) ] x u y = 1 / ( 1 + c ) 1 + J
yy s 2 + K yy K ( 1 + c ) s [ ( J yy 2 k + D yx - R D yy - T D xx )
+ ( J yx - R J yy ) s 2 + ( K yx - R sK yy ) s ] s x
[0056] where .delta..sub.c=D.sub.yy/K. For steady state drive
operation at s=j.omega..sub.o, the feedback torque becomes: 5 u y =
1 / ( 1 + D yy K ) 1 + - J yy o 2 + K yy K ( 1 + c ) j o [ ( J yy 2
k + D yx - R D yy - T D xx ) + - ( J yx - R J yy ) o 2 + ( K yx - R
K yy ) j o ] j o x
[0057] which can be approximated as:
u.sub.y.apprxeq.(1-.delta..sub.c)(1-j.phi..sub.c)(I.sub.o+Q.sub.oj)s.theta-
..sub.x
u.sub.y.apprxeq.(1-.delta..sub.c)[(I.sub.o+Q.sub.o.phi..sub.c)+j(Q.sub.o-I-
.sub.o.phi..sub.c)]s.theta..sub.x
[0058] where K=K.sub..omega.K.sub.cK.sub.T can be set by
compensator gain, K.sub.c to achieve closed loop bandwidth,
.omega..sub.c=K/J.sub.yy/2.omeg- a..sub.OL/.delta..sub.c, and open
loop bandwidth, .omega..sub.OL=D.sub.yy/- J.sub.yy/2
.phi..sub.c=(J.sub.yy.omega..sub.o.sup.2-K.sub.yy)/(K(1+.delta..sub.c).ome-
ga..sub.o)
Q.sub.o=-(-(J.sub.yx-.delta..sub.RJ.sub.yy).omega..sub.o.sup.2+(K.sub.yx-.-
delta..sub.RK.sub.yy))/.omega..sub.o
I.sub.o=(J.sub.yy2k.OMEGA.+D.sub.yx.delta..sub.RD.sub.yy-.delta..sub.TD.su-
b.xx)
[0059] Demodulation of feedback voltage V.sub.ty, which is
proportional to u.sub.y, with drive reference V.sub.thx produces an
output proportional to .OMEGA. plus an in-phase rate bias term due
to the real component of u.sub.y and is given by:
.OMEGA..sub.bi=(D.sub.yx.delta..sub.RD.sub.yy-.delta..sub.TD.sub.xx+.phi..-
sub.c(-(J.sub.yx-.delta..sub.RJ.sub.yy).omega..sub.o.sup.2+(K.sub.yx-.delt-
a..sub.RK.sub.yy))/.omega..sub.o)/2kJ.sub.yy
[0060] Demodulation of feedback voltage V.sub.ty with a signal in
quadrature to V.sub.thx produces a quadrature rate bias, which is
given by:
.OMEGA..sub.bq=(-.phi..sub.c(D.sub.yx-.delta..sub.RD.sub.yy-.delta..sub.TD-
.sub.xx)+(-(J.sub.yx-.delta..sub.RJ.sub.yy).omega..sub.o.sup.2+(K.sub.yx-.-
delta..sub.RK.sub.yy))/.omega..sub.o)/2kJ.sub.yy
[0061] Given the above analysis of the small motion on the y-axis,
the method of the present invention sets the sensor misalignment to
zero, .delta..sub.R=0 electronically, and then electrostatically
aligns the microgyroscope by introducing an electrostatic cross
coupling spring K.sup.e.sub.xy to cancel the misalignment torque.
For example,
T.sub.y=K.sup.e.sub.xyI.sub.y=(J.sub.xy.omega..sub.y.sup.2+K.sub.xy)I.sub-
.y. The remaining in-phase bias component of .OMEGA..sub.bi can
also be nulled. This can be accomplished by introducing a relative
gain mismatch .delta..sub.T.noteq.0 on the automatic gain control
voltage to each of the drive electrodes D1 and D2. This compensates
for the false rate arising from finite modal damping and
misalignment of the damping axes, i.e. set
D.sub.xy-.delta.D.sub.xx=0. The compensation also applies to any
systematic changes in damping affecting both axes, for example, as
may be caused by bulk temperature changes.
[0062] For a four-electrode cloverleaf micro-gyroscope like the one
shown in FIG. 1, the cross-coupled electrostatic stiffness can be
introduced by applying more or less bias voltage to one of the
drive electrodes, D1 or D2. The in-phase rate bias error is also
nulled as described above.
[0063] In the preferred closed loop operation of the present
invention, the compensation is set such that G(s)=sK and K is
maximized to be consistent with loop stability. In such a case,
dependence on scale factor and phase shift on the mechanical
response are minimized. Furthermore, with fully tuned
operation,
.omega..sub.nx.sup.2=K.sub.xx/J.sub.xx=.omega..sub.ny.sup.2K.sub.yy/J.sub.-
yy=.omega..sub.o.sup.2
[0064] and there is no closed loop phase error, .phi..sub.c=0. For
tuned conditions, maximum mechanical gain and maximum loop gain
occur. Therefore, noise due to input electronic noise is
minimized.
[0065] For an eight-electrode design, as shown in FIG. 4,
electrostatic cross-coupled stiffness, K.sup.e.sub.xy for alignment
purposes can be introduced by modification of the bias voltage of
either Q1 or Q2. Electrostatic modification of net K.sub.xx for
tuning purposes can be accomplished by increasing or decreasing the
bias voltage T1 as well.
[0066] For example, if .omega..sub.nx>.omega..sub.ny then the
bias voltage applied to T1 is made larger than the voltage applied
to S1 and S2. The total stiffness is the elastic stiffness plus the
electrostatic stiffness. The total stiffness about the x-axis is
lowered so that .omega..sub.nx is also lowered and brought into
tune with .omega..sub.ny. In this regard, the present invention
provides a tuning method for vibratory micro-gyroscopes in which
one of the bias voltages is increased or decreased until a minimum
value of the rms noise is obtained or until a transfer function
indicates tuning. In the alternative, a test signal may be
maximized.
[0067] For the eight-electrode design, a bias on Q1 or Q2 will
introduce cross axis electrostatic stiffness. To align the
gyroscope, Q1 bias is adjusted until the quadrature amplitude is
nulled. .delta..sub.T is adjusted until the rate output is
nulled.
[0068] To independently tune the micro-gyroscope according to the
present invention, the electrostatic tuning bias, electrode T1, is
adjusted until closed loop quadrature or in-phase noise, or another
tuning signal, is minimized.
[0069] While particular embodiments of the present invention have
been shown and described, numerous variations and alternate
embodiments will occur to those skilled in the art. Accordingly, it
is intended that the invention be limited only in terms of the
appended claims.
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