Serrano Slides Gyros2 2
-
Upload
abtinkamelii -
Category
Documents
-
view
20 -
download
0
description
Transcript of Serrano Slides Gyros2 2
-
Sponsored by the IEEE Sensors Council, www.ieee-sensors.org
SENSORS 2013Tutorials: November 3, 2013 Conference: November 4-6, 2013
,#!'''%4,#,(4+(,(),
#!(%#(++'(7+31
.1&(-24373.!'-.+.&;
-
SENSORS 2013
"-#,4+(,()7 CM -2.13'3,27123'-&+.113.!1.34.-)#''#'!4+(,(),
%8+.-2184.-.!-&7+1,.,-37, &-"3* !#%
).%4+(,(),
.1(.+(2"3
#+-(+44+(,(),
'*,!*'(*.%%&
1,.1122(.-3
4+(,(),
'*,!*'(*.%%&2*'
-
SENSORS 2013
))%#.(',(4+(,(), D
0-(&(.18%##%#-4
(',0&+8#5>(,-
'0,-+#%8(0,-',,
-3--23(+(
-
SENSORS 2013
1(%0.('(4+(,(), EM (1.+31.-(2^K:(2;1.2./N.-27,1O
M -8-2-2^K:(2;1.2./N.,,1(+OSource: Yole Dveloppement, STMicro L3G3250A Reverse costing, 2012
E3E3C&&E
;DBCE
-
SENSORS 2013
+(+&'#'4+(,(),;(',0&+
-
SENSORS 2013
)+.('+#'#)%,:"(+#(%#,-GM :,/+E'.77+3-7+7,
acor = 2
vdrv
M .1-:31311231(+.2181E/-7+7,29(-&2*-!.13'M .1311231(+.2181E1)3.1;.!29(-&'-&2; acor
-
SENSORS 2013
#+(&"'#%4+(,(), HM :,/+E'7-(-&.1*;1.2./NO
0&):%&'-(%
M 074.-2.!,.4.-.!-(+&;1.2./E(C (D
m2yt2
+ byyt+ ky y = Felecy 2mZ
xt
yt+m
2yt2 y
y = Zxt
m2xt2
+ bxxt+ kx x = Felecx + 2mZ
ytZyt
xt+m
2xt2 x
x =
-
SENSORS 2013
(,()+.(' I(-.(':-4+(, "(%:'!%(4+(,
M .\1(8-(-3..2(++4.-M .]723.331.34.-
M 1K8(14-&2317371M 3-(-&K98/1222
M 73/73/1./.14.-+3. M 73/73/1./.14.-+3.
-
SENSORS 2013
#+-(+4(-.(':-4+(,(), JM 9.2.-K.112;23,2
L 1(8N:(3(-3..2(++4.-OL -2N12/.-2/1./.14.-+3.1.34.-K13O
MODE 1 MODE 2
m2xt2
+ bxxt+ kx x = Felecx m
2yt2
+ byyt+ ky y = 2mZ
xt
Fcor = 2m
x
t
(+#(%#,77%&,$66>
-
SENSORS 2013
+#1#'!-"4+(,() KM .&-13(#(D.-,.(21(8-N727++;(-3..2(++4.-O
Amp TransducerTransducer
xFelecx
zDrive System
Fcor y/t
vx
Sense System
Amp TransducerTransducer
Felecx
Drive SystemDrive System
m2xt2
+ bxxt+ kx x = Felecx
M 312.--Ne0drvOE X( j)Felecx ( j) =Qdrvm0drv2
X( j)Felecx ( j)
= 90
X( j)Felec ( j)
=1
m
1
2 +0drvQdrv
j +0drv2
Qdrv =kx m
bx0drv =
kxm
M 107-;K.,(-E
-
+#1(
-
SENSORS 2013
%-+(,-.+',0+, CB+%%%:%-+',0+ (&:+#1-0.('
Micralyne DRIE etched comb-drive structures
(-1374.- ++.92+1&(2/+,-32 .9.7/+(-&.$(-3
dC
dx= 2n tg0
(&'+31.,'-(+.7/+(-& ,++-2;3.(,/+,-3 .-K+(-131-2!1!7-4.-
Device Overview DDDeevviiiccceee OOOOvvvveeerrrrvvvvvvvviiiieeewwwww Electrode
Resonating Proof-Mass
40-60m
Capacitive Gap
GATech/Qualtrs HARPSS parallel-plate gaps
dC
dx=
w tg0 x( )
2 w tg02
Micralyne DRIE etched comb drive structures
Motor
Stator
-
SENSORS 2013
-.'!(-.('- CCM (3'vdrv23+(2'D3'2-2,.12/.-2(-/12-.!
Amp TransducerTransducer
xFelecx
zDrive System
Fcor y/t
vx
Sense System
z
FFcor yyvxx
S S tSense System
',(
m2yt2
+ byyt+ ky y = Fcor Fcor = 2mZ
xt
M 739'1(20sns9(3'12/33.0drvC
Y ( j)X( j) =0 drv
= 2 j0drv0drv2 +
0snsQsns
j0drv +0sns2M 107-;K.,(-E
-
SENSORS 2013
-4+(,:(,()+.(' CDM .K/+(3E1(8-2-2!107-(21("1-3M .K3'E1(8-2-2!107-(21(-4+
107-;
&
-
(
3
7
+,
If 0drv
-
SENSORS 2013
(:)%#-1,9(:-"4+(, CE(:)%#-4+(, (:-"4+(,
M ;/(++;.!7-(-&K.1**(- M ;/(++;:(2;,,31(
Robert Bosch GmbH, single-axis gyroscope U. Michigan, Ring gyroscope
M .2!1.,("1-3,'-(2,2M 1&N+1.,3112/.-2OM +!3.1\JA]2-2
L 1&,22N(&&12(
-
SENSORS 2013
(:)%#--4+(,(), CFM ;/(++;2.912.--!107-;N\L^[*
-
SENSORS 2013
0%$:(0,.1;
-
SENSORS 2013
)+.('-4+(,(), CH
+#1:#'
+#1:(0-;L<
+#1:(0-;:< ',:(0-;L
-
SENSORS 2013
&)%&'-.('(4+(,(), CI
Q = 77,000
C7@3"+#2*'
;*'++*9$/$#
" !,=:=
-
SENSORS 2013
+(+&'()#.14+(, CJ'-'&$%(& M .91(261B
L (&'NS`[D[[[W\L\[.11OL +31K2,++/(48--.K&/2
$,'* M (&'1(261BL -/--3.!!107-;BB
!&"$'"+ M .91(261BL (&'!12V'(&'.,/-23!.1
2,++1(2/+,-32
&0",! M (&'1(261BL (&'!12.,/-232!.1'(&'
Rm =2 Meff g04 fres0 Aelec VP( )
2 Qfrff es g04 Q
Mefe fff []
SF =2 0 Aelec VP Q
180 g0Q
g0[A/(/s)]
MNE = 180 g0
kB T Meff fres QQ frff es g0 Mefe fff
[(/s)Hz]
BW =fres2Q
frff es2Q
[Hz]
-
SENSORS 2013
#-"'(%%''0%0,4+(,(), CK
+#1:#'
+#1:(0-;:< +#1:(0-;L<
+#1:-0'#'!
',:(0-;:
-
SENSORS 2013
''0%0,4+(,(),:,)(', DB ,++!107-;2/+(3N!713'1.,/-239(3'+31.-(2O
77.& ,$66>
-
SENSORS 2013
0%.:!+:(:+(&'-!+.(' DC'&'$",!"" "
X-Axis Axl. Response
Y-Axis Axl. Response
Z-Axis Axl. Response X-Axis Gyro Response X Axis Gyro Response
Q 28,000
Y-Axis Gyro Response
Q 28,000
Z-Axis Gyro Response
SSSSEEEENNNNSSSSOOOORRRRS
Q 118,000 Resonator
-
SENSORS 2013
++(+(0+,#'(:-"4+(, DD
M +&;1.2./E
m11 q1(t)+ d11 q1(t)+ k11 q1(t) = 2m22 q2 (t)(t)
m22 q2 (t)+ d22 q2 (t)+ k22 q2 (t) = 2m11 q1(t)(t)
M .\E
M .]E
01 =k11m11
=02 =k22m22
0 = 0
.1(.+(2.7/+(-&
M -(2.+24(3;EM -(2.(-14E
k22 k11
m22 m1101 02
-90
-85
-80
-75
-70
-65
-60
-55
-50
7251500 7252000 7252500 7253000 7253500 7254000 7254500
M
a
g
n
t
i
d
u
e
[
d
B
]
Frequency [Hz]
Mode 1
Mode 2
0 0
-
SENSORS 2013
(&)',.'!(++*0'4:)%#- DE +31.234/1(-&.%-(-&
-90
-85
-80
-75
-70
-65
-60
-55
-50
7251500 7252000 7252500 7253000 7253500 7254000 7254500
M
a
g
n
t
i
d
u
e
[
d
B
]
Frequency [Hz]
Mode 1
Mode 2
D-85
-80
-75
-70
-65
-60
-55
-50
7251500 7252000 7252500 7253000 7253500 7254000 7254500
M
a
g
n
t
i
d
u
e
[
d
B
]
Frequency [Hz]
Mode 1
Mode 2
DA
'9,!"&
k11elec =Ag03
VP VT , j( )j=1
l
2
Spring softening
01=k11mech k11elec
m11
+(&-9(3',.\
-
SENSORS 2013
(:-(:((0)%#'! DF +&;1.2./9(3'7-.7/+,.2
z
m
k1, b1
x
k1, b1
k2, b2
k2, b2
Fin
m
k1, b1 k1, b1
k2, b2
k2, b2
y
Fcoriolis
(+#(%#,-
Fcor = 2mZxt
,/1!3&;1.2./9(3'.7/+,.2
m
xk12, b12
Finy
k12, b12k12, b12
k12, b12
Damping coupling Stiffness coupling
m q1(t)+ d11 q1(t)+ d12 q2 (t)+ k11 q1(t)+ k12 q2 (t) = 2m q2 (t)(t)
Coriolis coupling
m q2 (t)+ d22 q2 (t)+ d21 q1(t)+ k22 q2 (t)+ k21 q1(t) = 2m q1(t)(t)
-
SENSORS 2013
.',,(0)%#'! DG .\(2/+,-3&-132!.13'3.7/+23..]
Felec
Drive Mode
q2QModeCoupling
k21
Sense Mode
q1 FQ
-90
-85
-80
-75
-70
-65
-60
-55
-50
7251500 7252000 7252500 7253000 7253500 7254000 7254500
M
a
g
n
t
i
d
u
e
[
d
B
]
Frequency [Hz]
Mode 1
Mode 2
-85
-80
-75
-70
-65
-60
-55
-50
7251500 7252000 7252500 7253000 7253500 7254000 7254500
M
a
g
n
t
i
d
u
e
[
d
B
]
Frequency [Hz]
Mode 1
Mode 2
!33e44N(FF+,+.23.[OE
q2Qq1
90 .*,.*
+31.234,.K.7/+(-&E
2000 2 37252500 72530002 2 00 2 3000
D7252 500 72500 7253000 725352500 7253000 72535
D
We"4e[N,.2.7/+O-39-,.2
-
SENSORS 2013
&)#'!(0)%#'! DH .\8+.(3;&-132!.13'3.7/+23..]q2 I (t)+
02Q2q2 I (t)+ b21m q1(t)+02
2 q2 I (t) = 0+b21mq1(t)
.1,.K,3'&;1.2./E q2 I ()q1() =01=02
= b21Q2m01
00
.,/1(-&9(3'.1(.+(2.7/+(-&73.1.34.-13
q2c ()q1() =01=02
=2Q201
( )00
q2c (t)+02Q2q2c (t)+022 q2c (t) = 2(t) q1(t)= 2(t) q1(t)
.1,.K,3'&;1.2./E
)>#,#'#,.'!0#,"%+(&)>
-
SENSORS 2013
(,,"'#,&,#',(''-4+(, DI (-12.--3&;1.2./2(2.,(-4.-.!("1-3"32E
1
Q=
1
QSFD+
1
QTED+
1
Qanchor+
1
Qsurface+
1
Qintrinsic
).39"$%%("& !*%'$+-%("& &!'*'++
1
QSFD effg03
1
1+jc
1
QTED=
E 2 T0C
mech n
1+ mech n( )2 fn
n
1Qanchor
=1
2WresonatorWanchor
(&'13'(&'1!10F /-2.--3'1,F,.2 W-'.1
-
SENSORS 2013
#5(%-+#*0+4+(,() DJ
7*"3"&6,7$766>
-
SENSORS 2013
"(%:'!%(4+(,(), DK +2.*-.9-213K(-3&14-&&;1.2./2NO 31/K.9--8(&4.-74+(
-
SENSORS 2013
)+.('("(%:'!%(4+(, EB 2.-1+48,271,-39(3'12/33.23-(-&K98 (,(+13.3'.77+3-7+7,:,/+'.'(%#!'-(+' ,*.,.*',,C
-
SENSORS 2013
0-"4+,,#('7 EC (123(2.81;FF1;-N(1\cd[O
#+.'!#+ 0'#'!(+$ #'!%,,
.-4-7.722.7-.-4-7.72 2.7- -31,(6-32.7- ]F_32/118.+74.- .2-.1(+.,/.--3N(FF-..1(.+(2"3O -4-.2:(,7,1(+(2/+,-3N(FF,:.1(.+(2O '72D-4-.2'83.1.33,7'!2313'--.2
-
SENSORS 2013
-.('((-.(''!% ED 1*(-&.9-3'8(14.-(-3..13'.&.-+.,/.--32E
q2q1= tan2
.2K2(-
.2
K.2 K.2
K2(-
2(-
2(-
9.232.!("1-4++31.2 .2(-+31.2E"3R.2NA[3O (-+31.2"4R2(-NA[3O
"3-"4.3(-;,.7+4.- 13-.!3'(114.?
?(23'/61--&++33.1.34.--&+3'1.7&'@
-
SENSORS 2013
"(%:'!%(4+(, EE
77* '*26','*$!+"+67"!" &6>
;+(-1(+13K(-3&14-&&;1.2./NO3&)%C 3&)%D7K,2237-(-&!.1*&;1.2./
77*.+'/6,7$76&+'*+'.*&$6>
-
SENSORS 2013
#-.(',("(%:'!%4+(,EF ../13D/61-.!8(14.-2'.7+-.3/1371 73D,/+(37.!8(14.-;29(3'4,+(,(3
V
i
b
r
a
t
i
o
n
A
m
p
l
i
t
u
d
e
Time [s]
Mode 1
Mode 2
)%'#,"'+!4
.-&;4,2- (&'D+.9!107-;
',(2/'1(+12.-3.1&;1.2SENSORS 2013
-
SENSORS 2013
0&&+4 EG ,/1.8,-32(-12.+74.-24++107(1!.1/12.-+-8(&4.-
'(%(-2(&-,3'..+.&;(2(,,(--33.'(8/1!.1,-
(14.--2'.*(,,7-(3;1,.1(,/.13-33'-3'.7&'3
(&'K!107-;&;1.2E 7&&231737129(3'+18-3&2.812(&-2 2;3.(-3&13(-3.,.-.+(3'(,7+4K7-(32
'.+K-&+&;1.2/+-3;.!1..,!.1(,/1.8,-3
-
SENSORS 2013
+', EHP\QF
-
SENSORS 2013
+', EIP\]QFF7-&DF++D-F;
-
Sponsored by the IEEE Sensors Council, www.ieee-sensors.org
SENSORS 2013Tutorials: November 3, 2013 Conference: November 4-6, 2013