Seismic Developments at LASTI LIGO-G050184-00-Z
Luarent RuetRichard Mittleman
Lei Zuo
March 2005
OUTLI NE1) Geophone tilt correction
HAMBSC (non-linear bending??)
2) BSC Stack CharacterizationResonant Gain
Noise Study3) Modal Control/Adaptive Filters 4) Estimators
5) HAM Plant Modifications 6) System identification noise subtraction Triple
BSC Noise Measurements7) Future Plans
Tilt CorrectionTilt Correction
The source of tilt can be divided into two categories, inherent and induced.
Geophone Tilt Subtraction
Assumptions
1) The plant is linear
2) The induced angle is proportional to the displacement
Tilt transfer function of an inertial sensor
f
sponceSensorOutput2
Re
We can then predict the tilt-induced signal from the geophones
STS
Wit
PS
Geo
FFstssts
FFSupSup
FFPSPS
FFGeoGeo
+
A
B++
+
+++
Output
+++
K2
K1
()
Output
()
()=0()
()
()
Plant
+
Ground
Input
Feedback
Control Strategy
+
FFTiltTilt
+
BSC Transfer Functions
Beam Bending
Blow UP
vs. drive
BSC Stack Transfer Functions
From the Support table to the Optics Table
BSC Stack X-Mode
Resonant Gain Results
Adaptive Algorithm
+- e
y
xd
][2
)(221
0
2
||
x
xe
iN
N
iiNi
iii
e
hdh
eydh
eh
FIR filter, of length N, has coefficients h
Gradient =
Simulink Diagram
STS
Wit
PS
Geo
FFstssts
FFSupSup
FFPSPS
FFGeoGeo
+
A
B++
+
+++
+++
K2
K1
()
()
()=0()
()
()
Plant
+
Ground
Input
Feedback
Control Strategy
Adaptive Filter++
HAM Optics Table Results
Modal control
Bode Diagram
Frequency (Hz)
Mag
nitude
(abs)
Step Response
Time (sec)
Am
plitu
de
10-1
100
101
10-10
10-5
100
105
0
1
2
To: re
al z
1
From: excitation
0
2
4x 10
-8
To: m
ode3
0
0.5
To: m
ode2
0 2 4 6 8 10 12 14 16 18 200
1
2
To: m
ode1
real z1mode 3mode 2mode 1
Modal Control Results
100
101
10-2
10-1
100
101
Freq (Hz)
magnitude (m
/sqrt(H
z))
Modal control with inertial and relative sensors
control offnoise levelcontrol on, inertial sensorscontrol on, relative sensors
Estimator Model
Ground Noise (w)
Drive (u) Plant
Sensor Noise (v)
Model
K
Gain -
+
ModalSignals
y
y
x
x
Estimator Math
vCexCexCeyy ˆˆWhere Ce is a selector Matrix
Where TFm is the model transfer function
emKCTF
xx
11
ˆ
xif A large K will
give xx
A small K will give
0ˆ x
KTFx mˆ
Noise Model
Estimator Results
10 11 12 13 14 15 16 17 18 19 20-1.5
-1
-0.5
0
0.5
1
1.5
Time (sec)
Z1 (m
)comparison real data / estimator
realestimated
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
Time (sec)
Z1(m
)
comparison real data /estimator with noise, K is big
realestimated
5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10-0.5
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
0.5
Time (sec)
Z3(m
)
comparison real data /estimator with noise, K is big
realestimated
10 11 12 13 14 15 16 17 18 19 20-1.5
-1
-0.5
0
0.5
1
1.5
Time (sec)
Z3
(m)
Comparison real data / estimator
RealEstimated
Estimator ModelGround Noise (w)
Drive (u) Plant
Sensor Noise (v)
Model
K
Gain -
+
ModalSignals
y
y
x
x
Filter
F dependant K
10-5
100
105
Magnitude (abs)
100
101
102
-180
-135
-90
-45
0
45
90
135
180
Phase (deg)
model z0 -> z1estimator gainmodel * gain
Bode Diagram
Frequency (Hz)
Results
22 24 26 28 30 32 34 36 38
-1
-0.5
0
0.5
1
Time (sec)
mode 1
comparison real data /estimator
realestimated
22 23 24 25 26 27 28 29 30
-1
-0.5
0
0.5
1
Time (sec)
mod
e 2
comparison real data /estimator
realestimated
Spectrum
100
101
10-2
10-1
100
101
Freq(Hz)
magnitude (m
/sqrt
(Hz))
Spectrum, control off and estimation+modal control on
control offestimation+modal control onsensor noise level
Future Estimator Work
How Good does the Model Need to Be?
How do we optimize the Estimator Gain vs. the Control Gain?
Try it on a piece of hardware; the triple pendulum control prototype.
Other Ideas?
HAM Table Resonance
Stiffener
Y-Optical table
X–Position Sensors
Noise Subtraction
BSC Vertical Noise
Vertical Noise 2
Horizontal Noise #1
Horizontal Noise Low
Horizontal Noise Mid
Horizontal Noise High
BPSPS
BGeoGeo
PSPSGeoGeo FF sup
Transfer Function from dSpace to Position Sensors
Transfer Function from dSpace to Support Table Geophones
Open Loop transfer function
Transfer Function from Ground STS to Witness Sensor
Transfer Function from dSpace to Witness Sensor
Closed Loop Transfer Function from ground to witness sensor
STSWitAW ~
WitAW
sup2
1sup2
1
)(~
)(
)(
KSTSWit
FKFFK
STS
Wit PSWitSTSPSw
Control Equations
THEEND