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