LIGO-G060161-00-Z

Adaptive FIRsAdaptive FIRstaking place at Lastitaking place at Lasti

Richard MittlemanLaurent RuetBrett Shapiro

April 2006

LIGO-G060161-00-Z

The Problem

LIGO-G060161-00-Z

FIR ImplementationThe basic block diagram for an FIR filter of length N. The delays result in operating on prior input samples. The hk values are the coefficients used for multiplication, so that the output at time n is the summation of all the delayed samples multiplied by the appropriate coefficients.

Or HXY

H = Filter CoefficientsX = Input ValuesY = Output Value

LIGO-G060161-00-Z

IIR Implementation

Or 1 YBXAY

LIGO-G060161-00-Z

IIR Implementation

LIGO-G060161-00-Z

Adaptive Algorithm

Plant

FIR-Filter

+- 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 =

LIGO-G060161-00-Z

STS

Wit

PS

Geo

FFstssts

FFSupSup

FFPSPS

FFGeoGeo

+

A

B++

+

+++

Output

+++

K2

K1

()

Output

()

()=0()

()

()

Plant

+

Ground

Input

Feedback

Control Strategy

LIGO-G060161-00-Z

FIR Implementation

Plant

H(FIR)

BPlant-B

Actuators

OutputFilter

ShapingFilter

+

-

PGOS

hS

h

S

kk

22

22

2

G

S = Shaping FilterO = Output FilterP = Plant(Actuator to Witness Sensor)G = Ground input

S

LIGO-G060161-00-ZNo Compensation Path

LIGO-G060161-00-ZSimple Implementation

LIGO-G060161-00-Z

Feed Forward Sensor On The BSC

Wilcoxon AccelerometerFeed Forward Sensor

LIGO-G060161-00-Z

SISO BSC ModelG +

A

+

++ +

+

++

+

+

Plant

To Pier top

To payload

STS

PS

GEOWIL

WITFIR

Geo_f

PS_f

STS_f

Sup_f

= Sensors = Filters

LIGO-G060161-00-Z

Closed Loop Response

)}]({*[

)}]({1[

fgfgffg

dfdfdffd

STSPSPSGeoGeoSupWILFIRG

STSSTSPSPSGeoGeoSupWILFIRA

YGZA )1(

Closed Loop Equation

Simplifying

Z

YWITWIT

GWIT

dg

1

And the Witness response is

A = Actuator Drive SignalG = Ground Signal

Where Y has ground to sensorTransfer Functions and Z has driveto sensor Transfer Functions

XXXf = A filterXXXg = Ground to sensor TFXXXd = Actuator to sensor TF

LIGO-G060161-00-Z

Extra Feed Back PathPlant

H(FIR)

BPlant-B

Actuators

+

-

122

BKPhk

G

K

-

+

= feed forwardsensor

K = feed back tofeed forward senor

Filter Update Coefficients

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Make an approximation

122

HKPhk

Initially H = 0After it has converged H ~= BSo use

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LIGO-G060161-00-Z***SENSOR CORRECTION IS OFF ***

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What needs to get Done

• Work more with the Model• Redo HEPI with 6 DOF and optimized

sensor correction– (hopefully after the installation of the controlQuad pendulum prototype in April)

• Port to LIGO controls• Other Ideas and wonderful

suggestions?

LIGO-G060161-00-Z

Adaptive FIR Filters(Gradient Minimization)

BSC

HEPI

G

Feed ForwardSensor

Adaptive FIRFilter

HEPI Geophones

Control PathAdaptive Path

Wednesday 10:10am (SEI)