Adaptive FIRs taking place at Lasti

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Adaptive FIRs taking place at Lasti. Richard Mittleman Laurent Ruet Brett Shapiro April 2006. The Problem. FIR Implementation. The 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

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### Adaptive FIRstaking place at Lasti

Richard Mittleman

Laurent Ruet

Brett Shapiro

April 2006

LIGO-G060161-00-Z

The Problem

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FIR Implementation

The 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

H = Filter Coefficients

X = Input Values

Y = Output Value

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IIR Implementation

Or

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IIR Implementation

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d

x

Plant

+

-

e

FIR-Filter

y

FIR filter, of length N, has coefficients h

LIGO-G060161-00-Z

Control Strategy

K1

A

B

+

+

+

+

+

+

+

+

+

STS

()

Fsts

()

Ground

Output

()

FPS

()=0

PS

+

Input

Geo

FGeo

()

()

()

Wit

+

Output

Plant

K2

FSup

Feedback

LIGO-G060161-00-Z

FIR Implementation

G

+

Plant

Plant-B

B

-

Actuators

Shaping

Filter

Output

Filter

H(FIR)

S = Shaping Filter

O = Output Filter

P = Plant(Actuator to

Witness Sensor)

G = Ground input

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No Compensation Path

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Simple Implementation

LIGO-G060161-00-Z

Feed Forward Sensor On The BSC

Wilcoxon Accelerometer

Feed Forward Sensor

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SISO BSC Model

STS

+

STS_f

G

+

To Pier top

+

+

+

+

PS

PS_f

+

Plant

+

A

GEO

Geo_f

WIL

FIR

WIT

+

Sup_f

+

= Sensors

= Filters

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Closed Loop Response

Closed Loop Equation

Simplifying

XXXf = A filter

XXXg = Ground to sensor TF

XXXd = Actuator to sensor TF

And the Witness response is

A = Actuator Drive Signal

G = Ground Signal

Where Y has ground to sensor

Transfer Functions and Z has drive

to sensor Transfer Functions

LIGO-G060161-00-Z

Extra Feed Back Path

G

+

Plant

Plant-B

B

-

K

Actuators

+

H(FIR)

-

Filter Update

Coefficients

= feed forward

sensor

K = feed back to

feed forward senor

LIGO-G060161-00-Z

Make an approximation

Initially H = 0

After it has converged H ~= B

So use

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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 control

Quad pendulum prototype in April)

• Port to LIGO controls
• Other Ideas and wonderful suggestions?

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Control Path

Feed Forward

Sensor

HEPI Geophones

HEPI

BSC