Adaptive FIRs taking place at Lasti

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Adaptive FIRstaking place at Lasti

• Richard Mittleman
• Laurent Ruet
• Brett Shapiro
• April 2006

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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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Adaptive Algorithm
d
Plant
x

-
e
FIR-Filter
y
Gradient
FIR filter, of length N, has coefficients h
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Control Strategy
STS
?(?)
Fsts
?(?)
Ground
Output
?(?)
FPS
?(?)0
PS

Input
Geo
FGeo
?(?)
?(?)
?(?)
Wit

Output
Plant
FSup
K2
Feedback
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FIR Implementation
G

Plant
B
Plant-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
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Feed Forward Sensor On The BSC
Wilcoxon Accelerometer Feed Forward Sensor
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SISO BSC Model
STS

• G

STS_f

To Pier top




PS
PS_f
To payload

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
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Extra Feed Back Path
G

Plant
B
Plant-B
-
K
Actuators

H(FIR)
-
Filter Update Coefficients
feed forward sensor
K feed back to feed forward senor
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Make an approximation
Initially H 0 After it has converged H B So
use
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(No Transcript)
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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 control
• Quad pendulum prototype in April)
• Port to LIGO controls
• Other Ideas and wonderful suggestions?

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Adaptive FIR Filters(Gradient Minimization)
Control Path
Feed Forward Sensor
Adaptive Path
HEPI Geophones
HEPI
BSC
Adaptive FIR Filter
Wednesday 1010am (SEI)
G