Adaptive FIRs taking place at Lasti
description
Transcript of Adaptive FIRs taking place at Lasti
![Page 1: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/1.jpg)
LIGO-G060161-00-Z
Adaptive FIRsAdaptive FIRstaking place at Lastitaking place at Lasti
Richard MittlemanLaurent RuetBrett Shapiro
April 2006
![Page 2: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/2.jpg)
LIGO-G060161-00-Z
The Problem
![Page 3: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/3.jpg)
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
![Page 4: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/4.jpg)
LIGO-G060161-00-Z
IIR Implementation
Or 1 YBXAY
![Page 5: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/5.jpg)
LIGO-G060161-00-Z
IIR Implementation
![Page 6: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/6.jpg)
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 =
![Page 7: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/7.jpg)
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
![Page 8: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/8.jpg)
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
![Page 9: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/9.jpg)
LIGO-G060161-00-ZNo Compensation Path
![Page 10: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/10.jpg)
LIGO-G060161-00-ZSimple Implementation
![Page 11: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/11.jpg)
LIGO-G060161-00-Z
Feed Forward Sensor On The BSC
Wilcoxon AccelerometerFeed Forward Sensor
![Page 12: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/12.jpg)
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
![Page 13: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/13.jpg)
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
![Page 14: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/14.jpg)
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
![Page 15: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/15.jpg)
LIGO-G060161-00-Z
Make an approximation
122
HKPhk
Initially H = 0After it has converged H ~= BSo use
![Page 16: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/16.jpg)
LIGO-G060161-00-Z
![Page 17: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/17.jpg)
LIGO-G060161-00-Z***SENSOR CORRECTION IS OFF ***
![Page 18: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/18.jpg)
LIGO-G060161-00-Z
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?
![Page 19: Adaptive FIRs taking place at Lasti](https://reader036.fdocuments.in/reader036/viewer/2022062409/56815029550346895dbe17ce/html5/thumbnails/19.jpg)
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)