1. Seismic Developments at LASTI LIGO-G050184-00-Z
Luarent Ruet
Richard Mittleman
 Lei Zuo
March 2005

2.  OUTLI NE
1) Geophone tilt correction
HAM
BSC (non-linear bending??)
2) BSC Stack Characterization
Resonant Gain
 Noise Study
3) Modal Control/Adaptive Filters
4) Estimators
5) HAM Plant Modifications
6) System identification noise subtraction
Triple
BSC Noise Measurements
7) Future Plans

3. Tilt Correction
The source of tilt can be divided into two categories, inherent
and induced.

4. Geophone Tilt Subtraction
Tilt transfer function of an inertial sensor
Assumptions
The plant is linear
The induced angle is proportional to the displacement
We can then predict the tilt-induced signal
from the geophones

7. A B Control Strategy Fsts FPS FGeo FTilt FSup STS PS + Geo + Wit Plant
()
STS
Fsts K1
()
Ground
Output
()
()=0 +
FPS PS +
Input A B + +
Geo
FGeo + +
()
()
Wit +
()
Output
Plant
FTilt
FSup K2
Feedback
Control Strategy

8. BSC Transfer Functions

9. Beam Bending

10. Blow UP

11. vs. drive

12. BSC Stack Transfer Functions
From the Support table to the Optics Table

13. BSC Stack X-Mode

14. Resonant Gain Results

15. Adaptive Algorithm e d x FIR-Filter y Plant + - Gradient =
FIR filter, of length N, has coefficients h

16. Simulink Diagram

17. A B Control Strategy Fsts FPS FGeo FSup STS PS Geo Wit Plant
()
STS
Fsts K1
()
Ground
()
()=0 +
FPS PS +
Input A B +
Geo
FGeo +
()
()
()
Wit +
Plant
Adaptive Filter + + K2
FSup
Control Strategy
Feedback

18. HAM Optics Table Results

19. Modal control

20. Modal Control Results

21. Estimator Model - + Ground Noise (w) Sensor Noise (v) Plant Drive (u)
Gain K +
Model
Modal
Signals

22. Estimator Math Where Ce is a selector Matrix
Where TFm is the model transfer function if
A large K will
give
A small K will give

23. Noise Model

24. Estimator Results

25. Estimator Model - + Ground Noise (w) Sensor Noise (v) Plant Drive (u)
Gain
Filter K +
Model
Modal
Signals

26. F dependant K

27. Results

28. Spectrum

29. 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?

30. HAM Table Resonance

31. Stiffener

32. Y-Optical table

33. X–Position Sensors

34. Noise Subtraction

35. BSC Vertical Noise

36. Vertical Noise 2

37. Horizontal Noise #1

38. Horizontal Noise Low

39. Horizontal Noise Mid

40. Horizontal Noise High

41. 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
Control Equations
Closed Loop Transfer Function from ground to witness sensor

42. THE END