LIGO-G050442-00-Z 1

E2e modeling of violin mode

S. Yoshida

Southeastern Louisiana University

V. Sannibale M. Barton, and H. Yamamoto

Caltech LIGO

NSF: PHYS-0354942LLO

2

Violin model

N oscillators (massless string + bob)

Lw1, Tw1Lw2, Tw2

Optic as final oscillator

i

State Space representation (ABCD matrix) V. Sannibale (LIGO I, Maple) M. Barton (AdvLIGO, Mathematica)

(Wire length, tension)

3

Two State Space boxes (LIGO I)

New dynamics included: Coupling among1) pos, pitch, yaw & violin2) bounce, roll & side

Sus pt motion

Actuation force

(COIL)

Opt motion

Pos*PitchYawBounce**Rollside

3DSusViolin.box(3DSus primitive)

* Under testing, ** Will be added soon.

4

LOS/SOS violin.box

Controller.box

3DSusViolin.box

Seismic noiseFloor motion DAQ & table motion model*Violin

Optic

OSEM sensor

Optical Lever

Length Sensing Control/Optical Spring

*Aug04/March05 LSC meetingT. Findley, et al., G050219-00-DS. Yoshida et al., T030159- 00-D

Actuation (coil) force

5

White Noise Input to sus point(free hanging)

Split due to wire asymmetry

6

Step Input to sus point z(free hanging)

3Dsus primitive3DsusViolin.box

Sus point z to Opt Yaw coupling: due to wire asymmetry

Z to Opt pos

Z to Opt pitch

Z to Opt yaw

10

-10

0

0.2

-0.2

0

2

0

1

2

0

1

10

-10

0

0.2

-0.2

0

Time (s) Time (s)

Z

7

Step Input to sus point yaw(free hanging)

3Dsus primitive3Dsus_Violin.box

Yaw to Opt pos

Yaw to Opt pitch

Yaw to Opt yaw

1

-1

0

x10-3

x10-3

1

-1

0

6

-6

0

2

0

1

1

-1

0

Time (s)Time (s)

Sus point Yaw to Opt Pos/Pitch coupling: due to wire asymmetry

2

0

1

8

Step Input to sus point z(pitch local damp on)

Time (s)

Free hangLocal-damped

coil force

Z to Opt pos

Z to Opt pitch

Z to Opt yaw

4

-4

0

3

-1

1

0.4

-0.4

0

Frequency (Hz)

yaw

pitch

pos

9

Step Input to sus point yaw(yaw local damp on)

Time (s) Frequency (Hz)

coil forceFree hangLocal-damped

Yaw to Opt pos

Yaw to Opt pitch

Yaw to Opt yaw

x10-4

x10-3

3

-1

1

0.4

-0.4

0

2

-2

0

10

Plan for AdvLIGO

- HAM, BSC boxes stack models needed!

- Suspension (Mark Barton’s model, 6DOF x stages, + violin) numerical experiment of MC performance

- Detailed analysis location of suspension on HAM table