Lock Acquisition ofthe Virgo CITF

Lisa BarsottiUniversity and INFN – PISA

on behalf of the on behalf of the VIRGO CollaborationVIRGO Collaboration

XXXVIII Rencontres de Moriond 27th March 2003

Summary

CITF

Lock acquisition problem

Lock acquisition strategy

Statistical approach about lock acquisition

CITF Configuration

0lPR

WI

NIBS

B1

B5

Simple Michelson

1l

2l

The CITF working conditions are:

resonance of the stored power in the RC

Michelson on the dark fringeTwo lengths must be

controlled

Two typical lengths:

• Recycling Cavity (RC) length:

• Dark Fringe (DF) length:2

llll 210r

++=21 lll −=∆

Lock Acquisition Problem

Frequencies below 4 Hz: seismic noise

Need of a control system in order to keep the ITF locked to the required interference conditions

Lock Acquisition Problem

Optical signals as correction signals sent to the mirrors by feedback

0l 1l

2l

PR

WI

NIBS

RC Correction signal

DF Correction Signal

B5B1

Lock Acquisition ProblemLimits on the mirrors speed which

can be controlled

Bandwidth grater than few hundreds Hz not feasible because of computational andantialiasing delay in the control chain

Limit on the maximum force applied related with noise considerations

Bandwidth of the Feedback

sm2.0~2Bv µλℑ< sm2~ m2

λF v MAX µℑ<

Maximum force applied

Finesse

Wavelength

Bandwidth

Maximum Force

m064.1 µλ=

Hz100B=

250=ℑ

mN40F max=

Lock Acquisition Problem

Mirrors speed out of the limits placed by the correction system

Energy transferred by actuators to the mirrors during lock acquisition trials

No local controls along optical axis

We need such a strategy to avoid these problems on the mirrors speed

Optical DampingIn order to reduce mirrors excitations (0.6 Hz resonance) and the time of lock acquisition we have studied the OPTICAL DAMPING, which allows to damp excited mirrors.

Low speeds are reached in few seconds

PR

WI

NIBS

Simple Michelson

WI excited

PR misaligned

Error signal: B1_quad

B1

PR

WI

NIBS

PR-NI Cavity

Error signal: B1_quad

B1

WI misaligned

PR excited

Example of optical damping

WI Correction

B1_DC

PR Mirror Misaligned

(Volt)

(a.u)

WI Velocity of the order of tens µm/s

optical damping

WI velocity reduced

to the order of µm/s

Lock Acquisition StrategyAsymmetric trigger on the stored intensity

Lock acquisition is tried only when the mirrors are near to the rightresonance (that is the fundamental mode of the stored intensity)

(s)

Opening

Closing

Volts Stored Power Trigger opening: about one half of the maximum power

Trigger closing: few % of the maximum power

Enlargement of the action time interval of the

feedback

Lock Acquisition StrategyLinearization of the error signals

In order to enlarge this action time interval of the feedback we should linearize the error signals

0=n

2=n 23=n

1=n

Search for RC error signal in the following form:

DCBphaseB

n_5_5

0=n

2=n 23=n

1=n

23_5_5

DCBphaseB

Best choice for RC error signal:

Lock Acquisition StrategyLinearization of the error signals

In order to enlarge this action time interval of the feedback we should linearize the error signals

Lock Acquisition StrategyLinearization of the error signals

(s)

a.u23_5

_5DCBphaseB

CITF Configuration(only-mirrors)

0l 1l2l

BS

WI

PR

NI

B5B1

23_5_5

DCBphaseB

DF Error signalquadB _1

RC Error signal

Example of a Lock Acquisition Event

Stored Power (B5_DC)

WI CorrectionPR correction

Output Power (B1_DC)

(s) (s)

(s)(s)

(Volt)(Volt)

(a.u) (a.u)

We have a lock acquisition algorithm

Following steps:

•Systematic study of locking attempts

• Computation of the efficiency

• Improvement of the efficiency

Algorithm efficiency

How can we improve the efficiency ?

Locking success is due essentially to the mirrors speed

Trigger on RC Speeds

Trigger on DF Speeds

Lock Algorithm Efficiency

0056.0897

5=

Data Analysis Results

897 failed attempts 5 locking successes

Data taking by locking and delocking the CITF – 1 hour of data

Looking for

2 independent signalswhich describe

the RC speed and the DF speed

•

DCBACpB

_5Pr__5Pr_

23RC Speed Trigger - TEST OF

Sweep on RC •

DCBACpB

_5Pr__5Pr_

23

(s)

(a.u)(Volt)

1

2

DCB _5Pr_

0.21 0.211 0.212 0.213 (s)

(s)

1

2

0

0.5 0.55 0.6

Sweep on DFDCB _5Pr_

(Volt)

0.5 0.55 0.6

0

50

100

(s)

•

DCBACpB

_5Pr__5Pr_

23(a.u)

4000

2000

0

0.2110.21 0.212 0.213

The difference between these values is about two order of magnitude

is a good trigger!•

DCBACpB

_5Pr__5Pr_

23

•

DCBACpB

_5Pr__5Pr_

23RC Speed Trigger - TEST OF

Trigger on the RC speedIf we place a trigger on the RC speed, how much does algorithm efficiency improve?

By seeing the 5 good events : 1.34 max RC Speed

Locking attempts with RC speed < 1.34 : 415

smµ

smµ

Efficiency with trigger

0120.0415

5=

Efficiency without trigger

0056.0897

5=

By simulation:(Volt)ACpB _5Pr_ DCB

ACpB_5Pr__5Pr_

23(a.u)

7~α

Final conditions on :v

smm

Fv

smBv

µλα

µλα

13~2

5.1~2

max

ℑ<

ℑ<

Analysis of Results

Now we are into the expected velocity

range!

DF Speed Trigger – TEST OF ACqpB _1Pr_ 3•

Sweep on RC

Sweep on DF

DCB _5Pr_

0.21 0.211 0.212 0.213 0.21 0.211 0.212 0.213

0.50 0.60 0.50 0.60

1

0

2

1

0

20.02

0

0.04

0

-0.02

-0.04

-2000

2000

(Volt)

(Volt) (A.u)

(A.u)

0.55 0.55

DCB _5Pr_

ACqpB _1Pr_ 3•

ACqpB _1Pr_ 3•

DF Speed Trigger – TEST OF ACqpB _1Pr_ 3•

The difference between these values is morethan two order of magnitude

is a good trigger!ACqpB _1Pr_ 3•

Combined triggersHow much does the efficiency improve if we place a

trigger on RC speed and a trigger on DF speed at the same time?

We consider as triggers threshold theMAX speeds of locking successes

Efficiency: 017.0~2975 Improvement

of a factor 3

Speeds Distribution

0 0.05 0.1 0.15 0.2 0.25 0.3

-4x100

5

10

15

20

25

30

35

40

Nent = 897Mean = 2.662e-06RMS = 3.02e-06

Nent = 897Mean = 2.662e-06RMS = 3.02e-06

(M/SEC)

RC Speed Distribution

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

-4x100

5

10

15

20

25

Nent = 897

Mean = 8.987e-07RMS = 5.831e-07

Nent = 897

Mean = 8.987e-07RMS = 5.831e-07

(M/SEC)

DF Speed Distribution

Speeds Distribution

-0.2 -0.15 -0.1 -0.05 -0 0.05 0.1 0.15 0.2

-4x10-0.2

-0.15

-0.1

-0.05

-0

0.05

0.1

0.15

0.2-4x10 Nent = 897

Mean x = 6.532e-07

Mean y = 4.345e-08

RMS x = 3.972e-06

RMS y = 1.07e-06

Nent = 897

Mean x = 6.532e-07

Mean y = 4.345e-08

RMS x = 3.972e-06

RMS y = 1.07e-06

m/s RC Speed

DF

Spee

dm/s

ConclusionsDevelopment of the lock acquisition algorithm

(thanks to a full digital control system):

• asymmetric trigger

• linearization

• optical damping

Systematic study of the lock acquisition

Triggers on the speeds

Starting point for full VIRGO

• Lock Acquisition Simulation in progress