The goal of the measurements we made ( my previous 3 elogs) was to characterize the laser frequency thermal actuator that is a part of the FOL- PID loop.

For this we made indirect TF measurements for the thermal actuator by looking at the PZT response by 1)arm cavity( ETM ,ITM) displacement  and 2) temperature offset excitation. The goal was to do something like getting G1=TF3/TF1 and G2=TF3/TF2 and ultimately dividing G2/G1 to get TF2/TF1 with correct calibration. The final TFs obtained are the X and Y arm TFs for Laser frequency response vs temperature offset in(HZ/count). The calculations  in detail are:

Obtained    G1 = PZT response/ Temperature Offset (count/count): (in detail here )

Obtained    G2 = PZT response/  X and Y arm displacement( count/ count) : (in detail here)

Calibrated G2 to count/m ( in detail here)

Divided G2/G1 to get X and Y arm displacement/ Temperature Offset( m/ count) to get G3

Did these calculations:

dL/ L = dF /F

F = c/lambda ;Lambda = 532 nm  ; L = 

X arm length = 37.79 +/- 0.05 m

Y arm length = 37.81 +/- 0.01 m

TF: Laser Freq/ Temperature Offset = G3 *F/L       (HZ/Count)

The calibration coefficients for the ends  are :

X End:  [23.04 +/-  0.23 ]* 10^3  (HZ/Count)

Y End:    [18.71 +/-  0.2 ]* 10^3 (HZ/Count)

For the TFs of the temperature actuator on laser frequency I used ITMs for both the arms. The bode plots for the calibrated( HZ/Temp Count) are attached.

 For the X-Arm Thermal Actuator, I calculated the TFs at two different frequency ranges and combined the results where the coherence is high(>0.7). At 1 Hz the coherence was not as good as the other frequencies(due to the suspension resonance at 0.977 Hz).

The poles and zeroes are estimated after fitting this data using Matlab vectfit tool.The  graphs showing fit and measured values are attached.

Y arm Thermal Actuator:

5th order TF fitted: 

Gain: 9000

Zeroes:

z1 = -0.9799;

z2 = 2.1655; 

z3 = -2.9746- i * 3.7697

z4 = -2.9746+ i * 3.7697

z5 =  95.7703 + 0.0000i 

Poles:

p1 = -0.0985- i* -0.0845

p2 = -0.0985+ i* -0.0845

p3 = -0.6673- i* -0.7084

p4 = -0.6673+ i* -0.7084

p5 = -8.7979.

X-arm Thermal Actuator:

5th order TF fitted: 

Gain = 20

Zeroes:

z1= -305.7766

z2 =   -18.2774

 z3 =  -16.6167

 z4 =   -1.2486

 z5 =   28.1080

Poles:

p1  = -0.1311 - 0.1287i

p2 =  -0.1311 + 0.1287i

 p3  =  -8.3797 + 0.0000i

 p4 =  -4.0588 - 7.5613i

  p5 = -4.0588 + 7.5613i

I will use get the poles and zeroes from these fitted  bode plots and use it to build the PID loop.