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:
z1 = -0.9799;
z2 = 2.1655;
z3 = -2.9746- i * 3.7697
z4 = -2.9746+ i * 3.7697
z5 = 95.7703 + 0.0000i
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:
Gain = 20
z2 = -18.2774
z3 = -16.6167
z4 = -1.2486
z5 = 28.1080
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.