Brad Ratto
The analysis for front end compensation of the TM PUM drivers along with quantifying the expected incurred systematic error continues. The procedure for which has been well documented: LHO:61729. Allow me to summarize.
Using measurements from the ITMX & ITMY PUM driver (LHO:61280), and ETMX & ETMY PUM driver (LHO:61313), a fit is made to find the zeros and poles for the response of each TM PUM driver and hence compensate accordingly. However, the fit yields super-nyquist zeros and poles, it is only possible to compensate for sub-nyquist zeros and poles in the front-end, hence either the super-nyquist poles and zeros must be ignored or compensated for in the low-latency and offline calibration pipeline. Therefore, a decision must be made, luckily the cost of ignoring the super-nyquist frequency poles and zeros can be quantified by the affect it has on the systematic error of the response function.
Before I show any plots let me walk through where to find the script and supporting files.
There are four individual scripts for each TM PUM driver found here: GitSuspensions
model_#TM#_PUM_driver_systematicerror.py
The pre-processed data used in the scripts are stored as .hdf5 files found here: SUSElectronics
The script also calls for a input file that is required to run pyDARM, that is found here-ye: pyDARMparams
The plots I produced used data from the following dates:
ETMX-PUM: 2022-01-14
ETMY-PUM: 2022-01-17
ITMX-PUM: 2022-01-10
ITMY-PUM: 2022-01-11
I will only present the results from analyzing State 3, "Low Pass ON", the intended state for operations. As a reminder, the other states include: State 1 (no switchable response on) and State 2 (highest range, high gain, "Acquire ON" state). The full list of plots for all the states can be found here in the same place where the data resides under the same date mentioned above.
In a very similar fashion to LHO:61729, let us begin by taking a look at the following comparisons for each of the TM PUM drivers and their coils.
ETMX-PUM: 2022-01-14_H1SUSETMX_PUMDriver_S1000343_40Ohm_State3_AllCoilsCompensationComparsion.pdf
ETMY-PUM: 2022-01-17_H1SUSETMY_PUMDriver_S1102652_40Ohm_State3_AllCoilsCompensationComparsion.pdf
ITMX-PUM: 2022-01-10_H1SUSITMX_PUMDriver_S1000346_40Ohm_State3_AllCoilsCompensationComparsion.pdf
ITMY-PUM: 2022-01-11_H1SUSITMY_PUMDriver_S1102654_40Ohm_State3_AllCoilsCompensationComparsion.pdf
The two panels on the left is the magnitude and phase response of each coil, the right two panels denote the systematic error between the measured data and the different models.
The color legend:
(BLUE) The the measured data, normalized the unity, we are not interested in the DC gain for this analysis, by dividing out the magnitude of the measured data at the lowest frequency point, 0.2 Hz.
(ORANGE) Shows the full zero-pole response, this includes the super-nyquist zeros and poles.
(GREEN) If we were to ignore the super-nyquist zeros and poles and only compensate with the zeros and poles at sub-nyquist frequencies.
(RED) If we compensate only for the coil driver response, and ignore the contribution from the AOSEM response.
As Jeff mentions in LHO:61729, and further supported by the additional plots, ignoring the AOSEM response would mean having to incur systematic errors which grow as a function of frequency, which already reach 2.5% and ~4 deg by 100 Hz.
However, the question still remains, how would this affect the systematic errors in the response function, and can we get away with throwing out the super-nyquist zeros and poles. By using pyDARM, it is possible to propagate the systematic errors of each scenario through the entire actuation response chain. this it is then folded into the DARM loop response function and as a result an estimate of the systematic error on the DARM response function. See bullets (3)-(5) LHO:61729. The final error in the response function is seen below -- that is again, the estimated error in the PUM stage, propagated to error in the response function..
ETMX-PUM: 2022-01-14_H1SUSETMX_PUMDriver_S1000343_40Ohm_State3_etaR_w_etaPUM_Comparison.pdf
ETMY-PUM: 2022-01-17_H1SUSETMY_PUMDriver_S1102652_40Ohm_State3_etaR_w_etaPUM_Comparison.pdf
ITMX-PUM: 2022-01-10_H1SUSITMX_PUMDriver_S1000346_40Ohm_State3_etaR_w_etaPUM_Comparison.pdf
ITMY-PUM: 2022-01-11_H1SUSITMY_PUMDriver_S1102654_40Ohm_State3_etaR_w_etaPUM_Comparison.pdf
Let the plots show that:
The results are mostly ubiquitous, and the following statements from LHO:61729 apply.
(i) The AOSEM response can not be ignored.
(ii) Ignoring the super-nyquist poles from the AOSEM response leads to frequency-dependent features in the response function where the systematic errors reaches 0.3% and ~0.2 deg between 10 Hz-150 Hz.
(iii) Lastly, compensating for all the zero and poles would mean that the systematic error in the PUM driver would manifest in the response function at the 0.1% and 0.2 deg level.
