I am pretty happy at this moment.
I definitely feel that it took me too much time to understand how to do the Matlab program and how to overcome difficulties,
but eventually at last my Matlab program seems to start working.
Briefly: What the program does?
--> take time-domain signal from two accelerometers near ITMX and ETMX (use 'get_data');
--> calculate the time-evolution of those two signals through the system "stack + pendulum" to the test-masses ITMX and ETMS (use 'lsim' in Matlab),
which gives us the time-domain evolution of the deviation of the position of individual test-mass from its average position.
--> Subtract the two results from each other in time-domain, this gives us the deviation of the length of the XARM-cavity from its average value
(roughly speaking, deviation of the length of the cavity from exactly 40 meters, although I am aware that the exact average length of XARM is less than 40 meters).
--> Take the amplitude spectrum of the result, using Sqrt(pwelch) and calibrate it from "counts" to "meters".
--> Calculate root-mean-square of peaks at different frequency intervals, for example near 0.8Hz,
and plot the three-dimensional surface showing the dependence of RMS on Q-factors Q_{ETMX} and Q_{ITMX}.
Eventually I am able to create these dependences of RMS.
I see that the minimum of the dependence is close to the diagonal corresponding to exact equality of Q_ETMX} and Q_{ITMX}, but not exactly along the diagonal. The plot allows to say
which of two conditions "Q_I > Q_E" or "Q_E < Q_I" should be fullfilled for optimization reasons. My plot is raw, I might have made a mistake in axis-label, I do not garantee now that the axis label "Q_ITMX - Q_ETMX" is correct,
maybe I need to change it for "Q_ETMX - Q_ITMX". I need some more time to determine this on Monday, but clearly there is asymmetry between Q_I and Q_E.
The peak at 0.8 Hz is pretty stable, while the peak at around 3Hz is not very repeatable, therefore in both experimental measurements and these simulations the amplitude of RMS of peak at 3Hz) is several orders of magnitude smaller than for RMS of peak at 0.8Hz, and I do not see minimum somewhere in the RMS-dependence, I see now only steady growth of RMS as Q_factors increase.
I will need to spend some time on Monday trying to understand how the sampling frequency and number of fft-points influence my results when I take amplitude spectrum using pwelch-command, as well I will need to double-check the correctness of normalization from counts to meters (I am not confident right now that amplitude of order of 10^(-12) meters is correct).
So, I need some time after the weekend to analyze my results and maybe make some slight changes, but I am glad that my Matlab model started to work in principle. I wanted to let others know about the status of the progress in my work. The fact that Matlab program works now is a good ending of a week.
Andrey. |