Now that we are in a moderately stable condition, its time to design the optical lever feedback transfer functions. We should think carefully about how to do this optimally.
In the past, the feedback shape was velocity damping from 0-10 Hz, with some additional resonant gain around the pendulum and stack modes. There were some low pass filters above ~30 Hz. These were all hand tuned.
I propose that we should look into designing optimal feedback loops for the oplevs. In principle, we can do this by defining some optimal feedback cost function and then calculate the poles/zeros in matlab.
How to define the cost function (? please add more notes to this entry):
1) The ERROR signal should be reduced. We need to define a weight function for the ERROR signal: C_1(f) = W_1(f) * (ERR(f)^2)
2) The OL QPDs have a finite sensing noise, so there is no sense in suppressing the signal below this level. Need to determine what the sensing noise is.
3) The feedback signal at high frequencies (30 Hz < f < 300 Hz) should be low passed to prevent adding noise to the interferometer via the A2L coupling. It also doesn't help to reduce this below the level of the seismic noise. The cost function on the feedback should be weighted apprpriately given knowledge about the sensing noise of the OL, the seismic noise (including stack), and the interferometer noise (PRC, SRC, MICH, DARM).
4) The servo should be stable: even if there is a negligible effect on the ERROR signal, we would not want to have more than 10 dB of gain peaking around the UGFs.
5) The OL QPDs are dominated by drift of the stack, laser, etc. at some low frequencies. We should make sure the low frequency feedback is high passed appropriately.
6) Minimize transmitted power rms in single arm lock etc.