The temperature variation of NI and WI TMs under etalon control can be reconstructed assuming three components:
- The effect of the YAG, following the lock/unlock of the cavities
- The effect of the heater used in etalon loop
- a compensation of a constant drift due to an external disturbance
A first attempt to do this reconstruction was done some time ago for NI, in a period when the control had some oscillation and the control correction was quite high. Using those data as a noise injection, it was possible to estimate the temperature response to the heater as two simple poles at 2.5 uHz and, on that estimation, develope a new more performing etalon controller. A good data reconstruction was possible assuming also a response to a YAG step as a simple pole at 2.5 uHz, with an amplitude 0.2 deg. Applying the same model to WI, the reconstruction did not work so well as for NI, mainly due to a larger sensitivity to a YAG step.
The analysis has be replied, trying to be more precise in the evaluation of an alternative step response to the YAG for WI. Two different models have been tested:
- simple pole at 2.5 uHz (the same as NI), amplitude 0.3 deg (50 % larger than NI)
- simple pole at 5 uHz (the double of NI), amplitude 0.2 deg (the same as NI)
Among the two, it seems that the second model works better. I don't know how to explain a so much different time scale for the heat absorbtion/dispersion in two TMs which should be very similar.
An attempt to use a different response to the heater did not give any better result.
The models applied to old data (March) or recent data (October), give results of similar quality, excluding a relevant change in time of the responses.
