We tried to estimate a model of the transfer function from NI heating belt (HB) correction and NI ring heater (RH) temperature from the in-loop data, given that in the recent data the etalon loop worked quite often in on-off mode. In this condition, very likely the loop injects noise and consequently the in-loop error is larger than the external disturbance on the temperature. This means that the temperature fluctuation can be estimated as the actuation filtered by the plant.

Applying this method to the square of the voltage sent to HB (the correction supposed to be linear vs the temperature), one can reconstruct quite well the data, if the plant is supposed to be given by two simple poles at 2.5 uHz (fig 1). This is a bit different wrt the plant used to develop the control: one of the two poles was supposed to be about there, but the other was estimated at a much higher frequency.

Assuming the new plant and assuming a given gain for the control loop, one can produce a model for the loop that explains an amplification of the noise at the frequency observed in the data (accidentally very close to the daily period).