Thanks to the opening of the slow python servo for the DET lab air conditioning I was able to evaluate the performance of the servo.

As it is visible in the trend, figure 1, after the opening of the loop (25th afternoon) the auto-oscillation of the air conditioning system is well visible (having a 0.5deg peak to peak oscillation) which can be compared to the temperature control accuracy when the slow servo is engaged.

From Figure 2 (servo on = purple, servo off = blue) is visible that the control accuracy is improved (from 0.5 peak to peak to 0.2 deg peak to peak) but I think there are still some margins of improvement.

It is worth to say that the requirements for the INJ and DET lab T variation were 0.1 deg.