Goal:

To estimate the transfer function and the noise in the FC that is a part of the FOL-PID loop.

Measurements Taken:

The setup used for the measurements is described in my previous elogs.

The input modulation signal and the FC output were recorded simultaneously for a certain period of time and the phase and gain are estimated from the data.

Analysis(Data and code attached):

The recordings must contain equal number of data points(around 6000 data points in my measurements) for analysis.

The steps I followed to generate these plots are:

• Took the FFT of both FC out data(from FC) and Modulation input(from SRS via ADC).
• Estimated the phase angles at the particular modulation frequencies from the FFT data(in Matlab using  angle(x) for phase at the frequency f(x);x: is the frequency bin)
• Then for the phase of the system at a particular modulation frequency, 

                              Phase(system) =Phase(FC Signal) - Phase(Input Signal)

• Plotted the acquired phase vs the modulation frequency on a Semi-log graph.

Results:

From the plots its can be inferred that :the delay of the FC is almost 0 until the modulation of 0.1 Hz. Then there are phase shifts of  +/- 180 degrees showing that the system has multiple poles and zeroes(will be estimated after I have phase plots at few more carrier frequencies).

To Do Next: 

Phase plots for varying carrier frequencies and different sampling times.

Installation of FC inside the 40m.