KAGRA Logbook

I measured all SR3 transfer functions and modeled them.

The strategy of this modeling is very simple. Procedures are as follows:

I hand-fit the transfer functions using a coupled oscillator model (sums of simple oscillator transfer functions).
Using the hand-fit as an initial guess, I minimize a cost function to obtain the final parameters.

The cost function is defined as

$J(\theta)=\frac{1}{N}\sum_{n=0}^N w(f_n)\log\left\lvert G_\mathrm{measured}(j2\pi f_n) - G_\mathrm{model}(j2\pi f_n ; \log\theta) \right\rvert$

where $w(f)$ is a weighing function, set equal to coherence function of the measurement and is masked within the frequency region of interest, typically below 10 Hz.

Every fit was done with python in Jupyter notebook which can be found in /kagra/Dropbox/Subsystems/VIS/vis_commissioning/sr3/notebook/transfer_function_fit/.

All suspension models are installed into the FM10 of the damping filters, DCCTRL for IP, DAMP for GAS filters and IM, and OLDAMP for TM.

Please also see attached figures for the results for all 15 degrees of freedom.