40m QIL Cryo_Lab CTN SUS_Lab TCS_Lab OMC_Lab CRIME_Lab FEA ENG_Labs OptContFac Mariner WBEEShop
  40m Log  Not logged in ELOG logo
Message ID: 10899     Entry time: Wed Jan 14 02:11:07 2015
Author: rana 
Type: Summary 
Category: Treasure 
Subject: 2-loop Algebra Loopology 

I show here the matrix formalism to calculate analytically the loop TF relationships for the IMC w/ both FSS actuators so that it would be easier to interperet the results.

The attached PDF shows the Mathematica notebook and the associated block diagram.

In the notebook, I have written the single hop connection gains into the K matrix. P is the optical plant, C is the Common electronic gain, F is the 'fast' NPRO PZT path, and M is the phase Modulator.

G is the closed loop gain matrix. The notation is similar to matlab SS systems; the first index is the row and the second index is the column. If you want to find the TF from node 2 to node 3, you would ask for G[[3,2]].

As examples, I've shown how to get the FAST gain TF that I recently made with the Koji filter box as well as the usual OLG measurement that we make from the MC servo board front panel.

Attachment 1: FSSloop.pdf  102 kB  | Hide | Hide all
FSSloop.pdf FSSloop.pdf
Attachment 2: FSSloop.png  54 kB  | Hide | Hide all
FSSloop.png
ELOG V3.1.3-