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Entry  Wed Feb 11 04:08:53 2015, Jenne, Update, LSC, New Locking Paradigm? 
    Reply  Wed Feb 11 22:13:44 2015, Jenne, Update, LSC, New Locking Paradigm - LSC model changes 
       Reply  Thu Feb 12 01:43:09 2015, rana, Update, LSC, New Locking Paradigm - LSC model changes TF.gif
       Reply  Thu Feb 12 11:14:29 2015, Jenne, Update, LSC, New Locking Paradigm - Loop-gebra ALS_REFL_comboLockingCartoon_11Feb2015.PDFALS_REFL_comboLocking_11Feb2015.zip
          Reply  Thu Feb 12 11:59:58 2015, Koji, Update, LSC, New Locking Paradigm - Loop-gebra 
             Reply  Thu Feb 12 19:18:49 2015, Jenne, Update, LSC, New Locking Paradigm - Loop-gebra 
                Reply  Fri Feb 13 03:28:34 2015, rana, Update, LSC, New Locking Paradigm - Loop-gebra 
                   Reply  Sat Feb 14 20:20:24 2015, Jenne, Update, LSC, ALS fool cartoon ALSfool_LoopDiagram.pngALSfool_LoopDiagram.graffle.zip
                      Reply  Tue Feb 17 04:04:32 2015, Jenne, Update, LSC, ALS fool math OpenLoopGainComparison_16Feb2015.pngCancellationTFs_DecouplingIsArefl.png
                         Reply  Tue Feb 17 16:36:08 2015, Jenne, Update, LSC, ALS fool math ALSfool_LoopDiagram_17Feb2015.pngALS_REFL_comboLocking_16Feb2015.nb.zip
       Reply  Thu Feb 12 22:28:16 2015, Jenne, Update, LSC, New Locking Paradigm - LSC model changes, screens modified 
          Reply  Sat Mar 7 19:15:17 2015, Jenne, Update, LSC, Modified zero crossing triggering LatchLogic_6March2015.png
    Reply  Thu Feb 12 03:43:54 2015, ericq, Update, LSC, 3F PRMI at zero ALS CARM Feb12_negativeTR.png
Message ID: 11042     Entry time: Tue Feb 17 04:04:32 2015     In reply to: 11030     Reply to this: 11043
Author: Jenne 
Type: Update 
Category: LSC 
Subject: ALS fool math 

I re-did the Mathematica notebook according to the most current diagram (note to daytime self: attach .nb file!!!), and found that the denominator has changed, such that plugging in the new D=-A_refl*P_als*S_als gives the same

full-system closed loop gain of    \frac{1}{1-H_{\rm als} - H_{\rm refl} + H_{\rm als}H_{\rm refl}}

where H_{*} = A_* G_* S_* P_*  is the open loop gain, and the * indicates either the REFL or ALS portions of the system. 

I have also plotted some things with Matlab, although I'm a little confused, and my daytime self needs to spend some more time thinking about this.

In the actuators (both for REFL and ALS), I include a pendulum, the digital anti-imaging filters that let us go from the 16kHz model to the 64kHz IOP and the analog anti-imaging filters after the DAC.  Note to self:  still need to include violin filters here.

For the servo gains, I copy the filters that we are using from Foton, and give them the same overall gain multiplier that is in the filter bank.  For the ALS going through the CARM filter bank, this is FMs 1, 2, 3, 5, 6 with a gain of 15.  For the RF (actually, POY here) going through the MC filter bank, this is FMs 4, 5, 7 with a gain of 0.08. 

For the plants of each system, since this is still single arm lock, I just include a cavity pole (80kHz for ALS, 18kHz for REFL). 

In the sensors (both for REFL and ALS), I include the analog anti-aliasing as well as the digital anti-aliasing to allow us to go from the 64kHz IOP to the 16kHz front end system.  For the ALS I also include in the sensor the closed loop response of the phase tracker loop (H/(1-H), where H is the open loop gain of the phase tracker).  For both sensors, I also include a semi-arbitrary number to make the full single-loop open loop gain have a UGF of 200Hz.  In the ALS sensor, I also include a minus sign to make the full open loop gain have the correct phase.

Here I plot the open loop gains of the individual single loops, as well as the open loop gain of the full system (Hals + Hrefl - Hals*Hrefl).  I feel like I must be missing a minus sign in my ALS loop, but I don't know where, and my nighttime brain doesn't want to just throw in minus signs without knowing why.  That will affect how the final ALSfool (blue trace) looks, so maybe it's not really as crazy as it looks right now.

Also, I was trying to explain to myself why we are getting the shape that we are in our measurements of the cancellation (http://nodus.ligo.caltech.edu:8080/40m/11041).  But, I can't.  Below are the plots of the transfer functions from either point 9 or 10 (before or after the G_refl) to point 5, which is the ALS error point.  The measurement in elog 11041 should correspond to the blue trace here.  For these traces, the decoupling is set to just (-A_refl), although there aren't any noticeable changes in the shape if I just set D=0.  If we start with the assumption that D=0, the shape and magnitude are basically identical to this plot, and then as we make D=-A_refl P_als S_als, the transfer functions both go to zero. 

So.  Why is it that with no decoupling, the transfer function from 10 to 5 is tiny?  Why do the shapes plotted below look nothing at all like the measured cancellation shape?  Daytime brain needs to think some more.

Attachment 1: OpenLoopGainComparison_16Feb2015.png  112 kB  | Hide | Hide all
Attachment 2: CancellationTFs_DecouplingIsArefl.png  112 kB  | Hide | Hide all
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