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Entry  Mon Jul 27 16:47:53 2015, ericq, Update, IOO, MC2 -> MCL Actuator TF mc2_2_mcl.pngMC2_2_MCL_TF.txt.zip
    Reply  Thu Jul 30 02:06:20 2015, Ignacio, Update, IOO, MC2 <-> MCL Actuator TF fitted TF_BODE.pngMC2_2_MCL.pngTF_INV_BODE.pngMCL_2_MC2.png
    Reply  Wed Aug 12 22:33:36 2015, Ignacio, Update, IOO, Re-measured MC2 -> MCL TF bode_TF.pngCoherence.png
    Reply  Fri Aug 28 20:15:49 2015, rana, Update, IOO, MC2 -> MCL Actuator TF 
       Reply  Mon Aug 31 07:49:11 2015, ericq, Update, IOO, MC2 -> MCL Actuator TF 
          Reply  Mon Aug 31 14:15:23 2015, Ignacio, Update, IOO, Measured the MC_F whitening poles/zeroes Data.ziptf.png
Message ID: 11462     Entry time: Thu Jul 30 02:06:20 2015     In reply to: 11447
Author: Ignacio 
Type: Update 
Category: IOO 
Subject: MC2 <-> MCL Actuator TF fitted 

Eric downloaded MC2 to MCL transfer function data (H) as well as its inverse, MCL to MC2 (Hinv). He also downloaded new MCL and MC2 data.

I used vectfit to fit the MC2 to MCL transfer function, 

The ZPK parameters for this fit were,

Zeros              1278.36719876674 + 0.00000000000000i
                   -100.753249679343 + 0.00000000000000i
                   -18.6014192997845 + 13.0294910760217i
                   -18.6014192997845 - 13.0294910760217i

Poles              -1.11035771175328 + 7.03549674098987i
                   -1.11035771175328 - 7.03549674098987i
                   -18.8655320274072 + 0.00000000000000i
                   -690.294337433234 + 0.00000000000000i

Gain               0.00207206036014220

Using the above vectfit model, I filtered the raw MC2 signal to get 'MCL'. The PSD's of the raw MCL data and the filtered MC2 result is shown below,

The lack of accuracy of the transfer function at replicating MCL at frequencies lower than 0.7Hz is expected, the vectfit model I generated fails to follow accurately the raw transfer function data. My question: Does it matter? My guess: Probably not. In order to mitigate seismic noise from the mode cleaner we are mainly concerened with the 1-3 Hz region.

I also used vectfit to fit the transfer function for MCL to MC2,

This one was harder to fit accurately for some reason, I could do it with four pairs of zeros and poles but it took some preweighting.

The ZPK parameters for the above fit were, 

Zeros              0.173068278283995 + 0.00000000000000i
                   0.995140531040529 + 0.0268079821980457i
                   0.995140531040529 - 0.0268079821980457i
                   0.894476816129099 + 0.00000000000000i

Poles              -19.9566906920707 + 18.0649464375308i
                   -19.9566906920707 - 18.0649464375308i
                   -109.275971483008 + 0.00000000000000i
                   -1791.88947801703 + 0.00000000000000i

Gain               1237.46417532120

Similarly, using this ZPK model, I filtered the MCL signal to get 'MC2'. I plotted the PSD for the MC2 signal and the filtered MCL to get,

Again, the lack of accuracy of the filtered MC2 at replicating MCL below 0.7 Hz and above 12 Hz is due to the inverse transfer function failing to converge in these ranges.

Attachment 1: TF_BODE.png  77 kB  | Hide | Hide all
Attachment 2: MC2_2_MCL.png  68 kB  | Hide | Hide all
Attachment 3: TF_INV_BODE.png  82 kB  | Hide | Hide all
Attachment 4: MCL_2_MC2.png  68 kB  | Hide | Hide all
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