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Message ID: 16467     Entry time: Tue Nov 16 11:37:26 2021
Author: Hang 
Type: HowTo 
Category: SUS 
Subject: Fitting suspension model--large systematic errors 

One goal of our sysID study is to improve the aLIGO L2A feedforward. Our algorithm currently improves only the statistical uncertainty and assumes the systematic errors are negligible. However, I am currently baffled by how to fit a (nearly) realistic suspension model...

My test study uses the damped aLIGO QUAD suspension model. From the Matlab model I extract the L2 drive in [N] to L3 pitch in [rad] transfer function (given by a SS model with the A matrix having a shape of 103x103). I then tried to use VectFIT to fit the noiseless TF. After removing nearby z-p pairs (defined by less than 0.2 times the lowest pole frequency) and high-frequency zeros, I got a model with 6 complex pole pairs and 4 complex zero pairs (21 free parameters in total). I also tried to fit the TF (again, noiseless) with an MCMC algorithm assuming the underlying model has the same number of parameters as the VectFIT results. 

Please see the first attached plots for a comparison between the fitted models and the true one. In the second plot, we show the fractional residual

    | TF_true - TF_fit | / | TF_true |,

and the inverse of this number gives the saturating SNR at each frequency. I.e., when the statistical SNR is more than the saturating value, we are then limited by systematic errors in the fitting. And so far, disappointingly I can only get an SNR of 10ish for the main resonances...

I wonder if people know better ways to reduce this fitting systematic... Help is greatly appreciated!

Attachment 1: L2L_L3P_fit.pdf  238 kB  | Hide | Hide all | Show all
L2L_L3P_fit.pdf
Attachment 2: L2L_L3P_residual.pdf  255 kB  | Show | Hide all | Show all
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