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Entry  Wed Sep 21 23:05:16 2011, Paul, Update, SUS, ITMY and SRM actuator response functions - fitting results ITMY_PITCH_actuator_response_FIT.pngITMY_YAW_actuator_response_FIT.pngSRM_PITCH_actuator_response_FIT.pngSRM_YAW_actuator_response_FIT.png
    Reply  Wed Sep 21 23:25:51 2011, kiwamu, Update, SUS, Re:ITMY and SRM actuator response functions - fitting results 
       Reply  Wed Sep 21 23:44:45 2011, Paul, Update, SUS, Re:ITMY and SRM actuator response functions - fitting results 
Message ID: 5507     Entry time: Wed Sep 21 23:05:16 2011     Reply to this: 5508
Author: Paul 
Type: Update 
Category: SUS 
Subject: ITMY and SRM actuator response functions - fitting results 

 I used an fminsearch function to fit the SRM and ITMY actuator response magnitudes. The testfunction was just that for a single second order pole, but it gave what I consider to be good fits for the following reasons:

*for 3 of the 4 fits the residuals were less than 0.5% of the summed input data points. The worst one (ITMY pitch) was about 2.7%, which I think is due to the resonance happening to be right in the middle of two data points.

*the tolerance of 1 part in 10^9 was reached quickly from not very finely tuned starting points.

The test function was: G=abs(Gp./(1+1i.*f./fp./Qp-(f./fp).^2)), where G(f) is the actuator response magnitude, Gp is the pole gain, fp is the pole frequency, and Qp is the pole Q factor.

In the end I just fitted the response magnitude. I was initially fitting the complex response function, but ran into problems which I think were cased by overall phase offsets between the data and test function. Can I canvass for opinion if fitting the magnitude is OK, or should I try again fitting the phase too?

Anyway, here are the results of the fits, and I've attached plots of each too (each one in linear and log y axis because each on its own might be misleading for fits):

EDIT - I added more points to the otherwise sparse looking fitted curves

 

ITMY PITCH actuator response fit

-- Fit completed after 190 iterations--

 Started with: Gain = 3e-06,

 Q factor = 5,

 Pole frequency = 1,

 Fit results:  Gain = 1.32047e-06,

 Q factor = 4.34542,

 Pole frequency = 0.676676

 Residual (normalised against the sum of input datapoints) = 0.0268321

 

ITMY YAW actuator response fit

-- Fit completed after 156 iterations--

 Started with: Gain = 3e-06,

 Q factor = 5,

 Pole frequency = 1,

 Fit results:  Gain = 1.14456e-06,

 Q factor = 8.49875,

 Pole frequency = 0.730028

 Residual (normalised against the sum of input datapoints) = 0.00468077

 

SRM PITCH actuator response fit

 -- Fit completed after 192 iterations--

 Started with: Gain = 3e-06,

 Q factor = 5,

 Pole frequency = 1,

 Fit results:  Gain = 7.94675e-06,

 Q factor = 7.16458,

 Pole frequency = 0.57313

 Residual (normalised against the sum of input datapoints) = 0.00301265

 

SRM YAW actuator response fit

 -- Fit completed after 156 iterations--

 Started with: Gain = 3e-06,

 Q factor = 5,

 Pole frequency = 1,

 Fit results:  Gain = 3.34179e-06,

 Q factor = 9.57601,

 Pole frequency = 0.855322

 Residual (normalised against the sum of input datapoints) = 0.000840468

Attachment 1: ITMY_PITCH_actuator_response_FIT.png  8 kB  Uploaded Thu Sep 22 00:19:15 2011  | Hide | Hide all | Show all
ITMY_PITCH_actuator_response_FIT.png
Attachment 2: ITMY_YAW_actuator_response_FIT.png  8 kB  Uploaded Thu Sep 22 00:19:29 2011  | Hide | Hide all | Show all
ITMY_YAW_actuator_response_FIT.png
Attachment 3: SRM_PITCH_actuator_response_FIT.png  8 kB  Uploaded Thu Sep 22 00:19:52 2011  | Hide | Hide all | Show all
SRM_PITCH_actuator_response_FIT.png
Attachment 4: SRM_YAW_actuator_response_FIT.png  8 kB  Uploaded Thu Sep 22 00:20:09 2011  | Show | Hide all | Show all
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