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 |