Finding transfer functions (as used in control theory)

[Gerrit van Donk]

It would be great if this software could be used to find transfer functions as used in control theory. Given the bodeplot (amplitude ratio and phase shift measurement data) Eureqa would present a transfer function, ideally in the Laplace domain.

1) Is this somehow already possible with the current software?

(if so, I haven't a clue of how to obtain the required results).

2) If not, is there a place one can put "requested features"

3) Anybody else interested?

[Michael Schmidt]

I haven't looked at bode plots or laplace transforms since undergrad, but you might be able to do some simple ones by modeling frequency as a function of the phase, or vice versa. If you have phase data t and frequency data s, model:

s = f(t)

Eureqa doesn't yet have an integral operator, but it does have a derivative operator, so you could do:

D(s, t) = f(t)

You could also try a more general approach like:

f0(s) = f1(t)

to search for more general transformations if your data is continuous and smoothed. 

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[Dave Nunez]

To add to that, if your data is not smoothed, you might want to try to interpolate your data before hand (even though that might not be what you are looking for) Linear, Circular, Trig, ect interpolation. and give that a try.  Have you taken a look at the ops yet ?  (building blocks)

hth, -d

--
When things get too complicated, it sometimes makes sense to stop and wonder: Have I asked the right question?
-Enrico Bombieri

[RRogers]

I am always interested in System Identification.  I was going to do some work to improve standard procedures but (as usual) let it drop off the radar.

I don't really see a problem for the Bode plot.  Remember not to get carried away with fitting instrumentation errors and responses beyond 20db of unity crossover for the target system.  To be conventional you would have to restrict the operators to those appropriate to rational polynomials in frequency when doing the amplitude and introduce arc-tangents and such for phase.  One key is to realize that coefficients are real (although the phase needs both sine and cosine) so arrange things around that.   As mentioned you should probably apply a filter/smoothing.

I don't recall the mathematical meaning of the built in smoothing but it seems to work fairly well; but make sure you don't fit the filter instead of the date :)

If you want to put up the data on a public site (dropbox?) and let me know.  I will give it a shot.

[Gerrit van Donk]

Thanks for all responses.

However, I'm still not able to grasp how you would end up with a transfer function, e.g. H(s)=k/(Ts+1) for a first order system.

 

My system is rather complex and hence the bode plot is not easily identified as a standard 1st order or 2nd order system.

I just post my measurement data here after, so if someone has any ideas: go ahead. I am interested in the approach and the results.

 

f(Hz)	AR	phase shift
0.01	0.038387	-51.7727
0.015	0.031534	-57.9436
0.02	0.027037	-64.0284
0.025	0.022847	-73.6817
0.03	0.017424	-81.9812
0.035	0.011359	-89.7384
0.04	0.00654	-70.0929
0.045	0.008651	-36.4662
0.05	0.011831	-35.8695
0.055	0.012972	-47.097
0.06	0.012728	-56.0108
0.065	0.011448	-64.6932
0.07	0.010106	-70.4063
0.075	0.008418	-72.6154
0.08	0.006693	-71.7666
0.085	0.006229	-60.2746
0.09	0.006334	-51.882
0.1	0.007812	-49.8696
0.15	0.00506	-65.0889
0.2	0.004252	-54.3713
0.25	0.004046	-54.8487
0.3	0.003554	-59.8114
0.35	0.003188	-61.868
0.4	0.003084	-57.6238
0.45	0.00261	-61.0314
0.5	0.002667	-55.4956
0.55	0.002315	-57.8626
0.6	0.002381	-62.8867

 

Op woensdag 14 augustus 2013 16:29:53 UTC+2 schreef RRogers: