Determine the fraction of critical damping out of the frequency response

[BLCGuru]

Hey there!

I`m searching a way to determine the fraction of critical damping out of the frequency response.
The half power bandwith method is quite inaccurate, because the curve of the amplitude response
is very vague. Furthermore I can't determine the logarithmic decrement out of the natural logarithm
of the ratio of the amplitudes of two successive cycles, because the signal isn't very good...

Does anybody have another suggestion? Isn't it possible do make a rough estimate just with the
maximum value of the amplitude response?

Thank you very much for your help!

 

[PNachtwey]

Can you record the excitation and response as a function of time?
Is this a mass on a spring type of system?

You can use least squares system identification for a quick and dirty result.

http://www.mathworks.com/help/ident/ref/arx.html

The least squares computes the coefficients for a difference equation. I then convert the difference equation parameters to a gain, natural frequency and damping factor.

Now I use the Levenberg-Marquardt method for finding the coefficients of the model. I also use differential equations and RK4.

These methods will use the excitation and response for many points and find the coefficients that minimize the sum of squared errors between the estimated value and the measured value. If you record the excitation and response for 1 second with a sample time of 1 millisecond there will be 1000 points these algorithms can use to minimize the sum of squared error. The Levenberg-Marquardt method is much better than the least squares method.

http://www.mathworks.com/help/optim/ug/least-squares-model-fitting-algorithms.html

If you don't have Matlab use Scilab.





Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

 

[GregLocock]

One option is to look at the circle in the Argand plane, and use the spacing of the datapoints. This should be more accurate than just using amplitude since it also uses the phase.

bear in mind that in a linear system all the data locations should have the same damping for a given mode (well that's a tautology but it might help)


As ever it might be a good idea to post your data so other people can look at it. Trust me, we can't reverse engineer your super top secret project from a list of pairs of numbers.



Cheers

Greg Locock


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