Getting the transfer function from the transient response

[mahmoudathab90]

Hello,

Is there a method to get the transfer function from its transient response. I have been researching for some time now and the only thing that I have found is this:

Control Theory

On page 41, the author states that it is possible using "Guillemin's technique" and referred me back to a book by Truxal but I am unable to find any information about the book or the method. does anyone have any references that I could possibly read?

 

[IRstuff]

Do you know what the stimulus is? If so, then hypothetically, yes. If you look at a table of Laplace transforms:

https://en.wikipedia.org/wiki/Laplace_transform#Table_of_selected_Laplace_transforms,

you can see that if your stimulus is an impulse, then the Laplace transform of the transient response should be the transfer function of the network. However, if it's not an impulse, then the results will be more complicated.

TTFN
I can do absolutely anything. I'm an expert!
faq731-376 forum1529

 

[PNachtwey]

Yes, but like IRstuff said you must know the stimulus.
For starters look up "least squares fit"
Least squares is easy to implement but it only yields a transfer function in the z-domain

If you look at a table of Laplace transforms:
...........

That is not the way to do it. With the least squares fit the driving function or control can be anything.
Good places to start.

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

http://www.mathworks.com

http://home.hit.no/~hansha/documents/control/theory/parameters_estimation.pdf

The are more advanced ways of doing this. When serious then use system of differential equations and BFGS. Then it is possible to model non-linear systems.

I use system identification for auto tuning motion systems.
Here is an example of auto tuning a small motor.
I was really testing the Screenflow program that I used to record this video.

http://deltamotion.com/peter/Videos/AutoTuneTest2.mp4

Auto tuning this motor is simple because it is just a gain and a time constant.
The gain and time constant was only briefly shown because I was really testing the screen capture software.
Hydraulic systems are much more difficult.















Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

 

[PNachtwey]

Ooops, I forgot. Since IRstuff is a Mathcad user I will show a Mathcad example.

http://deltamotion.com/peter/Mathcad/Mathcad - Sysid T1P2 ODE-Forum.pdf

Column 0 is the time. Column 2 is the measured position in inches. Column 5 is the control voltage.
The I use the Minerr function to find the parameters of second order underdamped system with some dead time.
Then I use my model to plot estimated positions, velocities and acceleration and compare them to the measured.
On the bottom of page 2/4 I compare the measured velocity and the estimated velocity. One can see the effects of quantizing on the feed back positions. The estimated value from the model is much more realistic. The control signal is not an impulse but ramps. I use ramps that are just fast enough to excite any high frequency systems but not too fast to cause damage in a real application.
When auto tuning a hydraulic system with a 90 ton coil of steel on it generating an impulse is the fastest way to cause a big bang and get kicked out.

Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com

 

[mahmoudathab90]

Hi guys,

Thanks for your replies. I have checked the documents, they have been really helpful. But the problem is that I only have the transient response "curve". Nothing else, while the second document that PNachtwey has attached assumes either I have a set of equations or a black-box system. Is there a way to extract the data from the curve alone to get a transfer function representation?

 

[IRstuff]

You have to at least know what the stimulus is, otherwise, you'll wind up incorporating the input into the transfer function.

TTFN
I can do absolutely anything. I'm an expert!
faq731-376 forum1529

 

[PNachtwey]

A good auto tuning system will try many models and use the one with the best fit to the actual data. There is a lot of trial and error but computers can do that in a few seconds.


Peter Nachtwey
Delta Computer Systems

http://www.deltamotion.com