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# Nonlinear system and transfer functions

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#### Electronics4you

##### Member
Hi there,

I have a system, that responds in a nonlinear way. I have modeled it to be a polynomial of 2nd order. Now I want to make it into a transfer function in the frequency domain, but how can I do that?

Is it only possible if I make a linear tf of the system?

Transfer functions do not work for non-linear systems.
There are precious few analytical techniques that can be applied to these cases.

Hi there,

I have a system, that responds in a nonlinear way. I have modeled it to be a polynomial of 2nd order. Now I want to make it into a transfer function in the frequency domain, but how can I do that?

Is it only possible if I make a linear tf of the system?

Hi there, Assuming your poly is a function of 't', you would transform each term into the 's' domain using the Laplace Transform. If you dont know what that is, do a quick search on the web and you should find many references. If your system is too non linear sometimes you have to work out the system around some quiescent operating point to find out the frequency characteristics, but they would only be valid at that operating point alone. You would have to do several such studies to find out more.

I work with Laplace every day, but have never worked with a non-linear system that may not be converted to a linear system. Will the t = s substitution to the trick so my block diagram will look like

------> as^2+bs+c ------>

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I work with Laplace every day, but have never worked with a non-linear system that may not be converted to a linear system. Will the t = s substitution to the trick so my block diagram will look like

------> as^2+bs+c ------>
NO! -- Laplace Transforms don't work on non-linear elements.
There is a method called Describing Functions
see
Graham, D., and McRuer, D.,Analysis of Non-linear Control Systems, Wiley, 1961
https://www.amazon.com/gp/offer-lis...?ie=UTF8&qid=1254166463&sr=8-4&condition=used

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Hello again,

I've worked with non linear systems before and it may not be possible to use those
methods with the system in question. I cant tell for sure from here, but then again
lets not overlook the good ol' fall back numerical methods which work for lots of
systems as long as you can write the differential equations for the system.
have to get a book

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