# How to get transfer function in real system?

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1. Nov 16, 2016

### gaus12777

I have a qusetion about getting transfer function in real system.
When I solve mechanical engeneering problem, transfer function is always just given. So, I`m curious how to get transfer function in real system.
I have searched something about that and have found some mechine called spectrum analyzer.
Can this machine serve us a transfer function of real system?
If it is right, what is the form of transfer function which this mechine give? (ex; graph or equation)

2. Nov 16, 2016

### Simon Bridge

Woah woah woah stop there.
There are lots of ways to find the transfer function in practise - and there are many specific machines that will help you do this.
What you are used to is called the forward problem - you have a physical model (in this case, represented by the transfer function and the rules for applying it) and you are given an input, and you have to figure out the output. Then you can test the output against an experiment to see if the experiment supports the theory.

You can also do this backwards - starting from the theory and the output, you can determine the likely inputs.

This sort of question in science always has the same answer ... just the details change:
In the case of a transfer function - you have the sort of theory that uses transfer functions and you want to know how to get the specific function for the system in question. You can do this by examining the system and then working out what the transfer function aught to be becuase you already know how the parts work. But that is begging the question because you still needed to work out the transfer functions for the parts somehow.
The functions for simpleparts can be worked out by guesswork and testing - simple bits are usually easier to guess, and you can use the results of failed guesses to get closer to a good one - comparing with eperiment. This builds up a body of knowledge that you can use for more complicated stuff.
However, you may not be able to examine the system in that kind of detail - so you need a purely empirical way to discover the transfer function ...
You can do this by sending input to your unknown system, and recording the output. Do this a lot, so you have good statistics. The matrix (or whatever) that turns the input into the output is the transfer function ... there may be more than one possible transfer function, in which case we use the one that requires the least work until we can do an experiment that will distinguish between them.
This is a special process - it has a special name... the tldr version of this answer is two words long ;)

Where a spectrum analyser can be useful is if you know the input spectrum for some system, and you record an output spectrum.
The analyser usually just allows you to compare them... with details depending on the machine. Read the manual.

That's the conceptual framework you need in a nutshell - if it does not answer your question, it should help you rephrase it so you can get a better answer.

I see you have a specific machine in mind, did you have a specific system in mind?

Last edited: Nov 16, 2016
3. Nov 17, 2016

### Staff: Mentor

4. Nov 20, 2016

### gaus12777

I have a specific system in mind called piezoelectric system.
I want to use it for fast scanning probe microscopy. But large frequency which can fast scan have some problem beacause of resonsant frequency.
So, I want to use IRC and for doing it I think I should know transfer function.

5. Nov 20, 2016

### Simon Bridge

With some luck someone will be able to help specifically with that if you get stuck.
Good luck.