How to get transfer function in real system?

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Discussion Overview

The discussion revolves around the methods for obtaining the transfer function of a real system, particularly in the context of mechanical engineering and its applications. Participants explore various approaches, including empirical methods and the use of specific instruments like spectrum analyzers, while also considering the challenges involved in identifying transfer functions for complex systems.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions how to derive a transfer function in real systems, noting that they are often provided in mechanical engineering problems.
  • Another participant explains that there are multiple methods to find transfer functions, emphasizing the difference between forward and backward problem-solving approaches.
  • It is suggested that empirical methods can be used to determine transfer functions by sending inputs to a system and recording outputs, although this may yield multiple possible transfer functions.
  • The role of spectrum analyzers is discussed, with one participant indicating that they can help compare input and output spectra, but the specifics depend on the machine's capabilities.
  • A participant expresses interest in a specific application involving a piezoelectric system for fast scanning probe microscopy, mentioning challenges related to resonant frequency.

Areas of Agreement / Disagreement

Participants generally agree that there are various methods to determine transfer functions, but no consensus exists on a single approach or the effectiveness of specific tools like spectrum analyzers. The discussion remains unresolved regarding the best method for the specific piezoelectric system mentioned.

Contextual Notes

Participants highlight the complexity of deriving transfer functions, noting that empirical methods may not always provide clear results and that the identification process can depend on the specifics of the system being studied.

Who May Find This Useful

This discussion may be useful for students and professionals in mechanical engineering, control systems, and experimental physics, particularly those interested in system identification and transfer function analysis.

gaus12777
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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)
 
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gaus12777 said:
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...
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.

What you are asking about amounts to "how do we comeup with the theory to start with?"... only a bit more specific.

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 because 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:
Simon Bridge said:
I see you have a specific machine in mind, did you have a specific system in mind?

Thank you for your kindness.
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 because of resonsant frequency.
So, I want to use IRC and for doing it I think I should know transfer function.
 
With some luck someone will be able to help specifically with that if you get stuck.
Good luck.
 

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