how can we obtain the desired characteristic equation of a system?

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JITHIN
JITHIN 2015-1-17
回答： Raj 2019-7-24
I am working on rotary arm inverted pendulum.While going through many articles I can see ,in most of the cases desired characteristic equation is given but never explained how it is obtained? How the desired pole locations can be obtained for my particular system?
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bryce howard
bryce howard 2019-7-24
@Walter Roberson ....What does that link have to do with a desired charateristic equation?
If you have a systems transfer function you can plot it with Root locus to see how it behaves, you can also get its characteristic equation. You can pick poles/zeros to make the system more stable which would be the desired poles for your system. Once you have the desired poles you can obtain a desired characteristic equation using the previous. MATLAB has lots of functions to do this.
Walter Roberson
Walter Roberson 2019-7-24
@bryce howard
I have lost the mental context for the reference to the link. The user might have flagged the question with a reference to the link, or the user might have posted something that they have since removed. I don't think that I was indicating that I was suggesting that the user check that link.

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Raj
Raj 2019-7-24
"How the desired pole locations can be obtained for my particular system" - Desired pole locations are obtained from desired system performance parameters. For your system you must be having some desired performance criteria in terms of time domain parameters (say rise time, overshoot, settling time etc.) or frequency domain parameters (like gain margins, phase margins etc.). I'll assume you have some time domain criteria since that is more common in practical problems. These time domain parameters are related to damping and natural frequency of your system's desired characteristic equation. See this lecture notes link for details:
https://nptel.ac.in/courses/101108056/module7/lecture20.pdf
This will be a good point to start. Revert in case you are having any difficulty.

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