There are some algorithm to obtain this poles?
Or some references to read?
Thanks,
Control theory,
Apply MATLAB command roots to denominator polynomial of Transfer function. It gives poles. The poles near to origin of s-plane are the dominant poles for a stable system.
Jose,
Broadly speaking, the dynamics that "appear strongest" in the response of a system represent the dominant modes. This includes two considerations:
#1 requires the initial amplitude to be significant relative to the others. #2 requires the real part of the eigenvalues to be close to the origin in analog systems, and close to unity in digital systems.
So as far as dominant poles are concerned, the answer is same as #2, that is real part of the poles to be close to the origin in analog systems, and close to unity in digital systems.
Hope that helps.
-Sanjay
Hellow
if you have an exact transfer function, you need to do the following steps:
- calculate the roots of the numerator polynomial
- focus your analysis in the real part of the roots
- The roots whose real part is closest to zero, corresponding to the dominant poles.
- To discard a root, calculates the relative distance between respect to the dominant pole. Usually the distance is calculated with a division
- If the relative distance is >5, you can discard this pole
i hope i've help you
best regards
Thanks for the answer and the algorithm to obtain the dominant poles.
I have another question. How I could compute the distance? what metric I could use?
Thanks
you have not mentioned your transfer function is open loop or closed loop transfer function. If it is open loop TF go for root locus plot of this TF. The poles near to the jw axis are called the dominant poles.
Or, get the closed-loop TF from Open loop TF. Determine the poles of the denominators. The poles which have very small real parts or near to the jw axis have small damping ratio. These poles are the dominant poles of the system.
for open-loop T.F, use the MATLAB statement, Roots(P),where P is the polynomial of Den. of T.F,after that the roots can be classified to dominant and non-dominant, where the root near the j-axis is dominant ,neglect the non-dominant root or in sometimes make pole-zero cancellation if the num. have zeros.Finally arrange the reduced T.F from the dominant root.
Thank you for your answer. It is very clear for Open loop TF.
What is the difference if I have a closed loop TF?
Thank you
for closed-loop T.F, doing the same thing, but here the close-loop poles differ from open-loop poles,also the closed-loop poles which are the closer to J axis,this can seen if you plot the root-locus
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