Damping Factor (or ratio) of a nth Order System

[dzt]

Hi,

I have a query regarding the Damping Ratio of a system. With a 2nd order system the damping ratio, denoted by zeta ζ, is obtained from the denominator of the transfer function, but how do you find and define the damping ratio from a higher order transfer function, please?
Especially, considering that each pole in the system has a damping ratio, which is the overall damping ratio of the system or closed loop system?

Any help would be really appreciated.

Thanks

 

[xnuke]

As you said, damping factors are associated with poles, not systems.

First-order poles (and you can count second-order overdamped and critically-damped systems as systems having two first order poles) have a damping factor of 1.

Second-order underdamped (i.e., complex) poles have damping factors between 0 and 1.

Second-order undamped poles have a damping factor of 0.

Systems that have more than two poles will have a damping factor associated with each pole.

The dominant pole or poles will have the associated damping factor dominate the system behavior.


xnuke
"Live and act within the limit of your knowledge and keep expanding it to the limit of your life." Ayn Rand, Atlas Shrugged.
Please see FAQ731-376 for tips on how to make the best use of Eng-Tips.

 

[dzt]

Thanks for the explanation, xnuke.