# Damping ratio of higher order systems

Discussion in 'Electronics Resources' started by zoom1, Nov 29, 2012.

1. ### zoom1 Thread Starter New Member

Nov 29, 2012
2
0
It's obvious how to find the damping ratio of a 2nd order system. Well, for 3rd order, I can still handle it with design parameter. However, what about 5th order, for instance ?

How can I find the damping ratio for higher order systems.

And one quick question. Every pole has its own damping ratio. So how the overall system damping ratio is determined ?

2. ### tshuck Well-Known Member

Oct 18, 2012
3,531
675
Any system at a higher order than a second order system can be modeled with a series of second and first order systems. In fact, most control systems only use the second order response even if there are higher orders as the response is fairly close to a second order system...

3. ### zoom1 Thread Starter New Member

Nov 29, 2012
2
0
so if my system's characteristic equation is s^5 + 13s^4 + 100s^3 + 1300s^2
How can I turn it into 2nd order to calculate the damping ration ?

I mean if I divite it into 2 second order and 1 first order system. Then the resulting damping ratio is what ? Multiplication of them or something ?