# How to find the damping ratio of this transfer function

#### lukus08

Joined Mar 14, 2009
34

#### steveb

Joined Jul 3, 2008
2,436
steve

steady state error = 1 / Kv
0.15 (given) = 1/kv
so kv = 1/.15
OK, I see that the steady state error is for an input ramp function.

all i want to know is how to find the gain of the system.

.... how did they find GAIN K?
It looks like they chose the gain which provides 2% overshoot. They place lines that correspond to 2 percent overshoot on the root locus plot and the intersection of those lines with the root locus shows the pole locations and gain K needed to achieve this. They mention that the interactive Matlab tool is used. I remember using this tool years ago and you can interactively move/change the gain K and see which value of K achieves the goal. There are mathematical ways to get the answer, or trial and error with simple Matlab tools (bode plots, time responses etc.) can also work. You can also write a loop program in Matlab to search for the correct K value.

EDIT: The name of the Matlab tool is "sisotool" .

Last edited:

#### lihle

Joined Apr 12, 2009
83
hey man its simple.
First, what you can do is to find the gain K.
T(s)=1 + K G(s)=0. then solve for K.
to get K , use Dk/Ds =0, then find the two values of s then sustitute back into the equation to get the value of K, remember that K should be positive.

to find the damping ratio, find the breaking points of the root locus, then sketch it. remember that cos(damping ratio )= angle.