Finding Time Constant from Root Locus of a Transfer Function

I have a transfer function: G_s is the open loop, V_R is the closed loop. I have plotted the root locus of the open loop with the complex poles of the closed loop. I am trying to find a way to pull the points of the poles in order to calculate the time constant. is there a way to get the location of the poles without having to look at the plot and then type them in manually?

G_s =

11.11

----------------------

s^2 + 1.333 s + 0.3333

V_R =

11.11

----------------------

s^2 + 1.333 s + 0.6665

figure %Make new Figure

rlocus(G_s) %Root Locus of G(s) (OPEN LOOP)

hold on %keep same figure

rlocus(V_R) %Root Locus of V(s)/R(s) with complex Poles in red X's

title('Open loop Root Locus of G(s)')

hold off

Answer 1

[Paul]

Right click a point on a rlocus plot and a data tip will pop up with useful information.

Unclear what Vr is or how it relates to G_s and why the root locus of V_r is needed. But if you really want the the root locus of both on the same plot, then try:

rlocus(G_s,V_R)

[benjamin schroll]

V_R is the closed loop where G_s is the open loop. I was told that the open loop was the transfer function that needed to be plotted other wise the closed loop would give the wrong thing, but that the closed loop would give the correct poles. As pictured below.

I am aware of the ablitiy to click on the graph, that is what I was trying to get away from having to do. If "rlocus" can plot it then it is calculating the poles, so is there a way to pull that information out and assign it to a verable or something?

[Paul]

If all you want is the pole locations of the closed loop transfer function then there is no need to use rlocus. There are several ways to get that information, some of which are:

doc pole
doc zpkdata
doc damp

[benjamin schroll]

That kinda helps. Is there a way to store the poles so that the Imaginary part and Real parts are broke up into rows or columbs? That way they could be called and stored to seprate verables?

[Paul]

Once you have the poles a vector, you can use

doc real
doc imag

to isolate the real and imaginary parts.

[benjamin schroll]

Perfect. Thank you