How to find out gain K in root locus for stable system through MATLAB program ?

MATLAB PROGRAM FOR RLOCUS FOR DETERMINATION OF GAIN K FOR STABLE SYSTEM

[Fatima Mohamad Hussein]

s^2 + 10 s + 10

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

3 s^3 + 10 s^2 - 4 s + 2

[Fatima Mohamad Hussein]

Find minimum K that makes the system stable.

Find K at the break in point.

Find the break in point.

Find K that makes -3 one pf the system poles.

If K=5, find the overshoot percentage.

If K=5, find the peak output.

If K=5, find the peak time.

Find the maximum value of K that makes the overshoot percentage 20%

Find K that makes the settling time 1.5 sec.

Is the system stable for all values of K?

Answer 1

[Sebastian Castro]

It's easier to get the Gain Margin of the system, which is the first output of the margin function:

>> Gm = margin(sys)

That will tell you the maximum gain you can use before your system goes unstable. For proof, see below (note that the tooltip I selected doesn't give me the exact location, but it's close enough):

- Sebastian

[Ahmad Ghareeb]

But what if there are roots on the right hand side? How to get the minimum gain there?

[Stephen Geraci]

The system is unstable if there are poles in the right half s plane

[Sultan Al-Hammadi]

but it can become stable if zeros are in the left half plane for certain values of zeros

[Jason Ivey]

How did you get the damping and other info in the plot?

[Ammon Traeden]

I want to know the same thing. When I use the plot I just get the x and y values.

Answer 2

[Sam Chak]

@Ammon Traeden

Click anywhere on the locus and the characteristic properties will appear.

s = tf('s');
G = (s^2 + 10*s + 10)/(3*s^3 + 10*s^2 - 4*s + 2)

G =
 
      s^2 + 10 s + 10
  ------------------------
  3 s^3 + 10 s^2 - 4 s + 2
 
Continuous-time transfer function.

rlocus(G)

[Ammon Traeden]

Thanks, that worked, just not in a live script file for whatever reason. Has to me a script file or in the command window.