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

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SUBHRAJEET DAS
SUBHRAJEET DAS 2015-8-17
评论： Ammon Traeden 2023-11-7
MATLAB PROGRAM FOR RLOCUS FOR DETERMINATION OF GAIN K FOR STABLE SYSTEM
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Fatima Mohamad Hussein
Fatima Mohamad Hussein 2020-4-17
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?

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Sebastian Castro
Sebastian Castro 2015-8-17
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
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Sam Chak
Sam Chak 2023-11-4
Ran in:
@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)

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