# stability of a system

Discussion in 'Homework Help' started by vj39, Feb 7, 2013.

1. ### vj39 Thread Starter New Member

Feb 16, 2012
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hi i need help in understanding how the transfer function of a system is used for analysing the stability in s domain..what happens if the poles of the transfer function lie on the origin? thanks in advance

2. ### tshuck Well-Known Member

Oct 18, 2012
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675
The system is stable as long as the roots remain on the left half of the s-plane. To the right side of the plane, the system is unstable. At x=0, the system is considered marginally stable, so the origin would result in a marginally stable system.

See root locus

3. ### vj39 Thread Starter New Member

Feb 16, 2012
17
0
yes when the poles lie on jw axis the system is critically damped or marginally stable the time response will be sustained oscillations at frequency of w... but at origin w=0 and damping factor σ=0(real axis) so what kind of time response does the system show to indicate its marginally stable?

4. ### tshuck Well-Known Member

Oct 18, 2012
3,531
675
Well, I couldn't think of how the thing would respond! A good question, I'd say!

I simulated the transfer function in MATLAB and got this:
Code ( (Unknown Language)):
1. %EDIT: renamed/fixed variables
2. TF = tf(1, [1 0])
3. figure(1)
4. rlocus(TF)
5. figure(2)
6. t = 0:.01:10;
7. step(TF,t)
8. stepinfo(TF)

...looks pretty unstable to me...

• ###### TransferFunctionResults.png
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Last edited: Feb 8, 2013
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5. ### vj39 Thread Starter New Member

Feb 16, 2012
17
0
thank you so the system is unstable because the response shows a steady rise and peak at infinity? I'm still new to matlab...tried running the code but t is not defined..not able to plot for t=0:.01:10

6. ### tshuck Well-Known Member

Oct 18, 2012
3,531
675
Sorry, I changed the variable for the transfer function from t to T, so you wouldn't think t was time, but forgot to change it for the root locus plot...that was a failure....

I'm going to fix that now....

It would seem that, assuming the simulation is correct, that the system is unstable, there is no settling of the system from a disturbance....

7. ### vj39 Thread Starter New Member

Feb 16, 2012
17
0
thanks I'm still working on root locus