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

 

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

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

 

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?

 

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?

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:

%EDIT: renamed/fixed variables
TF = tf(1, [1 0])
figure(1)
rlocus(TF)
figure(2)
t = 0:.01:10;
step(TF,t)
stepinfo(TF)

...looks pretty unstable to me...

 

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

 

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

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....

 

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

thanks I'm still working on root locus