stability of a system

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

  1. vj39

    Thread Starter New Member

    Feb 16, 2012
    17
    0
    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
    3,531
    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)
    [​IMG]
    ...looks pretty unstable to me...
     
    Last edited: Feb 8, 2013
    vj39 likes this.
  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:p...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
     
Loading...