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Nyquist Plot by hand

  1. May 13, 2015 #1
    I am trying to understand how to draw nyquist plot.
    Lets say the transfer function is
    G1Dqr.jpg
    Subbing in jω for s,

    Z1S5b.jpg ***Note: should be (jw)^4 , (jw)^3, (jw)^2

    Then separating the Real and Imaginary part,

    yvAZD.jpg
    So when
    w = 0, in the nyquist plot it is infinity
    w = infinity, it is 0
    Imaginary intercept is 1.25
    For real intercept I am not sure. Since imaginary part is 0 only when w is infinity, i plug in infinity for w in real part. Would the real intercept be infinity or 0? It would be infinity/infinity but numerator is lower order than higher order so would it be 0 instead?

    In any case, how am i supposed to plot the rough nyquist plot or at least be able to determine the stability using these 4 points?

    In Matlab the Nyquist plot comes out like this
    eB4Zn.jpg
     

    Attached Files:

    Last edited: May 13, 2015
  2. jcsd
  3. May 13, 2015 #2

    Hesch

    User Avatar
    Gold Member

    Sorry, I cannot see what you are doing. You have:

    G1Dqr.jpg
    Substituting s with jω, you should get:

    50 / ( ( jω )4 + 5( jω )3 + 4( jω )2 ) =

    50 / ( ω4 - j5ω3 - 4ω2 )

    Now, choose a ω and calculate the complex value of the denominator. Do the division and plot the result.

    Example: ω=1 → point = ( -4.412 + j7.353 )
     
    Last edited: May 13, 2015
  4. May 13, 2015 #3
    Sorry about that, just a typo. But it is not possible to plug in every single point that encircles the RHP of S-Plane to see how many times the nyquist plot encircles -1 to determine the stability. So my question is what are some key points that I need to plot so I can determine stability of a closed loop system.
     
  5. May 13, 2015 #4

    Hesch

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    Gold Member

    Try ω = 1, 2, 3, 4 . . . .

    If distances are to small then continue: . . . . 8, 16, 32

    If distance is to large between ω=2 and ω=3, then try ω=2.5. It's a "cut and try" process.
     
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