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Nyquist Diagram sketch

  1. Apr 29, 2015 #1
    1. The problem statement, all variables and given/known data
    I need to be able to sketch Nyquist diagrams for transfer functions. I spent a lot of time but I cannot wrap my head around the idea of mapping the GH(jw) in the complex plane. Let's consider the following example for this question:
    [tex]GH(s) = \frac{4} {s(s+2)^2}[/tex]

    2. The attempt at a solution
    The transfer function is factored as [tex] \frac{4}{jw}\times\frac{1}{jw+2}\times\frac{1}{jw+2} [/tex]
    [tex] MAG \frac{4}{jw}=\frac{4}{w}; ARG=\frac{-pi}{2} [/tex]
    [tex] MAG \frac{1}{jw+2}=\frac{1}{ \sqrt{w^2\times2^2} }; ARG=-tan^-1{w} [/tex]
    Then I make a table for all three elements of the transfer function and calculate their magnitude and angle for some values of frequency, including zero and infinity. After that, I convert the resultant polar coordinates to rectangular and plot them. This is what I understand I need to do, and it is not working.

    I have had only one lecture on this topic and did not had a chance to ask the professor anything. Please offer some help - I really need it! An example on how to sketch the above TF's Nyquist diagram will be very appreciated. Also, how can I decide what frequency values to use in the calculation?

    Thanks
     
  2. jcsd
  3. Apr 29, 2015 #2

    Hesch

    User Avatar
    Gold Member

    I don't know Nyquist diagrams, but anyway I will suggest:

    H(s) = 4/(s(s+2)2) =>
    H(s) = 4/(s(s2+4s+4)) =>
    H(s) = 4/(s3+4s2+4s)

    Now substitute s by jω and do some calculations

    H(jω) = 4/(-4ω2+j(4ω-ω3))

    Say ω=1, you will get

    H(jω) = 4/(-4+j3) = (-0.64 - j0.48) No ARG, no MAG, just plot it as is.
    Well, try ω=0, 1, 2, 3 . . .
    If a too big hole appears between 1 and 2 then try a value in the middle.
     
    Last edited: Apr 29, 2015
  4. May 3, 2015 #3
    Thank you very much! Because of your explanation I finally understand how to do the diagrams.
     
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