1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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?

  2. jcsd
  3. Apr 29, 2015 #2


    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted