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Education Help With Signal Analysis & Control

Discussion in 'General' started by Strudul, 7 May 2015.

  1. Strudul

    Strudul ~

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    Hey

    I'm trying to revise for my signal analysis and control exam, but I'm having trouble with a few of the questions. No matter how much I read through my notes and search on the internet, I can't work them out.

    If anyone could explain them to me or at least point me in the right direction it would be greatly appreciated.

    1a)
    [​IMG]

    I think I'm right in saying that Ta(s) / Vf(s) = K/ (1+Ts)
    But then I have no idea how to calculate K.
    For T, can I just say T = L/R (because it's an inductor)?

    1b)
    [​IMG]
    Honestly not a clue where to start here...

    2a)
    [​IMG]
    From what I can work out, the OLTF = G(s)H(s) and CLTF = [G(s)H(s)] / [1+ G(s)H(s)]
    So, CLTF would be:
    [​IMG]
    ?
    Then I would need to rearrange it and sub the values of a,b and c in?
    But then why am I told what the gain is?
    Or am I completely off track and should be doing Laplace or something?

    2b)
    [​IMG]
    Absolutely no idea and I'm assuming I need to know the answer to part a) to do it.

    3a)
    [​IMG]
    3b)
    [​IMG]
    Really don't know.



    Cheers

    xTatic
     
  2. Unicorn

    Unicorn Uniform November India

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    I'll have a look through my notes when I get a few minutes, I studied a module similar to that in Mechatronics. What year are you in?
     
  3. Strudul

    Strudul ~

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    2nd Year

    In 1st year we were given past questions and solutions that I could work through, but this year they are refusing to provide them for some reason and it's making it so much harder :/
     
  4. Unicorn

    Unicorn Uniform November India

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    Yeah I think I took that in 2nd year as well. I'll try to help but it's been a while! I tend to forget a lot of theory the week after the exam :/
     
  5. Strudul

    Strudul ~

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    Better then than before... or during :lol:
     
  6. SkiDave

    SkiDave Minimodder

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    I can't remember how to do q1.

    q2 a:
    CLTF = [G_c(s)G_c(s)H(s)] / [1+ G_c(s)G_c(s)H(s)]

    = [k_p / (s+a)(s+b)(s+c)] / [1+ k_p / (s+a)(s+b)(s+c)]

    q2b:
    You need to get the Closed Loop Characteristic Equation (CLCE). As the question hasn't said otherwise you can assume unity H(s). ie H(s)=1

    CLCE: 1+ G_c(S)G_p(s)

    = 1+ k_p / (s+a)(s+b)(s+c)

    sub in the values and rearrange into a cubic.
    They gave you one of the roots so that you only have to find the roots of a quadratic.

    I can't remember how to prove stability. I'll have another look at my notes and get back to you

    EDIT: To show stability all the roots of the CLCE have to have negative real parts
     
    Last edited: 7 May 2015
  7. SkiDave

    SkiDave Minimodder

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    For q3a:

    The steady state error is given by:

    e = r / [1 + G(0)]

    In this case r=1 as it is a unit step.

    so
    e = 1 / [1 + k.G(0)]

    q3b:

    you have to show the e = 0 when

    e = 1 / [1 + (k + ki/s).G(s)] when s=0
     
  8. Strudul

    Strudul ~

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    Thanks Dave. Really helped.

    2a) That seems like a very easy 7 marks.

    2b) Rearranging and subbing the values, I got:
    s^3 + 8s^2 + 6s + 260 = 0
    (s+10)(s^2 -2s + 26) = 0

    (s^2 -2s +26) only has imaginary roots, therefore the system is unstable.

    3a) Subbing s = 0 into the OLTF gave G(0) = A.
    Which fit nicely to give the correct error.

    3b) I'm still kinda stuck on how to prove this one.
    Am I okay to use my result from part a) and sub G(s) = A?
    Giving 1/ [1 + (K+ Ki/s)A]
    But then I have something divided by s, which would be divided by 0, which I can't do....
    I tried rearranging, multiplying and factoring things, but I couldn't seem to be able to get it to a point where i can sub s=0 in.
    What am I missing here?
     
    Last edited: 7 May 2015

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