Please help, infinite gain margin in bode plot.

Discussion in 'Homework Help' started by YukiWong, Dec 13, 2011.

  1. YukiWong

    Thread Starter New Member

    Dec 5, 2011
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    1
    Hi everybody :),

    I got a transfer function which is 2/[s*(0.5s+1)] and figure below show the bode plot of the system. My quesiton is, why is the gain margin of this system is infinite?

    [​IMG]

    Thank you very much.
     
  2. thatoneguy

    AAC Fanatic!

    Feb 19, 2009
    6,357
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    The function simplifies to \frac{1}{s (0.25s + \frac{1}{2})}

    No clue why it would be infinite, it should converge to 1
     
    Last edited: Dec 14, 2011
  3. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    It is infinite - the total phase shift tends to exactly 180° as the frequency tends to infinity at which point the transfer gain is infinitesimal.
     
  4. YukiWong

    Thread Starter New Member

    Dec 5, 2011
    27
    1
    thanks t_n_k,

    erm, is that every second order system will cause infinity gain margin?
     
  5. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    Consider a [2nd order?] transfer function like

    G(s)=\frac{(10-s)}{s(s+5)}

    Which has a non-infinite gain margin but has an unbounded step response.

    Considered in isolation, gain margin of itself doesn't tell us much about system stability - so a system could have an infinite gain margin but be unstable or unbounded in transient response.

    For instance the transfer function

    G(s)=\frac{0.3}{{(s-0.001)}^2+0.09}

    has infinite gain margin but has an unstable step response.
     
    YukiWong likes this.
  6. YukiWong

    Thread Starter New Member

    Dec 5, 2011
    27
    1
    thanks t_n_K, i got it :)
     
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