Please help, discrete time vs continuous time overshoot

Discussion in 'Homework Help' started by YukiWong, Dec 15, 2011.

  1. YukiWong

    Thread Starter New Member

    Dec 5, 2011
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    The original continuous system has a overshoot of 16.3% and the discrete system of the continuous system with 100ms sampling time has a overshoot of 20.6%.

    Can anyone explain to me why the discrete system for the 100ms sampling time has much more overshoot compare to the original continuous system.

    [​IMG]

    and also why the bode gain of the discrete system with 100ms have 2 gain margin.

    [​IMG]

    Thank you very much.
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    One would expect a sampled system to give a more oscillatory response than its equivalent 'pure' continuous system. The sampling process gives rise to dead time which is known to destabilize a system. If you make the sampling frequency high enough (notionally sufficiently higher than the system bandwidth) then the discrete and continuous responses should converge.

    Your bode plot shows two distinct gain margins because the sampled data phase plot crosses the 180° axis twice - the second (higher) value presumably being at the Nyquist frequency of 31.42 rads/sec.
     
    Last edited: Dec 16, 2011
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  3. RRITESH KAKKAR

    Senior Member

    Jun 29, 2010
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    Which software are you using??
     
  4. YukiWong

    Thread Starter New Member

    Dec 5, 2011
    27
    1
    Thank t_n_k,
    Which gain should be chosen according to the bode plot?
     
  5. YukiWong

    Thread Starter New Member

    Dec 5, 2011
    27
    1
    Matlab R2011b
     
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  6. t_n_k

    AAC Fanatic!

    Mar 6, 2009
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    Not the one at the Nyquist frequency.
     
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