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Math Help - critical gain

  1. #1
    Member disclaimer's Avatar
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    critical gain

    Hi there;

    How to calculate the critical gain needed for the output signal to begin to oscillate when a step (1) signal is used as the input and the transfer function of the main branch of a closed-loop system with negative unit feedback is known? Something like this:



    For now, I just keep guessing and it looks like it's something between 3.5 and 3.6.

    Help appreciated.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by disclaimer View Post
    Hi there;

    How to calculate the critical gain needed for the output signal to begin to oscillate when a step (1) signal is used as the input and the transfer function of the main branch of a closed-loop system with negative unit feedback is known? Something like this:



    For now, I just keep guessing and it looks like it's something between 3.5 and 3.6.

    Help appreciated.
    Try writing the ODE satisfied by the output (its a linear constant coefficient inhomogeneous ODE). To get ringing you need at least one complex root of the characteristic equation.

    CB
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