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:

http://i40.tinypic.com/eg8rk4.jpg

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

Help appreciated.

Quote:

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Originally Posted by disclaimer

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:

http://i40.tinypic.com/eg8rk4.jpg

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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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