So I'm finishing a little write-up for the presentation that I'm giving in March, and I realize that I can look at a Bode plot and have a pretty good idea of what the system step response is going to look like. But what I can't do is explain why, or justify any conclusions without mathematics that go way beyond the scope of my talk.
On the one hand I have the utter precision of taking the inverse Fourier transform of the frequency response, which doesn't yield much intuition but does give you an impulse response thats as exact as your frequency response. On the other hand I have some hand-waving observations about looking for sharp amplitude or phase changes, or that long, low bump in the amplitude response you get from a well-damped PID controller that results in a long, small tail in your time-domain response, but all that'll do is speed up someone else's acquisition of their own intuition.
Is there a middle ground? Can anybody recommend any good references for anything in between? Something that would take 2 - 4 slides in a presentation would be absolutely perfect.
Thanks much.