Placing Poles and Zeroes
(pt3: How and why to use gain and/or phase margin(s) as tools...)
As we've seen, to insure closed-loop stability when we "close the feedback loop", we would like to have an open-loop system for which we have:
Positive gain margin
Positive phase margin
...and we would (in general) like to AVOID
Negative gain margins
Negative phase margins
The past few pages have shown how adjusting a constant gain times a transfer function:
will slide the Bode plot of magnitude up and down the y-axis. This, in turns, moves both
the frequency at which 'crossover' [0db gain] occurs [which is where we'll read off the phase margin data...]
- and -
the gain at the critical point(s) where the phase is -180 degrees [which will determine the gain margin].
but this multiplication of the open-loop system TF by a constant gain will not change the plot of phase (of course).
We can therefore sometimes* adjust a constant GAIN value times an open-loop system, which will in turn create systems which are either stable or unstable when we close the loop.
(*Of course, some open-loop systems may remain solely unstable or solely stable for all gains values we might choose...)