Assume that you have the feedback control system shown below.  In this system you are using proportional control, and you have a gain, K_p, that you can adjust.  (If you are using integral control, or something else, you can still put it into this framework.)

If you have a Bode' plot for the system system being controlled (G(s)), then you can determine the gain at which the system becomes unstable.

        Here is a Bode' plot for a simple system.

• The magnitude starts off at 20db (a gain of 10) at low frequencies.
• The phase starts at zero degrees and goes to -270^o.
• The form of the plot is one that could encircle -1.  (It's probably a rosette.)
• When all else fails, check what the Nyquist plot looks like.  Try to sketch it.

• Determine the frequency at which the phase crosses -180^o.
• That frequency is about 0.28 on this plot.
• Determine the gain at that frequency.
• On this plot, the gain is about 1 db.
• Modify the gain so that the plot goes through 0 db at this frequenc.
• If the gain is larger than 1 (0 db), you need to decrease the gain.
• If the gain is less than 1, you need to increase the gain.
• In this case, you need to decrease the gain by 1 db, so you need a gain of -1 db, i.e K_p = 0.89.