FAQ: Under what conditions is the Bode plot misleading versus the Nyquist plot for stability?
Posted by Sean Humber, 11 November 2002
Both the Bode plot and the Nyquist plot (of the loop transfer function L=PC) can be used to determine closed loop stability. In fact, the portion of the Nyquist plot corresponding to the mapping of the positive imaginary axis is exactly the Bode plot when the bode plot is plotted parametrically. The only thing you need to be careful of is when the open loop system has an unstable pole, then you need a CCW encirclement of -1 in order to guarentee closed loop stability so the Nyquist plot should be utilized in this case.
As a general rule, if the loop transfer function contains right half plane zeros, right half plane poles (including poles at the origin), or a negative steady state gain, you should check stability using the Nyquist criterion.