It's not enough to know that a system is stable.  Often you want to know how stable a system is.  The answer to that question is simple for a second order system because damping ratio gives you a measure of relative stability - answer the question "How stable is the system?".  Knowing the damping ratio lets you compute things like overshoot for step response, resonant peaks in frequency response, etc.  In higher order systems there is no measure that lets you compute those things, but phase margin is a mesure of relative stability that lets you estimate overshoot and resonant peaks.

• Why learn about phase margin?
• Phase margin is a useful measure of how well a system performs.  (Phase margin estimates relative stabilitiy.  Other numerical indices estimate speed of response and accuracy.)  Systems are bought and sold on the basis of things like phase margin.
• What should you know if you want to learn about phase margin.?
• You first need to know about the Nyquist Stability Criterion - because phase margin is a measure of how far you are from being unstable in the Nyquist sense.
• You also need to be knowledgable about Bode' plots - because phase margin is usually measured on a Bode' plot.
• What do you need to know about phase margin?
• You need to know what phase margin is.
• You need to be able to calculate phase margin using open loop Bode' plot data.
• How do you use phase margin?
• You use phase margin to estimate system performance, particularly other relative stability measures like percent overshoot for a step input.
• Problems
• Additional Information
• Links to Frequency Response Calculators
• Link to material on Gain Margin