Gain and phase margin

A feedback loop becomes unstable when its corrections arrive late enough, and strong enough, to reinforce the error instead of reducing it. Gain margin is how much the loop gain could increase before that happens; phase margin is how much additional phase lag (effectively, delay) the loop could absorb. Both are read from a frequency-response (Bode) plot of the loop, measured or modeled.

Margins matter because real products drift: motors warm up, loads change, batteries sag, and sensors and components vary from unit to unit. A loop tuned to the edge of stability on one prototype may oscillate on the thousandth production unit, or on a cold morning. Target margins depend on the application and on how much the plant is expected to vary.