DIAGNOSIS That burning dust smell is typically the exhaust filter—the big round HEPA filter at the top—being completely saturated with fine dust. The motor is pushing air through a clogged filter, which overheats the dust particles.
FIX Take off the dust cup. Then, twist the large, round filter housing at the very top of the vacuum counter-clockwise to remove it. Pull out the HEPA filter inside. Do NOT wash this one. Tap it gently over a trash can to dislodge loose dust. If the smell persists, the filter is done for. You need to replace it. The model number for the replacement HEPA filter is typically printed on the filter frame itself.
IF THAT DIDN'T WORK If a new filter doesn't solve it, the smell might be coming from inside the motor housing itself. Debris could have gotten past the filters and be sitting on the motor, burning off. This requires opening the housing, which isn't a simple user fix.
HEADS UP Never wash the HEPA filter—it's made of paper and will fall apart. Only the pre-motor (foam/felt) filters are washable.