I have a briggs & stratton / Powermate portable generator; there is a lever with a black plastic handle on the end of it, right next to the 'choke - run' lever which has a red plastic tip on it. what is the black handled lever for? it looks like it can move the throttle, but it has 2 set-screws holding it fast.

The engine on your generator is also used for other applications some of which require an adjustable  throttle control. On a generator the engine must turn about 3600 rpm to obtain proper output of voltage and cycles. Upon further inspection of your throttle/governor you will probably find an adjustment consisting of a screw, nut or a tab on one end of the governor spring that can be reset for proper engine speed. (tab can be bent for more or less tension on spring) To check present governor setting, use a volt meter that has frequency setting. Make sure that generator is set to about 60 hz. (3600rpm) Good luck with your generator.