Voltage ergulators for this application are cheap, and readily available. Sorry I don't know off the top of my head where. Trust me, cheap and available. They connect to the ouptut, and rectify it and output it to the field windings. A friend of mine generates his own electricity, and uses them.
Since the output is AC, and the field is DC, the polarity of the field can't possibly matter can it? It can't! It really can't.. Yet it does..... ???? This caused some _HUGE_ confusion, and an argument.
Here is why it matters, and what to watch out for. As the generator starts up, residual magnetism generates a very weak output. That weak output is enough to supply a little voltage output, for a little more field, and the generator bootstraps up to full outout in a matter of a couple of turns. The key here is residual magnetism is what starts the generator initially. If the polarity of the residual magnetism matches the output of the regulator, it will bootstrap up. If someone disconnects a working regulator, from an idle generator, and swaps the leads to the field, it will not come back on line. Everyone might think the regulator just went bad. What is happening is that the generator starts to output a weak voltage from the residual magnetism left over from the last time it ran. The regulator outputs a field current that now bucks the residual magnetism. It bootstraps the residual field down to zero.. And the perfectly good alternator and perfectly good regulaotr output zero volts. Even a zap from a AA cell will start it outputting full power. But talk about strange symptoms!!! Everthing was working perfect, the regulator is disconnected, reconnected, and everything is dead!
This scenario can also plague you if you build your own regulator. It was so "interesting" that I had to share it. Even though I hate typing.
So, your homemade regulator might not start up on its own. The comercial units that I saw did not have a stepdown transformer. This allows the residual startup voltage to be sufficient to initially bootstrap the field. The field might be pulse width modulated, toreduce power lost in the regulator, I don't know. The units were a little box the size of a mouse.