do you have a schematic for your generator/charge circuit? where did you find your alternator?
It's just the (permanent magnet) alternator connected to the battery and inverter. Charge control is done by manually checking a voltmeter. I got the alternator for $5 from a surplus store in Houston many years back.
Normally, that alternator is used in a grid tied system, with a step up DC/DC converter that performs MPPT and a grid tie inverter. (That's part of my senior design project.) The typical MPPT voltage for my setup is about 18V when I'm using it, so it doesn't work as well charging a 12V battery (14.4V charging voltage). It's not used much in that mode, so that's not really an issue. And with most modern consumer electronic devices using well under 100W, it still generates enough to run the essentials (LAN hardware, laptop, LED light).
The actual MPPT voltage depends on the user. That's not surprising since as with all fixed field machines, the voltage/current from an alternator relate to speed/torque at its input. Therefore, the impedance seen by the DC/DC converter is the electrical equivalent of the mechanical "impedance". Modeling that impedance is easier said than done, so I just experimentally tune the MPPT algorithm. I have got it to settle to a good state when I use it but it doesn't work very well when the other group members use it.