Some mummblings
All traditional rotary generators are essentially AC., they have to be adapted to produce DC (split slip rings, electronic rectification etc.).
In a simple generator, you'd have fixed windings with a rotating permanent magnet. As you suggest, the only way you could vary the output voltage would be varying the shaft speed; this would render the frequency uncontrollable (A380??). The rotor therefore is designed as an electromagnet. The armature is rotated at whatever speed is required to maintain frequency (a function of the RPM (RPS) and number of pole pairs on the stator). You can see that if zero voltage if applied to the rotor, there would be no magnetic field and hence no voltage on the stator. Increase the voltage across and current through the rotor and you increase your stator voltage. All you need then is automatic feedback to create a closed loop system and controlled output voltage.