You will learn a lot about your task if you understand this simulation of a standard 50A 14V automotive alternator and charging system. If you like, I can upload the running LTSpice simulation so that you can modify it to match the characteristics of your alternator. Study the alternator model; note the important parameters.
The sim shows how a simplistic bang-bang voltage regulator controls the field voltage/current which in turn adjusts the output of the alternator to match the load condition. Note that the average field current results from PWM; but notice that this is not a fixed frequency PWM, rather both the period and on-time adapt automatically. The PWM is largely dependent on the field inductance; not the VR.
The important parameters of the VR are the trip point (14.25V) and hysteresis (4mV), typical of automotive voltage regulators. Note that the VR is a bang-bang system, not a linear regulator.
The sim shows the VR initially charging a battery, then stabilizing with a light load, then a big load is applied, and finally the big load is turned off. Note how the feed back loop keeps the battery voltage more-or-less constant, and look at the PWM frequency/duty cycle that produces that. This is typical of charging systems in hundreds of millions of automobiles built since the 1960s.