It is NOT, OMG, NOT a PMW controller. A resistor drops part of the DC voltage to the fan, reducing the voltage to the fan, thus slowing it down. A bit of math to do it right is involved.
That is ALL a resistor across the 12VDC input to the fan does.
PWM fan control needs a input from a .... GAAAA Never mind It's Toms............ Don't expect or see many electronics folks here.