Fan speed control - Voltage (0-5V) to PWM (0-100%) with minimum value
You may wish to try adding a common diode in series with your divider network between it and ground. The diode will raise the lower leg of your divider by 0.3 to 0.6 volts depending on the type of diode selected.

If this method isn't granular enough for your application, consider an op amp circuit with an adjustable offset. 

Note that either solution would change your resistive divider calculation to keep the input range &lt;= 1 volt.