Mahmood : this must be a turbine similar to those used in helecopters as they also operate in constant speed variable power mode.
The biggest problem with speed control comes from variable speed outputs such as Torque converters or transmissions as they change the response of the motor to changes in throttle position. The other problem stems from lack of linearity in throttle position to power relationship.

What is the allowed droop/overshoot for this application and the regulation specification no load to full load?

For safety insure that a mechanical over speed limiter or shut down device set to just above your maximum design speed is in place and functioning before you test your control. This safety device must control properly if your control fails or is misadjusted. Terry