"I wonder what the transfer function of an engine to its throttle control is ?
"

At the most basic level this transfer function will involve the engine RPM, Torque developed, throttle-angle versus fuel flow rate, the backpressure of the fuel intake manifold as a function of the engine RPM and the like. Not simple. ( I know - nobody said its simple )

However for some cases I have seen the following setup to work quite adequately :

Have a precise regulating mechanism for the fuel throttle. The command for this will be the output of a closed loop control with required speed as the SP ( user setpoint ) and the Engine RPM as the PV ( process variable). A simple PI loop should work in most cases. Much depends on what speed accuracy is desired.

Raghu