A computer-implemented method for controlling a fuel flow to a gas turbine engine of an aircraft includes determining a control initiated fuel flow demand that is based, at least in part, on an operator command. In addition, the method includes determining a first rate of change of fuel flow demand based, at least in part, on a tracking error of the gas turbine engine that indicates a difference between a desired rotational speed and an actual rotational speed. The method also includes integrating the first rate of change of fuel flow demand to determine a tracking error fuel flow demand. In addition, the method includes summing the control initiated fuel flow demand and tracking error fuel flow demand to determine a composite fuel flow demand. The method also includes controlling a fuel flow to the gas turbine engine based, at least in part, on the composite fuel flow demand.