A power turbine control system for a gas turbine engine may comprise a controller comprising one or more processors in communication with the gas turbine engine. The processors may comprise an engine control module configured to receive a torque request signal and generate a torque achieved signal. A rate of change of power turbine speed estimation module may generate an estimated rate of change of power turbine speed signal. A dynamic inversion power turbine governor module may generate the torque request signal based on the torque achieved signal and estimated rate of change of power turbine speed signal.