A power turbine control system for a gas turbine engine, comprising: a controller comprising one or more processors in communication with the gas turbine engine, the one or more processors comprising: an engine control module configured to receive a torque request signal, determine an estimate of a torque achieved, and generate a torque achieved signal indicative of the estimate of the torque achieved; a rate of change of power turbine speed estimation module configured to generate an estimated rate of change of power turbine speed signal; and a dynamic inversion power turbine governor module configured to: determine a difference between a target power turbine speed signal and a power turbine speed signal; determine a desired rate of change of power turbine speed error signal based on the difference between the target power turbine speed signal and the power turbine speed signal; determine a difference between the desired rate of change of power turbine speed error signal and the estimated rate of change of power turbine speed signal; and generate the torque request signal based, at least in part, on the torque achieved signal and the difference between the desired rate of change of power turbine speed error signal and the estimated rate of change of power turbine speed signal. a controller comprising one or more processors in communication with the gas turbine engine, the one or more processors comprising: an engine control module configured to receive a torque request signal, determine an estimate of a torque achieved, and generate a torque achieved signal indicative of the estimate of the torque achieved; a rate of change of power turbine speed estimation module configured to generate an estimated rate of change of power turbine speed signal; and an engine control module configured to receive a torque request signal, determine an estimate of a torque achieved, and generate a torque achieved signal indicative of the estimate of the torque achieved; a rate of change of power turbine speed estimation module configured to generate an estimated rate of change of power turbine speed signal; and a dynamic inversion power turbine governor module configured to: determine a difference between a target power turbine speed signal and a power turbine speed signal; determine a desired rate of change of power turbine speed error signal based on the difference between the target power turbine speed signal and the power turbine speed signal; determine a difference between the desired rate of change of power turbine speed error signal and the estimated rate of change of power turbine speed signal; and generate the torque request signal based, at least in part, on the torque achieved signal and the difference between the desired rate of change of power turbine speed error signal and the estimated rate of change of power turbine speed signal. determine a difference between a target power turbine speed signal and a power turbine speed signal; determine a desired rate of change of power turbine speed error signal based on the difference between the target power turbine speed signal and the power turbine speed signal; determine a difference between the desired rate of change of power turbine speed error signal and the estimated rate of change of power turbine speed signal; and generate the torque request signal based, at least in part, on the torque achieved signal and the difference between the desired rate of change of power turbine speed error signal and the estimated rate of change of power turbine speed signal.