Systems and methods for optimal speed protection for power turbine governing

A control system for limiting power turbine torque (QPT) of a gas turbine engine includes a controller including a processor and memory configured to control the gas turbine engine, the controller including an engine control module that provides an effector command signal to a gas generator of the gas turbine engine; a power turbine governor module that outputs a preliminary torque request (QPT_req_pre); and a power turbine torque (QPT) optimal limiter module that outputs a maximum torque topper (QPT_max) to limit a power turbine speed overshoot of the gas turbine engine; wherein the controller outputs a minimum value between the preliminary torque request (QPT_req_pre) and the maximum torque topper (QPT_max) to the engine control module.