A system and methods are provided for controlling turboshaft engines. In one embodiment, a method includes receiving input signals for a collective lever angle (CLA) command and real-time power turbine speed (NP) of an engine, determining system data for engine effectors by the control unit based on the input signals for the collective lever angle (CLA) command and the real-time power turbine speed (NP) based on an integrated model for the turboshaft engine including a model of a gas generator section of the turboshaft engine and a model of a power turbine and rotor load section of the turboshaft engine. The method may also include determining control output based on model-based multi-variable control including optimization formulation and a constrained optimization solver. The method may also include outputting one or more control signals for control of the turboshaft engine.