Doubly fed induction generators (DFIG) are widely used in wind power generation because of their ability to be operated at varying rotational speeds while producing power output at a constant frequency. Electrical dynamics of a DFIG is modeled using field oriented control and represented as fourth order system. This fourth order dynamics exposes a two-time scale behavior. Using singular perturbation techniques the time scales can be separated as slow and fast subsystems. Feedback control schemes can be designed and the closed-loop stability of each model can be compared. In this work, a linear quadratic feedback controller is designed for the DFIG electrical dynamics using exact, reduced order and composite models. The performances of the closed loop models are compared based on the system cost. The robustness and reliability of the control schemes are analyzed for each controller designs based on the nominal system. Based on the analysis and results, the reduced order controller performance is equally as good as the exact and composite designs during steady state operations.