Abstract: Based on the differential geometry theory, the optimal control strategy of rotor side converter and grid side converter of doubly fed induction generator (DFIG) are designed independently from the perspective of state space. By applying diffeomorphism transformation, the dynamic model of DFIG is linearized exactly. The corresponding nonlinear control law is designed, realizing multi-objective optimal control. The simulation results show that the optimal control of DFIG based on feedback linearization can effectively resist the drastic changes of wind conditions and grid voltage, demonstrating excellent anti-disturbance characteristics.