In this paper, the nonlinear Buck_Boost DC/DC converter is taken as the research object, and the model is transformed into linear standard form by using state feedback linearization. In view of the fluctuation of constant power load and resistive load, a Luenberger observer is designed to observe the total load power and calculate the new stable working point of the system according to the observed total load power. Finally, by solving the linear quadratic optimal control problem, the system performance index is optimized, and the control input is selected. The driving system state quickly reaches the steady state point, which is also robust to disturbances. The simulation results verify the effectiveness of the design method.