To improve the efficiency of electric vehicles (EVs), a planetary two-speed transmission is\nproposed, which consists of a brushless direct current (BLDC) motor, a turbo-worm reducer, two\nmulti-disc wet brakes, and a Simpson planetary gearset. Based on the devised electronic actuator\nfor shifting, the rotation direction of the BLDC shaft determines the gear ratio of the transmission.\nFor acquiring smooth shift, the state-space equations with control variables of transmission are\nderived, and a three-stage algorithm is suggested. During the brake engagement process, the\noptimal control strategy has been developed using linear quadratic regulator control, considering\nthe jerk and friction work of the brake. The simulation results show that the proposed optimal\ncontrol strategy could reduce the slipping friction work of the brake and improve the shifting\nquality of EVs. The optimal control trajectory of the BLDC motor was conducted on the electronic\nshifting actuator bench test.
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