Seamless dual brake transmission for electric vehicles: Design, control and experiment

• A compact two-speed clutchless seamless transmission is proposed for EVs.
• The kinematic analysis of the proposed transmission is studied.
• The dynamical model of the system is developed.
• Optimal control problems are formulated.
• The backstepping method is applied to design a closed-loop controller.

Transmission is one of the crucial elements of a motor vehicle's driveline that affects efficiency and dynamic performance of the vehicle. This paper studies the dynamical modeling, controller design, and experimental validation of a two-speed transmission for electric vehicles which has a specification of seamless gear shifting. The transmission incorporates a two-stage planetary gear set with common sun and common ring gears and two braking mechanisms to control the flow of power. The dynamical modeling of the driveline of an electric vehicle equipped with such a transmission is derived by exploiting the torque balance and virtual work principle. Thereafter, the Pontryagin Minimum Principle is applied to design an optimal shifting controller. This controller keeps the output speed and the output torque of the driveline constant during the gear shifting operation while minimizing the shifting time and the dissipation of energy caused by the internal brakes. Since the optimal control law provided by the Minimum Principle is open loop, a backstepping controller is designed to provide a stabilizing feedback law based on the optimal control inputs. Simulation and experimental results demonstrate the ability of the proposed transmission to exhibit smooth shifting without excessive oscillations in the output speed and torque.