Dynamic modeling and controller design for a seamless two-speed transmission for electric vehicles

Transmission is one of the crucial elements of the driveline that affects vehicle fuel economy and comfort. It can transfer power in different combinations of torque and speed. This paper focuses on the modeling, simulation and control of a two-speed transmission for electric vehicles which has seamless gear shifting specification. The transmission incorporates two-stage planetary gear sets and two braking mechanisms to control the gear shifting. The dynamic model is developed by using the kinematic equations of the planetary gear trains and the Euler-Lagrange equations to derive the equations of motion. The mathematical model is validated by using the SimDriveLine library of MATLAB/Simulink®. The controller design employs optimal control methods to provide seamless shifting with minimum transition time. Then, by relaxing ideal constraints, a feasible controller is designed based on input-output and input-state feedback linearization. Simulation results demonstrate the ability of the proposed transmission to have smooth shifting without excessive oscillations in the output torque and speed.