The backlash between engaging components in a driveline is unavoidable, especially when the gear runs freely and collides with the backlash, the impact torque generated increases the vibration amplitude. The power-split hybrid electric vehicle generates output torque only from the traction motor during the launching process. The nonlinear backlash can greatly influence the driveability of the driveline due to the rapid response of the traction motor and the lack of the traditional clutches and torsional shock absorbers in the powertrain. This paper focuses on the launch vibration of the power-split hybrid electric vehicle, establishes a nonlinear driveline model considering gear backlash, including an engine, two motors, a Ravigneaux planetary gear set, a reducer, a differential, a backlash assembly, half shafts, and wheels. For easier control, some components of the power-spilt system are simplified, after verifying the reliability of the simplified model, a linear observer(LSO) and a nonlinear observer(ESO) are designed to estimate the system state variables respectively. Based on the estimated information a dynamic matrix controller(DMC) is designed to correct the motor output torque. Through the feedback torque of the motor, the active control system can reduce the shock and vibration of the nonlinear driveline caused by the transient change of the motor torque during launch conditions.
