The stability of vehicles is very important for the operation of the rail transit system. Duringa the operation, the hunting motion will occur due to the creep force and the geometric relationship between the rail-wheel, which will cause the vibration of the vehicle system and affect the safety of the vehicle operation. For the power bogie with motors, the motor suspension can also have a significant impact on the hunting stability of the bogie. To explore methods to improve vehicle dynamics, firstly, the study about how to improve stability by optimizing the motor suspension to achieve the functions such as lifting the critical speed, bifurcation control, and reducing the amplitude of the limit cycle by altering the motor suspension is made. Then a study about how to further optimize vehicle stability through active control of motor suspension is also made. Finally, the research focuses on the time delay problem in active control, and the impact of this problem on vehicle stability is taken, providing a reference for the related research of vehicle dynamics.