# Simulation Model and Method for Active Torsional Vibration Control of an HEV
## 4 Discussion
### Vibration Control Performance  
Vehicle speed with and without active control is shown in Figure 14. From 0 to 26 s electric drive mode is used to accelerate from 0 to 35 km/h; from 26 to 42 s, it accelerates slowly in hybrid drive mode to 48 km/h; from 42 to 65 s regenerative braking is used to decelerate to 20 km/h, and a constant speed is maintained until 102 s; finally, from 102 to 160 s acceleration, then braking to a stop are performed. The partial magnified view of the red dotted line in the figure shows the fluctuation of the vehicle speed before and after active torsional vibration control during mode switching was used.  
It can be seen from Figure 15 that body jerk was \(\pm\)6 m/s\({}^{3}\) due to mode switching at around 26 s, but is reduced to \(\pm\)2 m/s\({}^{3}\) with active control. It also can be seen that for the start, sudden acceleration, and deceleration conditions, body jerk is generally within \(\pm\)2 m/s\({}^{3}\) both with and without active control.  
The output torque of the ICE, ISG motor, and TM motor both with and without active control are shown in Figures 16-18.  
With and without active control, the engine output torque is basically the same, that is, the main excitation source characteristics of the system have not changed according to Figure 16. In Figure 17, for active control, the ISG motor drives the engine with a constant torque of 500 Nm between about 27 and 27.5 s. However, with active control during the start-stop process, the ISG motor not only outputs fluctuating torque at the beginning but also outputs varying-frequency fluctuating torques to reduce system vibration from 47 to 52 s during the engine shutdown process.  
Figure 14: Vehicle speed and drive mode.  
Figure 15: Vehicle body jerk.  
From 26 to 45 s in Figure 18, the hybrid drive mode is being used. Before active control, the output torque of the TM motor quickly changes from 500 Nm to 0 Nm after receiving the mode-switch command. However, active control causes the TM to output fluctuating torque to counteract the vibration transmitted from the engine.  
For the start and stop conditions of the APU, the engine speed and the damper torsion angle are shown in Figures 19 and 20:  
Figure 16: Engine output torque.  
Figure 17: Integrated starter generator (ISG) motor output torque.  
Figure 18: Traction motor (TM) motor output torque.  
It can be seen from Figure 19 that the engine speed has a large difference at 30 s and 1200 r/min and at 52 s and 300 r/min. In Figure 20, during the engine start-stop process, the real-time rotation angle of the torsional damper is shown in two partial enlarged views in the figure. It can be seen that with active control, the amplitude of the torsion angle fluctuation is greatly reduced. At 50.5 s, the resonance caused by the system speed at 200 to 300 r/min was successfully eliminated.  
Figures 21 and 22 are the time-frequency spectrograms based on the short-time Fourier transform (STFT) of the TM motor speed with and without active control.  
It can be seen from Figures 21 and 22 that, in hybrid drive mode, the high order components such as the second- and third-order of the TM motor speed fluctuation are eliminated, and the first-order component is greatly weakened when using active control.