# Control Strategy Development of Driveline Vibration Reduction for Power-Split Hybrid Vehicles
## 4 Simulation Results  
### Driving Cycle  
For a clearer representation of showing the elastomer vibration derived from the great change of M/G torque while the internal combustion engine was running and shifting modes during driving, the driving cycle applied in this research is shown in Figure 6. The vehicle initially accelerated to 32 miles per hour in 10 s, held in the fix-speed for 5 s and then dropped at rest in 10 s. In addition, this research set the mode shift at the time when the speed reached 30 miles per hour. It has shown a greater torque in the power source while the mode shifted. After we added the control methods, the curve difference between the half-shaft vibration and the foundational model was observed, as shown in Figure 7. In addition, due to the torque of the power  
Figure 6: Driving cycle. source changing greatly during acceleration and deceleration, as shown in the brown and blue frames, it resulted in significant vibration. The comparison during vehicle acceleration and deceleration are shown in Figures 8 and 9. The PC was able to reduce 593 N-m, about 22.5% of the peak-to-peak torque vibration during acceleration, but the PC mainly worked while the internal combustion engine was running. Thus, there was no vibration reduction during deceleration. PID and PC-PID were able to reduce 1055 N-m, about 40% of the peak-to-peak torque value during acceleration; and were able to reduce 419 N-m, about 14% during declaration. The overall effect of vibration reduction performed better than PC. However, the analysis of peak-to-peak vibration reduction during deceleration in the time domain was almost identical to PC. Therefore, the frequency domain response was needed to compare the difference between them. The effect of the Peak-to-Peak vibration reduction in half-shaft torque under each control method was compared, as shown in Table 1.  
Figure 8: Vehicle half-shaft torque during acceleration in time domain. Figure 7: Half-shaft torque comparison with different control methods in time domain. The half-shaft torque that was added to the control methods was then applied to the Fast Fourier Transform (FFT) to further confirm the effect of vibration reduction. The observation of the half-shaft torque and curve was shown in Figure 10. With PC, the amplitude at 16 Hz, the engine damper natural frequency, was reduced by 60%, and the amplitude at 11 Hz, the half-shaft natural frequency, was also reduced by about 25%. This result was mainly caused by the PC addressing only the vibration derived from the internal combustion engine. When the speed difference between the two ends of the damper decreased, the elastomer vibration would be reduced. Therefore, the vibration in the internal combustion engine damper reduced, and the vibration reduction was also able to be observed in the half-shaft natural frequency. However, the result of PC at 5 Hz was limited. By adding PID, the overall vibration was able to be reduced by more than 75%. In PID control, there was no similarity to the PC control method, which addressed only specific vibration source, but instead to reduce vibration according to the condition of the output axis, so the overall vibration reduction effect was ideal. It was observed that low-frequency vibration was basically neutralized while adding the PC-PID curve. The overall vibration was able to reach over 75%, while the vibration reduction range at 16 Hz was about 8% higher than the effect of PID control. The range of vibration reduction of each control method at each frequency is shown in Table 2.  
The two-mode power-split hybrid system was developed by vehicle manufactures, and the simulation model was accurately represented by the driveline system. The control strategies could be implemented in the vehicle without difficulty, and the benefits of vibration reduction could be expected.