## 5 Simulations and Assessments
### Comparative Analysis of Different Control Methods
#### 5.2.1 Results of Three Control Methods under Case D  
Figure 19 shows the results of engine-demand angular acceleration before and after optimization under engine-starting condition point D. It can be seen that the amplitude of the optimized demand-angle acceleration of the engine is smaller, and the change trend is gentler than that before optimization. This is mainly because the optimized engine demand-angular acceleration reduces the motor-distribution torques of Equation (14), so as to prevent the motor-output torques from being limited by battery charge and discharge power. The torque results of the power source obtained by the three control methods during stages 3 and 4 under case D are shown in Figure 20, which shows that when the ADCC method started the engine the torque of the engine output shaft fluctuated clearly. The MG1 torque is basically at the maximum peak value. The MG2 torque shows the fluctuation phenomenon of torque compensation, but some of the torque reached the maximum peak value of MG2, which cannot completely compensate or offset the fluctuating torque of the  
Figure 19: Optimized engine demand-angular acceleration before ignition under case D. \begin{table}
\begin{tabular}{c c} \hline
**Control Methods** & **Method Description** \\ \hline ADCC & Only feedback damping torque in Equation (22) obtained by a PID controller \\ ADCC-EAC & Engine active control + feedback damping torque in Equation (22) obtained by a PID controller \\ DTCC-ESC & Engine segment active control + feedforward control considering engine starting conditions and \\  & feedback control considering engine optimal target speed + ADFC-SR \\ \hline \end{tabular}
\end{table} 
Table 3: Three Control Method Description. transmission system. From Figure 10b, as the ADCC-EAC method was used to start the engine, the torque fluctuation of the engine output shaft were significantly reduced. This shows that the engine active control can effectively reduce the torque fluctuation of the engine output shaft. However, the torque of MG1 is still at the maximum peak. Some of the MG2 torque still reached the maximum peak value of MG2. It can be seen from Figure 10c that when the proposed DTCC-ESC method started the engine, the MG1 torque gradually increased to its peak value and then decreased. The pulsating torque of the engine output shaft was effectively reduced by the segmented active control method of engine. The MG2 torque did not exceed the limit of its own maximum torque, which means that the proposed DTCC-ESC method can compensate or offset the pulsating torque of the transmission system better. In addition, it was further found that the compensation fluctuating torque of MG2 had a highly symmetrical trend with the corresponding fluctuating torque of the engine output shaft. This showed that the fluctuating torque of the transmission system was mainly compensated for by MG2, while MG1 was mainly used for starting the engine rather than compensating for the fluctuating torque of the system. The jerking results of the three control methods during the engine-starting process under case D are shown in Figure 21 and Table 4. From Figure 21, when the engine was started by the three control methods, respectively, the vehicle jerk fluctuation generated by the ADCC method was the largest, while that generated by DTCC-ESC method was the smallest. As shown in Table 4, the maximum value of absolute vehicle jerks, J\({}_{\text{a-max}}\), reached 114.5 m/s\({}^{3}\) using the ADCC method. It is difficult for drivers to accept such a large jerk. The J\({}_{\text{a-max}}\) value produced by the DTCC-ESC method is 34.58 m/s\({}^{3}\). Compared with the result produced by the ADCC method, the jerk produced by DTCC-ESC improved by 69.8%, which showed that the proposed engine active control method can reduce system shocks. When the DTCC-ESC method was used to start the engine, vehicle jerks were successfully reduced to 9.94 m/s\({}^{3}\). This result is 91.32% better than that of the ADCC method, and 71.26% better than that of the ADCC-EAC method.