## 4 Performance Analysis
### Tracking and Economic Analysis  
In the initial phase of the simulation, the vehicle was set 8 m in front of the host vehicle, and the SOH of the battery was set to 1. Figure 10 shows a comparison between the expected and actual distances between the two vehicles with the PID, SMC, MPC1, MPC2, and AMPC controllers, respectively. It can be found that under the PID, SMC and MPC1 controllers, both vehicles show better tracking ability. Excellent tracking performance is accompanied by frequent changes in electric machine torque and battery current, resulting in increased energy consumption and shorter service life. Therefore, for this paper, we designed economic indicators and variable weight coefficients to ensure low-speed tracking while considering the economy of high-speed following. As shown in Figure 10, a controller that takes the aging characteristics of the battery into account will exceed the expected distance during the high-speed driving phase. However, when the vehicle is driving at a high speed, the larger following distance can ensure that when the car in front brakes suddenly, the main car has enough distance to brake, ensuring safety. Figure 11 shows the tracking speed curves with the PID, SMC, MPC1, MPC2 and AMPC controllers. As can be seen from Figure 11, in the low-speed section, due to the small economic weight, the effect of each controller is similar. In the medium-speed section, due to the increase in speed, the economic weight is gradually increased and the MPC2 and AMPC controllers, which consider the aging characteristics of the battery, are slower than the other controllers. This reduces the output of electric machine torque while ensuring acceleration and following driving, which is conducive to improving driving economy. In the high-speed segment, the AMPC controller is more effective. Figure 12 shows the current curve of the battery cells when the main vehicle was driving under the action of each controller. At low speeds, the current of the battery under the action of the MPC2 and AMPC controllers was smaller than under the rest of the controllers. In the medium- and high-speed section, it can be seen from the current curve that the vehicle will adopt an acceleration-coasting method to reduce the continuous output of battery current during driving and to improve driving economy. Figure 9: The acceleration and jerk of the host vehicle under each controller, (**a**) acceleration,(**b**) jerk. Figure 11: Speed tracking curve of each controller. Figure 10: Distance tracking curve of each controller. Figure 13a shows the capacity attenuation curve of the battery under each control, and Figure 13b shows the SOC decline curve, the specific value of which is shown in Table 7.  
Since the MPC controller can optimize multiple targets during driving, that is it can limit the acceleration and jerk of the host vehicle, it can be seen from Table 6 that the decline rate of battery capacity under the MPC controller is better mitigated compared to under the PID and SMC controllers. Compared to the MPC1, MPC2 and AMPC controllers, controllers that consider battery degradation characteristics further reduce battery capacity degradation. Compared with the PID, SMC, MPC1 and MPC2 controllers, the battery capacity attenuation was reduced by 18.99%, 15.43%, 3.27% and \(-\)0.04%, respectively, and the battery energy consumption was reduced by 32.32%, 29.46%, 4.71% and 0.43%, respectively. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Controller** & **PID** & **SMC** & **MPC1** & **MPC2** & **AMPC** \\ \hline Q\({}_{\text{loss}}\) (\%\({}_{\text{cc}}\)) & 3.8063 & 3.6463 & 3.1877 & 3.0822 & 3.0835 \\ SOC & 0.6295 & 0.6364 & 0.6789 & 0.6841 & 0.6846 \\ \hline \end{tabular}
\end{table} 
Table 7: Capacity loss value and SOC of battery under each controller after the WLTC (SOHini = 1). Figure 12: Current curve of each controller. Figure 13: Under WLTC working conditions, the battery (SOHini = 1) parameters under the action of each controller: (**a**) battery capacity loss (**b**) SOC.