## 4 Performance Analysis
### Tracking and Economic Analysis
respectively, indicating that under the condition of battery SOH = 1, the AMPC controller can more effectively improve the energy utilization of the battery, while the MPC2 controller will improve the service life more effectively. This shows that the control method that optimizes energy consumption is not necessarily optimal for life improvement. In order to further verify that the battery attenuation characteristic controller proposed in this study is still effective after battery degradation, the battery SOH was set to 0.9 for verification. Figure 14 shows the battery capacity attenuation curve and the SOC degradation curve for each controller, as shown in Table 8.  
As the battery's state of health decreases, the resistance in the battery model increases, the battery current demand increases significantly when the vehicle is driving at high speeds, and the AMPC controller is more effective in reducing energy consumption and extending service life. In order to verify the adaptability of the method to working conditions, the performance of the battery controller under different SOH conditions, different working conditions and different cycle times of working conditions was compared. Figure 15 shows the battery capacity degradation curve and the SOC reduction curve under the action of each controller when the vehicle is driving under 5 WLTCs. It can be seen that the controller which takes battery aging characteristics into account performs better, and after the simulation, the battery still has a certain amount of power, while the PID and SMC controllers ran out of power during the simulation. In Table 7, it can be seen that when the battery SOH = 1, the MPC2 controller performs better than the AMPC controller in extending battery life, and with the increase in simulation time, the high-speed driving time also increases. Within this range, the increase in the economic weight in the cost function of the AMPC controller can make economic adjustments to the driving state, as shown in Figure 15a. In the simulation process, when driving in the high-speed range, the effect of the AMPC controller on life optimization was better than that of the MPC2 controller. This slows down the rise rate of \(\mathsf{Q}_{\mathrm{loss}}\). Figure 14: Under WLTC working conditions, the battery (SOHini = 0.9) parameters under the action of each controller: (**a**) battery capacity loss (**b**) SOC. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Controller** & **PID** & **SMC** & **MPC1** & **MPC2** & **AMPC** \\ \hline \(\mathsf{Q}_{\mathrm{loss}}\) (\(\%_{\infty}\)) & 3.8390 & 3.6642 & 3.2015 & 3.0984 & 3.0967 \\ SOC & 0.6295 & 0.6157 & 0.6643 & 0.6700 & 0.6846 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Capacity loss value and SOC of battery under each controller after the WLTC (SOHini = 0.9). Next, the UDDS working conditions were simulated and verified, and Figure 16 shows the Qloss and SOC changes in the battery under different SOH conditions. Figure 16a shows that, under the action of the AMPC controller, the vehicle driving adopts the acceleration-coasting method, which can slow down the capacity decline process of the battery. Figure 16b shows the change in battery SOC, and it can be seen that the controller which considers the aging characteristics of the battery can effectively reduce energy consumption. The specific values are shown in Table 9.  
Figure 16: Under UDDS working conditions, the battery (SOHini = 1) parameters under the action of each controller: (**a**) battery capacity loss (**b**) SOC. Figure 15: Under 5 WLTCs, the battery parameters under the action of each controller: when SOH = 1, (**a**) battery capacity loss (**c**) SOC. When SOH = 0.9, (**b**) battery capacity loss (**d**) SOC. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Controller** & **PID** & **SMC** & **MPC1** & **MPC2** & **AMPC** \\ \hline Qloss (\(\%_{\text{occ}}\)) & 1.9921 & 1.8604 & 1.8418 & 1.7978 & 1.7940 \\ SOC & 0.7431 & 0.7470 & 0.7545 & 0.7562 & 0.7566 \\ \hline \hline \end{tabular}
\end{table}