# Adaptive MPC Based Real-Time Energy Management Strategy of the Electric Sanitation Vehicles
## 4 Results and Discussions
### Comparison of Other Variables  
The distribution of optimal control variable sequences is shown in Figure 27. Compared with the MPC-based EMS, the rotating speed of working motor and velocity under DP control was more dispersed and had a slightly lower average, which reflects that DP tended to have the control variables change evenly and realize the global optimization because of grasping global information.  
As shown in Figure 28a, for one thing, the general mode of the working motor was dismissed by all three strategies, indicating that excessively low power of the working motor is not adequate for cleaning jobs in the target environment. For another, based on the distribution of optimization method, the regular rotating speed set at about 1700 rpm in the rule-based strategy proved to be reasonable for a fixed deterministic strategy. However, optimal results indicated that more accurate and flexible adjustments ranging from 1675 rpm to 1750 rpm tend to be a better choice.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Strategy** & **Consumed Energy (kWh)** & **Relative Improvement (\%)** \\ \hline Rule-based & 32.44 & - \\ DP & 27.40 & +15.43 \\ Adaptive-AMPC & 27.43 & +15.53 \\ Fixed standard mode & 28.38 & +12.50 \\ Fixed extreme mode & 35.74 & \(-\)10.19 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Energy consumption performance comparison of different strategies.  
Figure 28: Distribution of the control variables: (**a**) rotating speed of the working motor and (**b**) velocity of the vehicle.  
Figure 27: battery SoC variation of different EMSs.  
In terms of velocity, which is shown in Figure 28b, both optimization strategies had a higher range than the rule-based one. Because higher velocity meant a greater discount on the cleaning effect of the working motor, there was redundant power of the rule-based strategy that could be spared. Hence, regular vehicle speed might be more desirably set at 8.5 km/h for ordinary segments like level 1-level3, and at 7 km/h for the extreme conditions. Moreover, due to a lack of flexibility on the adjustment of vehicle velocity, the rule-based strategy failed to decrease the consumed power in some regions as 500-700 m or 2200-2500 m, which are shown in Figure 29a, leading to unnecessary energy loss.  
Details about vehicle operating states are shown in Figure 29. It is noted that the DP-based EMS performed a few more combinations of high rotating speed and low velocity than the AMPC, which explains the reason why the SoC under the AMPC decreased a little more slowly but had more garbage residue left than DP during the early stage in Figures 25 and 26.  
Additionally, considering the sanitation vehicle equipped a full water-filled tank, frequent changes of acceleration should be avoided in pursuit of driving comfort. Hence, it is rational that both DP and the AMPC restricted acceleration to fluctuating slightly between 0.5 m/s2 and \(-\)0.5 m/s2, as shown in Figure 30.  
Figure 29: Magnified control variables: (**a**) vehicle velocity and (**b**) rotating speed of the working motor.  
As shown in Figure 28b, due to the higher average velocity, the AMPC proposed in this study lessened operating time from 35 min to 29 min, which was a 16.7% improvement by contrast with the rule-based strategy. Time cost of each strategy is shown in Table 7.  
Eventually, some guidelines for driver manipulations were concluded, such as reasonably adjusting regular driving speed to be a little higher and decreasing the use of the highest rotating speed of the working motor as much as possible. In addition, instead of pure manual operation, accurate and flexible manipulations of the real-time AMPC-based EMS could be realized with the assistance of automatic driving.