# Adaptive MPC Based Real-Time Energy Management Strategy of the Electric Sanitation Vehicles
## 2 Modeling and Energy Consumption Analysis on an Electric Sanitation Vehicle
### The Systematic Modeling
#### 2.2.3 Modeling the Power Requirement of the Working Motor  
In practical applications, the operating state of the working motor only had three options (or three fixed rotating speeds), which are named general mode, standard mode, and extreme mode. The nominal parameters of the three modes are displayed in Table 2, which were measured when the vehicle was stationary. Since the working motor was controlled based on a certain rotating speed, the output torque changed against the resistance force from the road. To investigate how garbage density on the road interacts with vehicle energy consumption, a series of field experiments, which were devised based on actual operations of drivers, were conducted to establish the power requirement model of the working motor. The real garbage was replaced with sand and rubble in the experiments. Figure 9 displays the main experimental results. It is indicated that the residues after cleaning were basically consistent or even less, despite having more and more \"garbage\" on the road surface. From Figure 9, it seems the \"garbage\" could not be cleaned completely. However, due to far less existing garbage in real scenarios, hardly any residues would be \begin{table}
\begin{tabular}{c c c} \hline \hline
**Mode Name** & **Fixed Rotating Speed (rpm)** & **Nominal Power (kW)** \\ \hline General mode & 1500 & 28 \\ Standard mode & 1700 & 39 \\ Extreme mode & 1900 & 54 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Working motor theoretical parameters of the three modes. Figure 8: Characteristic curves of the battery. left after cleaning. Setting the quantity of \"garbage\" in experiments to be significantly more than the real would achieve a clearer visual comparison. The detailed results of the experiments are summarized in Table 3, where the performance was evaluated by the proportions of residues in the total amount of garbage. As mentioned before, the working motor was controlled based on rotating speed, which is formulated as  
\[T_{wm}=f(n_{wm},F_{resist}) \tag{6}\]  
where \(T_{wm}\) is the working motor output torque, \(n_{wm}\) is the rotating speed, and \(F_{resist}\) represents the resistance from the road surface, which is theoretically related to the velocity, garbage density, and the rotating speed of the working motor. Based on the experiment data, it can be summarized that the variations of vehicle speed and garbage density exerted very limited impact on the motor torque, which is also testified in Figure 5. Consequently, assuming being immune from those minor factors, the relationship between power and the rotating speed of the working motor could be approximated mathematically. Furthermore, it is evident the clean force, which ranged from 0-1, representing normalized cleaning ability of the vehicle, increased with the power of the motor but decreased with the vehicle velocity. Hence, the discount factor \(\gamma\) dependent on velocity is defined and the cleaning effect of the vehicle is formulated as  
\[\psi_{res}=\delta_{garbage^{*}}(1-\gamma(v)\cdot\phi(P_{wm})) \tag{7}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Working Mode** & **Vehicle Velocity (km/h)** & **Motor Rotating Speed (rpm)** & **Garbage Density (g/m2)** & **Performance (\%)** \\ \hline General mode & 8 & 1500 & 200 g sands + & 97.3 \\ Standard mode & 8 & 1700 & 400 g sands + & 98.5 \\ Extreme mode & 8 & 1900 & 600 g sands + & 99 \\ Maximum ability test & 4 & 1900 & 1500 g sands + & \\  & & & 200 g rubbles & 97.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experiment results. Figure 9: Field experiment results: (**a**) under general mode, (**b**) under standard mode, and (**c**) under extreme mode. where \(\delta_{garbage}\) represents the garbage density on the road, \(\text{g}/\text{m}^{2}\); \(\gamma\) represents the discount factor; \(\phi(. )\) represents the functional relationship between clean force and motor power; and \(\psi_{res}\) represents the garbage residue, \(\text{g}/\text{m}^{2}\). All functional relationships, which include \(f(.