## 4 Result and Discussion
### Comparison of Different Methods  
To verify the proposed method, PMP-MPC is compared in different prediction horizons of 5 s, 10 s, and 15 s, as shown in Figure 11. The results of three different prediction horizons are shown in Tables 2 and 3. The temperature and temperature change rate of the battery in the 5 s prediction horizon are shown in Figures 12 and 13. When the prediction horizon is 5 s, the total cost is the lowest and the best results are obtained. The prediction horizon is too long to affect the accuracy of the prediction. In flight mode, the engine and battery run at high power, and the battery temperature rises faster. When in ground mode the engine runs to charge the battery, and the battery temperature rises slowly. Different driving cycles under the same method have the same curve trend in both flight and ground states, which verifies the reasonableness of the method.  
\begin{table}
\begin{tabular}{c c c} \hline
**Horizon (s)** & **FC (L)** & **Temperature (\({}^{\circ}\)C)** \\ \hline
5 & 78.47 & 29.42 \\
10 & 78.94 & 29.07 \\
15 & 79.62 & 28.74 \\ \hline \end{tabular}
\end{table}
Table 2: Results of PMP-MPC with three prediction horizons in driving cycle A.  
In order to further verify the proposed method, PMP-MPC, DP, PMP, and RB methods are used for comparison. The initial temperature was set at 20 \({}^{\circ}\)C. The comparison SOC  
Figure 10: The HEAGV driving cycles. (**a**) Driving cycle A. (**b**) Driving cycle B. The red line represents the speed of the ground; the green line represents the vertical takeoff and landing speed; the blue line represents the speed of the horizontal cruise.  
Figure 9: The HEAGV mission profile in flight and on ground. (**a**) Driving cycle A. (**b**) Driving cycle B.  
curve is shown in Figure 14. It can be seen from the figure that SOC curves obtained by these different methods have the same general trend. The SOC curve drops in flight mode and rises in ground mode. The results show that the proposed PMP-MPC method can achieve nearly global optimal results and has the potential of online real-time application. There is a performance improvement compared to the rule-based method. The fuel consumption and battery temperature for the different methods in driving cycles A and B are shown in Figures 15 and 16. Temperature comparison only considers the real-time online method.  
Figure 12: Validation of the PMP-MPC strategy under the air-ground driving cycle A. (**a**) The blue line represents the engine-generator set power; the red line represents the battery power; the green line represents the demand power. (**b**) Battery temperature profiles. (**c**) Battery temperature change rate per instant.  
Figure 13: Validation of the PMP-MPC strategy under the air-ground driving cycle B. (**a**) The blue line represents the engine-generator set power; the red line represents the battery power; the green line represents the demand power. (**b**) Battery temperature profiles. (**c**) Battery temperature change rate per instant.  
Figure 14: SOC profiles of different approaches. (**a**) SOC profiles of different approaches in driving cycle A. (**b**) SOC profiles of different approaches in driving cycle B. (Prediction horizon = 5 s for PMP-MPC).  
Figure 15: _Cont._  
Figure 16: Battery temperatures for different methods. (**a**) Battery temperatures for different methods in driving cycle A. (**b**) Battery temperatures for different methods in driving cycle B.  
Figure 15: Fuel consumption for different methods. (**a**) Fuel consumption for different methods in driving cycle A. (**b**) Fuel consumption for different methods in driving cycle B.  
The results show that the proposed approach has higher fuel consumption than the global optimization approach because MPC-based EMS is essentially a local optimization algorithm. Overall, the PMP-MPC algorithm may provide a better alternative for developing an efficient and low-cost EMS. In addition, the RB-based method, although capable of online implementation and fast computation, has a significantly higher fuel cost.