## 4 Experiments  
### Model-in-the-Loop Simulations  
In Figure 5, the TBD strategy was simulated on a model-in-the-loop (MIL) platform. MATLAB Simulink was applied to model the TBD strategy, battery model, driver model, slip ratio control (SRC), and direct yaw moment control (DYC), while CarSim provided the vehicle dynamics. The driver model simulated human driver behavior by a proportional-integral (PI) controller. The SRC was responsible for stabilizing vehicle motion through the tractive control system (TCS) during acceleration and the anti-lock brake system (ABS) during deceleration. The TBD strategy was performed after vehicle safety was confirmed. Because of the limited motor speeds and battery voltages, only the UDC part of NEDC was used for MIL simulations. Both the straight and circular road tests were simulated. Figure 6a shows the SOC records of the three battery packs during the TBD process for the EV driving a clockwise cornering on a circular path of radius 100 m for 3.5 UDCs of the NEDC. The indices \(\rho\) and \(\kappa\) were assigned at 1.0056 and 1, respectively. At the beginning, the SOC of the front battery (91%) was higher than that of both rear batteries (90%). In addition, \(SOC_{r}>1.0056\), the torque distribution of Mode 1, was executed until the \(SOC_{r}\) reduced to 1.0056 at approximately 170 s, where the PSO of Mode 2 was executed for torque distribution. The torque distribution mode shifted from Mode 2 to Mode 3 when the \(SOC_{g}\) was less than \(-1\%\) at approximately 1375 s. The torque distribution mode shifted back to Mode 2 about 1575 s when the SOC gap was reduced. The SOC of the front and rear batteries remained within a SOB by shifting  
Figure 5: Simulation block diagram of torque and battery distribution strategy. the torque distribution mode during the driving cycle. The torque distribution histories from three traction motors are presented in Figure 6b. It was also interesting to compare the differences of the energy economy of the proposed TBD strategy by having the battery energy storage in balance and using other torque distribution strategies without balancing the batteries. In these simulations, the initial SOC of each of the three battery packs was 90%, and their corresponding amounts of energy are 10.45, 5.2, and 5.2 kWh for the front, rear right, and rear left battery packs, respectively. The EV stopped when any of the batteries was depleted. It was found that both the rear batteries were exhausted soon for \(P_{r}=0\), 0.25, and 0.5 when the rear motors took higher priority for delivering more torque than the front motor; while the front battery was depleted soon for \(P_{r}=0.75\) and 1 when the front motor had the first priority for delivering the torque to the EV. Figure 6: (**a**) The state of charge records for the three battery packs and (**b**) torque distribution from the front, rear left, and rear right traction motors during the torque and battery distribution process for the electric vehicle driving on a circular path of radius 100 m and using the urban driving cycle of the New European Driving Cycle. Energy consumption efficiency was defined as the ratio between the total energy consumption and the initial battery energy. The energy consumption rate was defined as the total energy consumption per travel distance. Table 3 shows the energy consumption results for both the circular and straight road simulations. For clockwise cornering on a circular path of radius 100 m during the UDCs, the proposed TBD strategy had a travel distance: 142.6 km, which was 7.7% higher than the PSO strategy without the balancing of the SOC of the battery packs. The torque distribution strategy under PSO without battery balancing had a better energy consumption rate at 104.5 Wh/km than the TBD strategy, but the front battery was depleted after 132.4 km, and the energy consumption efficiency was 73.6%. The rear battery packs had 26.4% energy remaining when the EV stopped.