## 4 Experiments
### Hardware-in-the-Loop Simulations  
Figure 7 presents the architecture of hardware-in-the-loop experiment. A Mitsubishi Colt-Plus was retrofitted with a 15-kW radial-flux PMSM and a 144-V battery pack for front wheels and two 7-kW axial-flux PMSMs and two 72-V battery packs for rear wheels. This EV was set up on a Horiba MAHA-AIP ECDM-48 emission chassis dynamometer. The maximum test speed was 200 km/h, the maximum power absorbing was 150 kW at 100 km/h, the maximum tractive force was 5400 N for light duty and 6750 N for heavy duty, and the maximum vehicle inertia simulation was 4540 kg for 4-wheel drives.  
In experiments, the battery SOC information and throttle command were received by a real-time rapid control prototyping unit dSPACE MicroAutoBox II, in which the TBD strategy was built to determine the torque command for each motor. This MicroAutoBox took a role of vehicle control unit with an 800-MHz processor, 18-MB main memory, 16-MB flash memory, and dual CAN interfaces.  
In the HIL experiment, the vehicle followed the complete NEDC but the maximum speed at EUDC was restricted at 40 km/h in the HIL experiment. The initial SOCs of the front, rear left, and rear right batteries were 94.8%, 93.6%, and 95.5%, respectively. In order to make the experiment efficient, driving modes were shifted at \(SOC_{g}\)= \(-\kappa\%\) = \(-\)1% and \(SOC_{r}\)= \(\rho\) = 1.006, according to the flowchart of the TBD strategy in Figure 4.  
Figure 8 illustrates the time history of mode, state, \(SOC_{r}\), and \(SOC_{g}\) and the corresponding torque distribution histories of the front, rear left, and rear right motors during the TBD process in the hardware-in-the-loop experiment. During the first 95 s, the SOC of the front battery pack was higher than the SOC of anyone of the rear battery packs. Therefore, State 1 (\(SOC_{g}\)\(>\) 0) was identified and \(SOC_{r}\) was larger than 1.006, the front motor took the first priority of delivering torque and Mode 1 (\(P_{r}=1\)) was executed. Between 95 and 200 s, it was still at State 1 (\(SOC_{g}\)\(>\) 0) but \(SOC_{r}\) was less than 1.006, Mode 2 was executed with the PSO strategy.  
Between 200 and 300 s, State 2 (\(SOC_{g}\)\(=\) 0) was identified, i.e., the SOC of the front battery pack was equal to any one of the two rear battery packs. Mode 2 with the PSO strategy was working. Between 300 and 485 s, the SOC of the front battery pack was lower than the SOC of the rear battery packs, and State 3 (\(SOC_{g}\)\(<\) 0) was identified. Because \(0>SOC_{g}\)\(\geq\)\(-\)1% and \(|SOC_{g}|\) was increasing, Mode 2 remained.  
When \(SOC_{g}\) was less than \(-\)1% at State 3 between 485 and 585 s, the rear battery packs and motors started to take their top priority for delivering more power than the front battery and motor, and Mode 3 (\(P_{r}=0\)) was executed. Between 585 and 680 s, the SOC gap was between \(-\)1% and 0%, but \(|SOC_{g}|\) was decreasing, Mode 3 remained.  
Figure 7: Architecture of the hardware-in-the-loop experiment.  
The corresponding SOCs of the three battery packs is shown in Figure 9. In the first 500 s, the front battery provided all power to the vehicle. After 500 s, the rear and front batteries powered the vehicle alternatively, so that the SOC gap would always remain in 1% as expected.  
Figure 8: Histories of the mode (solid line), state (dashed line), state of charge (SOC) ratio, SOC gap and the torque distributions of the front, rear left, and rear right motors during torque and battery distribution process for the electric vehicle in the hardware-in-the-loop experiment.  
Figure 9: Histories of mode and the states of charge of the front, rear left, and rear right battery packs during torque and battery distribution process for the electric vehicle in the hardware-in-the-loop experiment.