## 4 Results and Discussion  
In order to validate the performance of the proposed strategy, the conducted HIL simulations are described in this section. The verification platform included a real-time parallel HEV model platform and a real-time control platform. Both of the two development platforms can generate the C code and perform online calibration in the MATLAB/Simulink environment [40]. In this study, the development process of the verification platform could be divided into three steps. First, both the parallel HEV model and the control strategy were designed in the MATLAB/Simulink environment. Second, by using the automatic code generation technology, the real-time kernels of the parallel HEV model and control strategy were generated. Third, the real-time kernel of the parallel HEV was downloaded into the SCALEXIO LabBox, which exhibits a strong computing capacity. In addition, the other kernel was flashed into the MicroAutobox, which is an electronic controller [41; 42]. All set parameters and verification results in SCALEXIO LabBox and MicroAutobox were monitored by the software Control Desk operating on a laptop [40; 41; 42; 43]. The HIL test bench is depicted in Figure 9.  
As shown here, the unified model of parallel HEV was constructed with the specifications listed in Table 1. The test cycle was taken from a stretch of typical driving cycles that are widely used by manufacturers, as shown in Figure 9. The whole testing process consisted of the mode transition from the electric mode to the hybrid driving mode. When the vehicle velocity reached about 20 km/h, the engine was dragged to the idle speed by the starting motor and immediately ignited with fuel injection. The clutch was then engaged. After the clutch lockup, the parallel HEV entered the hybrid driving mode. To prove the effectiveness of the proposed coordinated control strategy, the performances of three different cases are compared in this section. A detailed description of three test cases is listed in Table 4.  
The simulation results for the two power sources for case I are shown in Figure 10. Because the coordinated control strategy was not considered in case I, the control commands for the engine and motor came directly from the energy management strategy. It can be observed that the mode transition occurred around 13.62 s. At the initial stage of the clutch slipping process, the driven plate speed was immediately reduced by about 89 r/min due to the speed difference of the clutch. At this moment, the torque transmitted by the clutch is regarded as an interference torque, which corresponds to a negative torque (\(-\)98.7 Nm) on the output shaft of the engine. If this disturbance torque cannot be suppressed or compensated in time, it will lead to a noticeable jerk and vibration in the hybrid powertrain. This means that the coupling torque on the driveshaft does not correspond to the torque required by the powertrain, which results in a large deviation from the actual velocity to the target value. In addition, the variation in the friction plate coefficient with temperature interacts with the engine torque on the driving plate side, which exacerbates the speed fluctuations at both ends of the clutch. Until 15.69 s later, the clutch was completely engaged and in a locked state. With the gradual increase in engine torque, the motor torque decreased to 100 Nm, and the parallel HEV completed the mode transition. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & & & & & \(\dot{e}\) & & & \\ \cline{3-8}  & & NB & NM & NS & ZO & PS & PM & PB \\ \hline \multirow{4}{*}{\(e\)} & NB & ZO & ZO & ZO & PS & PB & PB & PB \\  & NM & ZO & ZO & PS & PS & PS & PS & PB \\  & NS & ZO & PS & PS & PS & PS & PS & PB \\  & ZO & NS & PS & ZO & ZO & ZO & PS & PS \\  & PS & NB & NS & NS & NS & NS & ZO \\  & PM & NB & NB & NS & NS & NS & ZO & ZO \\  & PB & NB & NB & NB & NS & ZO & ZO & ZO \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fuzzy inference rules for the parameter \(K_{\text{i}}^{\prime}\).