## 3 Control Strategy during Engine Start-Up Process  
A compound PSHEV starts in pure electric mode. When the battery state of charge (SOC) is less than its threshold, or the vehicle speed exceeds its threshold, or the driver's required torque exceeds the maximum torque threshold, the system starts to enter the engine start-up process. Figure 2 illustrates these four steps as follows: (1) electric vehicle (EV) phase in which B1 is locked, (2) EV phase in which B1 is being opened, (3) electric engine starting phase before the engine is firing, and (4) electro continuously variable transmission (ECVT) phase after the engine is firing. \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Engine maximum torque/speed (Nm/rpm) & 145/3600 \\ MG1/MG2 maximum torque (Nm) & 96/246 \\ Planetary parameter of front row \(i_{1}\) & –3.179 \\ Planetary parameter of rear row \(i_{2}\) & 2.342 \\ Final drive ratio \(i_{0}\) & 4.044 \\ Carrier inertia \(I_{C}\)(kg\(\cdot\)m\({}^{2}\)) & 0.0039 \\ Ring inertia \(I_{R}\)(kg\(\cdot\)m\({}^{2}\)) & 0.0017 \\ Inertia (\(I_{MG1}+S_{1}\)) of MG1 and \(S_{1}\)(kg\(\cdot\)m\({}^{2}\)) & 0.041 \\ Inertia (\(I_{MG2}+I_{S2}\)) of MG2 and \(S_{2}\)(kg\(\cdot\)m\({}^{2}\)) & 0.0723 \\ Engine inertia \(I_{Eng}\)(kg\(\cdot\)m\({}^{2}\)) & 0.18 \\ Vehicle equivalent mass \(m_{v}\)(kg) & 1538 \\ Wheel radius \(r_{v}\)(m) & 0.31 \\ Vehicle frontal area \(A\)(m\({}^{2}\)) & 2.19 \\ Air resistance coefficient \(C_{d}\) & 0.307 \\ Tire rolling resistance coefficient & 0.0137 \\ Rated capacity of battery (Ah) & 37 \\ Rated voltage of battery (V) & 308 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Main structure parameters of hybrid powertrain system. Figure 1: Structure diagram of powertrain system of a compound power-split hybrid electric vehicle. In Figure 2, the solid black line is the lever balance line, where the speed on the balance line is zero, the speed below the balance line is negative, and the speed above the balance line is positive. The torque arrow facing upward is positive, and the torque arrow facing downward is negative. According to the lever chart in Figure 2 and the dynamic relationship of the transmission system, the torque relationship of two motors during the engine start-up process can be expressed as follows: The basic control strategy can be expressed by Equations (1)-(3). (1) EV phase in which B1 is locked. In the first stage, B1 is braked by the hydraulic system. The whole car is driven by the torque of MG2. At this stage, the torques produced by two motors can be expressed as follows:  
\[\left\{ \begin{array}{ll}T_{\text{{MG1}}}=&0\\ T_{\text{{MG2}}}=&-T_{\text{{WH\_Lim}}}/(i_{0}i_{2})+(I_{\text{{MG2}}}+I_{ \text{{S2}}})i_{0}i_{2}\ddot{\theta}_{\text{{WH}}}\\ &+(i_{1}/i_{2})(I_{\text{{MG1}}}+I_{\text{{S1}}})i_{0}i_{1}\ddot{\theta}_{ \text{{WH}}}\\ T_{\text{{B1}}}=&-T_{\text{{WH\_Lim}}}(i_{2}-1)/(i_{0}i_{2})\\ \end{array} \right. \tag{1}\]  
where \(T_{\text{{WH\_Lim}}}\) is the wheel demand torque, \(T_{\text{{B1}}}\) is the balance torque produced by brake 1, \(i_{1}\) and \(i_{2}\) are the speed ratio parameters of the front row and the rear row, and \(i_{0}\) is the final drive ratio. \(I_{\text{{MG1}}}\) and \(I_{\text{{MG2}}}\) are the rotational inertias of MG1 and MG2, respectively. \(\ddot{\theta}_{\text{{WH}}}\) is the angular acceleration of the vehicle in longitudinal motion. (2) EV phase in which B1 is being opened. In the second stage, B1 is rapidly opened through the electro-hydraulic control system. The torques of the two motors keep the engine stationary as much as possible while the car is driven. At this stage, the torque relationship of the two motors can be expressed as follows:  
\[\left\{