# Motor Vector Control Based on Speed-Torque-Current Map
## 4 Verification of the Proposed Vector Control Strategy
### Simulation Analyses
#### 4.2.3 Speed Coupling Mode Performance Simulation  
In the speed coupling mode, when the required torque is constant, the speeds of both motors can change within a certain range, and the system power consumption corresponding to different speed combinations is also different. According to the flow shown in Figure 16, the simulation condition is designed as follows: from 0 to 0.05 s, the vehicle speed is adjusted to 60 km/h. In this process, the torque is adjusted to the demand torque. Then, the vehicle travels from the initial speed of 60 km/h to the target speed of 60.43 km/h, with an acceleration of 0.48 m/s\({}^{2}\) for 0.25 s.  
Under the above conditions, the demand torque and speed of the main reducer are 75 Nm and 2430 rpm, respectively. The corresponding torques of MG1 and MG2 are 51 Nm and 24 Nm, respectively. Under the restriction of corresponding speed, the maximum speeds of MG1 and MG2 are 5600 rpm and 8500 rpm, respectively. The speed ranges of MG1 and MG2 are [-5600 rpm, 5600 rpm] and [-8500 rpm, 8500 rpm], respectively. In addition, the speeds of MG1 and MG2 are also constrained by the demand speed of final drive, which is described as follows:  
\[\omega_{\mathrm{o}}=\frac{\omega_{\mathrm{m1}}\cdot\mathrm{k}+\omega_{ \mathrm{m2}}}{\mathrm{i}_{0}\cdot(\mathrm{k}+1)}. \tag{18}\]  
To meet the requirements of the main reducer output characteristics, the speed range of MG1 under this condition is [-295 rpm, 5600 rpm] based on Equation (18). The target speed \(\mathrm{n_{1}}^{*}=3590\) rpm of MG1 is taken as an example to analyze the speed-torque characteristics during the working point transfer process. The dynamic responses of MG1 and MG2 are shown in Figure 20.  
As shown in Figure 20, in the period of 0-0.045 s, the speed of the two motors are adjusted to the speed when the vehicle speed is 60 km/h. In the period of 0.045-0.05 s, the torques of the two motors are adjusted to the demand torque corresponding to the condition (i.e., 60 km/h speed and 0.48 m/s\({}^{2}\) acceleration). At the moment of 0.05 s, the MG1 speed is adjusted to the target speed of 3590 rpm; meanwhile, the torque of MG1 increases and that of MG2 decreases as these two motors need extra torque to overcome the rotational inertia force when the speed changes. According to the power distribution flow in Figure 16, all of the energy consumption corresponding to the target speed n1\({}^{*}\) of MG1 can be obtained. When the vehicle speed is 60.43 km/h, the range of n1\({}^{*}\) is [-295 rpm, 5600 rpm]. When the initial speed of MG1 is set to 3242 rpm, the target speed of MG1 traverses in the interval of [-295 rpm, 5600 rpm] to obtain the demand power of the electric drive  
Figure 20: Changes of speed and torque of MG1 and MG2. system. The demand power of the system, corresponding to different target speeds of MG1, is shown in Figure 21.  
The optimal speed of MG1 n1* obtained from the static model of the motor is 3590 rpm. In the dynamic model, it is seen from Figure 21 that with the increase of target speed n1* of MG1, the system demand power first decreases and then increases. The following points of the MG1 target speed n1* are selected in the simulation studies: the starting point of the decreasing function is \(-295\) rpm, the trough point is 1867 rpm, and the final point of the increasing function is 5600 rpm. Table 5 shows the demand power at different MG1 target speeds. Table 5 shows that the power of MG1 increases and that of MG2 decreases, with the increase of the MG1 target speed n1*. When the optimal speed (3590 rpm) obtained by the static model is taken as the target speed of MG1, the average demand power of the drive system is 23.543 kW, which is not the minimum demand power of the electric drive system under this condition. When the MG1 target speed n1* is 5600 rpm, the maximum power demand of the electric drive system is 28.595 kW. This is because when the target speed of MG1 is 5600 rpm, the speeds of motor MG1 and MG2 need to be adjusted from 3242 rpm to 5600 rpm, and from 733 rpm to \(-4165\) rpm, respectively.