# Motor Vector Control Based on Speed-Torque-Current Map
## 3 Motor Vector Control Strategy Based on Speed-Torque-Current Map
### Speed-Torque-Current Map Integrated Current Control  
At present, the control strategies of the motor current mainly include the maximum torque current ratio (MTPA) control, maximum current voltage (MCMV) control, and maximum torque voltage ratio (MTPV) control.  
MTPA control is a control method aiming to obtain the maximum output torque with the minimum input of a stator current vector within the limits of voltage and current [19; 20]. The control equation of its boundary line is as follows:  
\[\mathrm{i_{d}}=\frac{-\varphi_{f}+\sqrt{\varphi_{f}{}^{2}+4\left(\mathrm{L_{d }}-\mathrm{L_{q}}\right)^{2}\mathrm{i_{q}}^{2}}}{2(\mathrm{L_{d}}-\mathrm{L_{q }})}. \tag{11}\]  
MCMV control is one of the weak magnetic control methods. Its characteristic is that the current vector and voltage vector are the limits of the current and the voltage of the inverter bus,respectively [21]. When the motor speed is adjusted to a certain speed of \(\omega_{\rm m}\), the control equation of (i\({}_{\rm q}\), i\({}_{\rm d}\)) in this region is as follows:  
\[\left\{\begin{array}{c}\rm{i}_{q}=\frac{\sqrt{\left(\frac{U_{dc,lim}}{\omega_{ m}}\right)^{2}-\left(L_{d}\dot{\rm{i}}+\varphi_{\rm{f}}\right)^{2}}}{L_{q}} \end{array}\right.. \tag{12}\]  
MTPV control enables the motor to achieve the maximum speed by making full use of the voltage vector supplied by the inverter [22; 23; 24]. For the tab-mounted PMSM, the reference current vector and the voltage control equation of MTPV is as follows:  
\[\left\{\begin{array}{c}\rm{i}_{d}=\frac{-\varphi_{f}}{L_{d}}\\ \rm{i}_{q}=-\frac{U_{dc,lim}}{L_{q}\omega_{s}}\end{array}\right. \tag{13}\]  
\[\left\{\begin{array}{c}\rm{u}_{q}=\frac{\varphi_{f}-\sqrt{\varphi_{f}{}^{2} +8U_{dc,lim}^{2}\left(\frac{L_{d}-L_{q}}{L_{q}\omega_{s}}\right)^{2}}}{-4 \left(\frac{L_{d}-L_{q}}{L_{q}\omega_{s}}\right)}\\ \rm{u}_{d}=-\sqrt{U_{dc,lim}^{2}-u_{q}^{2}}\end{array}\right.. \tag{14}\]  
To sum up, the running trajectories of the boundaries of the three control strategies in the d-q coordinate system are shown in Figure 4. OA, AB, and BC represent the running trajectories of the three control strategies (MTPA, MCMV, and MTPV) in the d-q coordinate system, respectively.  
To analyze the influence of different current control strategies on the motor speed-torque characteristics, the external characteristics under different strategies are obtained, as shown in Figure 5.  
Figure 4: Running trajectories of three current control strategies. MCMV: maximum current voltage; MTPV: maximum torque voltage ratio; MTPA: maximum torque current ratio.  
Aiming to combine the advantages of the above three control strategies, a comprehensive control strategy is proposed in this paper to expand the motor working range to its maximum within the scope of the inverter bus capacity. The principles of the comprehensive control strategy are as follows:  
1. The MTPA control strategy is adopted in the peak torque area to minimize the copper loss and iron loss.
2. In the high-torque region of the weak magnetic field, the MCMV control is adopted to transit to the MTPV control range.
3. MTPV control is used to extend the speed range of the motor in the high-speed region of the weak magnetic field.  
With the above principles, the external characteristic boundary of current control is obtained, as shown in Figure 6. Compared with the single current control strategy, the designed comprehensive control strategy has a wider speed range under the same torque, which improves the utilization ratio of the input current vector and voltage vector and maximizes the overall working range of the motor.  
Figure 5: Speed-torque characteristics of different control strategies.  
Figure 6: Boundary design of comprehensive control strategy.  
Based on the designed current control boundary curve, the speed and torque are traversed and substituted into Equations (8) and (9) to obtain the current of the d axis and q axis of all the work points. The resulting speed-torque-current map of the d-axis and q-axis are shown in Figure 7.