# Overview of Predictive Control Technology for Permanent Magnet Synchronous Motor Systems
## 3 An Overview of the Recent Development for Predictive Control Methods of PMSM
### FCS Model Predictive Control of PMSM
#### 3.2.4 Reduce the Computational Burden  
The traditional model predictive control method has higher computational complexity and control difficulty in the control of the polyphase motor. A simplified MPTC strategy for a dual three-phase permanent magnet synchronous motor is proposed in [131], which used 36 voltage vectors as prediction vectors \(\alpha\)-\(\beta\). The flux position and torque deviation in the x-y subspace were screened again to reduce the calculation time and effectively suppress the harmonic current. Meanwhile, considering the existence of a delay in the prediction process, a two-step prediction was approved to resolve delay issues.  
For the problem of multiple predictive vectors, the initial response strategy was to use only 12 voltage vectors with the largest amplitude as the prediction sequence [132; 133]. Although the number of predictive vectors was reduced to a certain extent, this led to problems such as large torque ripple and stator current distortion. The auxiliary space voltage vector was proposed [134; 135; 136]. Reference [126] proposed a model predictive control based on the combination of voltage vectors. The required reference voltage vector was obtained by using deadbeat direct torque and flux control methods, and the appropriate predictive vector was determined according to the position of the reference voltage vector in the sector. Additionally, the prediction model and cost function were simplified without redundancy constraints through voltage vector combination. The comparison results of the execution time of the above methods are shown in Table 4. In [137], the method of combining DPC and MPCC was proposed. According to the position of the reference voltage vector in the vector sector, the optimal voltage vector output was selected through the preset cost function Equation (13). The vector sector diagram is shown in Figure 9.  
\[\begin{array}{l}J=\left|\left|v^{*}\right|-\left|k(av_{i})+l(av_{j})\right| \right|\\ k=\cos(15^{{}^{\circ}}+30^{{}^{\circ}}n-\theta_{\alpha-\beta}^{*})\\ l=\sin(15^{{}^{\circ}}+30^{{}^{\circ}}n-\theta_{\alpha-\beta}^{*})\end{array} \tag{13}\]  
where \(av_{i}\) and \(av_{j}\) are the selected two auxiliary vector combinations; \(v^{*}\) is the reference voltage vector.  
\begin{table}
\begin{tabular}{l c c c c} \hline \hline \multirow{2}{*}{**Methods**} & **Conventional** & \multirow{2}{*}{**Method in [126]**} & \multirow{2}{*}{**Method in [131]**} & \multirow{2}{*}{**Method in [135]**} \\  & **MPTC** & & & \\ \hline Measurement (\(\mu\)s) & 7.32 & 7.25 & 7.65 & 8.12 \\ Reference vector & 0 & 5.62 & 6.2 & 0 \\ Calculation (\(\mu\)s) & & & & \\ Prediction and & 48.51 & 27.36 & 31.28 & 50.18 \\ evaluation (\(\mu\)s) & & & & \\ \hline \hline \end{tabular}
\end{table}
Table 4: Execution Time Comparison.  
In [138], a low-complexity six-phase PMSM model control is proposed which simplifies the cost function of the prediction model and reduces torque ripple by establishing two sets of auxiliary voltage vectors with different amplitudes. According to the relationship between vector and torque error, a lookup table was established to reduce the number of prediction vectors, thus reducing the prediction time. A similar method was applied in [139]. The torque ripple was reduced by virtual voltage vector synthesis, and the vector table was established according to DTC, and then the selection was made according to the error change of flux linkage and torque. In [140], the optimal vector was selected according to the switch signal corresponding to the previous cycle, so the voltage vector was reduced from 27 to 7.