# 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  
#### 3.2.1 Optimization of the Cost Function  
FCS-MPC can control multi-objective constraints. However, it is often necessary to consider the weight coefficient [90,91] when considering the parameter dimension. In order to simplify the design of the weight coefficient, many scholars have split or designed the cost function separately. For example, in [92], the flux torque cost function is split separately, as shown in (12). On this basis, Ref. [93] evaluated \(J_{t}\) and \(J_{\psi}\) twice in sequence, and reduced the number of alternative switch states for the second evaluation. In addition,  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Methods** & **Accuracy** & **Complexity** & **Advantage** & **Disadvantage** \\ \hline \multirow{2}{*}{MRAS} & \multirow{2}{*}{Medium} & \multirow{2}{*}{Medium} & \multirow{2}{*}{Wide speed range} & Additional conditions \\ \cline{3-3} \cline{5-5} \multirow{2}{*}{RLS} & \multirow{2}{*}{Slightly High} & & Easy to implement implementation & Low accuracy \\ \hline \multirow{2}{*}{KLF} & \multirow{2}{*}{High} & \multirow{2}{*}{High} & Lower impact of measurement noise & Complex computations \\ \cline{3-3} \cline{5-5} \multirow{2}{*}{KLF} & \multirow{2}{*}{High} & \multirow{2}{*}{High} & Lower impact of measurement noise & Complex computations \\ \hline \hline \end{tabular}
\end{table}
Table 2: Comparison of PMSM Parameter Identification Methods.  
Figure 5: Deadbeat predictive control based on compound disturbance observer [88]. (**a**) Control block diagram; (**b**) comparative experiment.  
the optimization of multi-cost functions were examined in [94], the optimization of serial cost functions in [95], the standardization of control variables in [96], and the control of corresponding vectors in [97].  
\[J=K_{t}[T_{e}^{ref}-T_{e}(k+1)]^{2}+K_{\psi}[\psi_{s}^{ref}-\psi_{s}(k+1)]^{2} \tag{12}\]  
where \(K_{t}\) and \(K_{\psi}\) are weight coefficients; \(T_{e}^{ref}\) is reference torque; and \(\psi_{s}^{ref}\) is reference magnetic flux.  
For the design of weight coefficients, genetic algorithms, the neural network, and fuzzy control are widely used [98; 99; 100]. In [101], the neural network was used to conduct training data and realize the best full-time fast automatic selection; the control block diagram is shown in Figure 6. In [102], An optimization scheme based on an intelligent neural network is proposed to calculate the weight coefficient, but this strategy still needs to establish a cost function to evaluate the constrained target and involve the weight coefficient.  
In addition to calculating accurate weight coefficients, Refs. [103; 104; 105] only considered the relationship between voltage vectors to optimize the design of the cost function and eliminate the weight coefficients. In [106; 107], the weight coefficient was canceled by replacing torque and flux vector, so that the cost function only included flux. For polyphase PMSM, an auxiliary voltage vector combination was referenced. In [108], the harmonic current was eliminated by vector combination and the weight coefficient of the x-y subspace in the cost function was eliminated.