# High-Performance Flux Tracking Controller for Reluctance Actuator
## 4 Simulation Analysis
### Model Validation  
To verify the accuracy of the Hammerstein model, additional simulation was performed by inputting a group of multiple frequency sine signals, and the sine signals are composed of 0.1/1/10/100 Hz, as shown in Figure 14.  
Figure 15 shows the comparison results of the reluctance actuator, Hammerstein model, and Bouc-Wen models. Table 3 gives the accuracy of modeling. From what has been analyzed, we can draw a conclusion that the Hammerstein model has a better matching ability than the Bouc-Wen model.  
Specifically, Figure 15a depicts the hysteresis loop obtained by experiments and the identified Hammerstein model. In addition, Figure 15b compares the results between the Bouc-Wen model data and experimental data. In Figure 15c, the red line is the experimental output, the green line indicates the Hammerstein model output, and the blue line represents the Bouc-Wen model output; as seen in Figure 15c, compared with the blue line, the green line is more suitable for the red line, which means that the Hammerstein model fits the reluctance motor model well. Moreover, the fitting error is described in Figure 15d. Obviously, the Hammerstein model has better matching ability than the Bouc-Wen model.  
Figure 14: A group of multiple frequency sine signals.  
Figure 13: Hammerstein model identification results: (**a**) Hysteresis loop obtained by experiments and the identified Hammerstein model; (**b**) Hammerstein model error with respect to experimental data.  
**Remark 4**.: _Many high-precision hysteresis models, including the neural network model, improved operator model, and so on, were proposed in the electromagnetic field. However, it is worth noting that the motive is the pursuit of the appropriate control strategy to reduce the hysteresis effect and heighten the flux tracking accuracy of the reluctance motor in this paper. Therefore, the model accuracy is as important as the design of the controller, whereas in practice, they are contradictory. Specifically, the exact model is proportional to the complexity of its structure; in other words, the higher the accuracy of the model, the more factors are considered in the modeling process and lead to a complex model structure, which further results in a problematic controller design._  
Here, the Hammerstein structure is used to model the reluctance motor due to its structural simplicity and ease of control design controller. Compared with the Bouc-Wen model, the Hammerstein model can better characterize its rate-dependent hysteresis. In the process of comparison, considering the applicability and popularity of the model at the same time, some rate-dependent modeling methods with complex structures, such as the operator model, improved J-A model, and neural network, are popular but not  
Figure 15: Comparison results of reluctance actuator, Hammerstein model, and Bouc-Wen models. (**a**) Comparison between experiment and Hammerstein model; (**b**) Comparison between experiment and Bouc-Wen model; (**c**) Flux output comparison diagram of the reluctance actuator, Hammerstein model, and Bouc-Wen models; (**d**) The error between Hammerstein model, and Bouc-Wen model and reluctance actuator.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Bouc-Wen** & **Hammerstein** \\ \hline RMSE & \(1.365\times 10^{-4}\) & \(5.299\times 10^{-5}\) \\ RE & \(0.0097\) & \(0.0037\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The accuracy of modeling.  
considered in this paper. Considering the modeling error of the Hammerstein structure, discrete sliding mode control based on the disturbance observer is adopted.