## 4 Results and Discussion  
By modeling with the improved model, a range of \(\gamma\) values were obtained. Figure 15 exhibits the trend of \(\gamma\) as H and K vary. It can be observed from Figure 15 that \(\gamma\) is directly proportional to H and inversely proportional to K over the experimental range. Figure 14: PWM waveforms in the excitation winding before and after iteration. Figure 13: Waveform iteration steps. With the help of the experimental platform, the magnetic hysteresis loop measurement results are obtained. Furthermore, the classical model and the improved model are used to model, and the magnetic hysteresis loops can be obtained. The results are compared and analyzed as follows. Figures 16-19 show the measurement results of bipolar PWM excitation with modulation ratios of 1.3, 1.1, 0.9, and 0.7 (\(K=1.3\), 1.1, 0.9, and 0.7) respectively, as well as a fundamental frequency of 50 Hz and 11 pulses, and give the comparison of modeling results before and after improvement, where the blue line is the experimental value of \(B\) and \(H\), the orange line is the modeling value of \(B\) and \(H\). The plotting sequence for Figures 16-19 is in Appendix A. Regarding the calculation of the curves, a period of 0.02 s is taken for a period of 2000 points. That is, the integration interval is \(10^{-5}\) s. In order to compare the effects of the two methods, the results of the above two situations were analyzed. Table 5 shows the values and errors of residual and saturated magnetic induction intensities under different modulation ratios. It can be seen that when the excitation is PWM, the error of the improved model is much smaller than that of the conventional model. The improved model is 1.4% to 9% more accurate than the classical model. Figure 16: Comparison of results between the classical model and improved model (K = 1.3). Figures 16–20: ‘CPM’ stands for the classical Preisach model and ‘IPM’ for the improved Preisach model. Figure 17: Error comparison between classical and improved Preisach models. (**a**) Error\({}_{\text{Br}}\) comparison; (**b**) Error\({}_{\text{Bm}}\) comparison. The error of the improved model and the classical model changes with the change of \(K\). Figure 20 shows the change in error of both models for different values of \(K\). The reference value is the corresponding experimental result as stated in Table 5. It shows that the error of the improved model is always less than the traditional model, i.e., the improved model is superior. The error values of the two models fluctuate with the change of \(K\). When \(K>1.3\), the change of error of the two models tends to stabilize. Figure 19: Comparison of results between classical model and improved model (K = 0.9). Figure 20: Comparison of results between classical model and improved model (K = 0.7). From the point of view of numerical calculation, the improved Preisach model combines the data from the magnetic property experiments to ensure the accuracy of the turning point of each local loop, which makes the magnetic property curves obtained by this method of modeling closer to the real values. From the analysis of the properties of the Preisach model itself, in the simulation of the classical Preisach model, the initial magnetization curve segment has a large deviation from the experimental measurements, and there is also a certain error in the rising and falling segments inside the limiting magnetic hysteresis loop. The reason lies in the fact that the basic theory of the adopted classical Preisach model is to equate the magnetic domains to the magnetic hysteresis operator, which has only step properties and does not reflect the intermediate states of the magnetization process in the model. Therefore, when the external excitation signal is complex, it will produce a large error. In contrast, the improved Preisach model adds correction coefficients to offset the process not embodied in the model.