## 4 Simulation and Experimental Verification
### Simulation Verification  
The output comparison of speed and torque under the control of the EI-BELBIC, BELBIC and PI controller is shown in Figure 16 when the system is loaded suddenly. As shown in Figure 16a, the EI-BELBIC is faster than the BELBIC and PI controller and recover to the rated speed faster when a 20 N load is applied to the SynRM under two different controllers at 0.1 s, which shows that the EI-BELBIC has a more vital anti-interference ability. Moreover, as seen in Figure 16b, the torque-output capacity of the EI-BELBIC is consistent with that of the BELBIC and PI controllers. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Parameter** & **Symbol** & **Value** \\ \hline Rated voltage & \(U\) & 380 V & Rated current & \(I\) & 15.8 A \\ Rated speed & \(n\) & 1500 \(\mathrm{m}\mathrm{p}\mathrm{m}\) & Number of pole pairs & \(p\) & 2 \\ \(d\)-axis inductance & \(L_{d}\) & 165 \(\mathrm{m}\mathrm{H}\) & \(q\)-axis inductance & \(L_{q}\) & 20 \(\mathrm{m}\mathrm{H}\) \\ Stator Resistance & \(R_{s}\) & 1.008 \(\Omega\) & Moment of Inertia & \(J\) & 0.008 kg\(\cdot\)m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Basic parameters of the SynRM. In order to verify the control effect of the EI-BELBIC under different magnetic saturation degrees of the SynRM, Figure 17 is obtained. As shown in Figure 17a, the inductance value of the SynRM decreased with the increase in magnetic saturation. However, the motor still maintained flawless operation under the control of the EI-BELBIC and the deeper the magnetic saturation, the smaller the \(K_{s}\), and the stronger the anti-interference ability of the EI-BELBIC. In Figure 17b, the time for the SynRM to reach the rated speed when \(i_{d}=15\) A is 16.6% less than when \(i_{d}=10\) A and 29.4% less than when \(i_{d}=5\) A. The comparison diagram of current waveforms at different \(i_{d}\) are shown in Figure 18a shows the corresponding \(q\)-axis current change curve when \(i_{d}\) is 5 A, 10 A, and 15 A, respectively. Since the current limit of the \(q\)-axis is 15 A, the motor is driven to run with the current of 15 A when \(i_{q}\) reaches the maximum limit and then \(i_{q}\) drops to about 0 due to the no-load state when the motor reaches the rated speed. The three-phase current of factors with different \(i_{d}\), as shown in Figure 18b, is also consistent with the situation shown in Figure 17: the current waveform changes into a sine wave when the speed reaches the rated value. Figure 16: Comparison diagram of SynRM performance response under sudden load: (**a**) Speed; (**b**) Torque. Figure 17: Comparison diagram of SynRM performance response at different \(i_{d}\): (**a**) Magnetic saturation parameter \(K_{S}\); (**b**) Speed. With the same stator current, the output torque of the SynRM under magnetic saturation is lower than that of the ideal case. In order to verify the control effect of the EI-BELBIC on the SynRM under magnetic saturation, load capacity simulation and comparison experiment were carried out between the EI-BELBIC and the SynRM ideal model and Figure 19 was obtained. Due to the difference between magnetic saturation and load, the starting process of the motor is significantly different, as shown in Figure 19a. When the motor is started at half load under ideal conditions, the SynRM has the fastest starting speed, which can complete the on-load start with 0.02 s. However, the starting time is extended to 0.03 s when the motor is affected by magnetic saturation. When the load is increased, the motor takes longer to start at full load under ideal conditions, but the difference is insignificant compared to starting at half load under magnetic saturation. Furthermore, the SynRM has the longest startup time when it starts at full load under magnetic saturation.