## 4 Conclusions  
According to the characteristics of the sensorless control system, this paper proposes a sensorless control scheme that combines the integral backstepping controller with the ELESO to improve the performance of the system.  
The LESO proposed by the control algorithm has the advantage of estimating the system disturbance without requiring an accurate motor model. On this basis, the algorithm improves the performance of the sensorless system by cascading another new LESO to estimate and compensate for the sixth harmonic component. Moreover, the control system provides the integral speed backstepping controller with the estimation value of the rotor speed obtained by the ELESO. The q-axis current reference value is obtained by designing a Lyapunov function. The current reference values in the synchronous rotating coordinate system are transferred to the integral current backstepping controllers to obtain the d and q-axis voltages. The reference voltages and the estimated rotor position obtained by the ELESO are transmitted to the SVPWM to realize the whole FOC sensorless control process. The acceleration and load startup experiments are carried out on the control model to verify that the improved algorithm has a faster convergence speed and more accurate position estimation. In addition, the control algorithm can effectively eliminate motor chattering and phase delay, which has good stability under static and dynamic conditions. The simulation results show that the PMSM sensorless control system based on the integral backstepping controller and the ELESO is effective and has good load interference suppression capability.  
Figure 22: Experiment 2 PMSM electromagnetic torque waveforms of the (**a**) Control scheme of combining the backstepping controller with the ESO and (**b**) Control Scheme of combining the integral backstepping controller with the ELESO.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Time (s)** & **Id (a)** & **Id (b)** & **Torque (a)** & **Torque (b)** \\ \hline
0.1 & 0.35 & \(-\)0.002 & 8.84 & 6.06 \\
0.3 & 0.50 & 0.002 & 8.49 & 6.02 \\
0.5 & \(-\)0.013 & 0.002 & 6.39 & 6.01 \\
0.7 & 0.28 & 0.002 & 6 & 6 \\
0.9 & 0.132 & 0.002 & 6.72 & 6.01 \\ \hline
1.1 & \(-\)0.15 & 0.002 & 3.68 & 6.04 \\
1.3 & \(-\)0.011 & \(-\)0.001 & 6.57 & 6.01 \\
1.5 & \(-\)0.12 & \(-\)0.001 & 6.07 & 6 \\
1.7 & \(-\)0.36 & \(-\)0.001 & 4.74 & 6 \\
1.9 & \(-\)0.05 & 0 & 5.34 & 6.01 \\ \hline \hline \end{tabular}
\end{table}
Table 5: D-axis current and torque of experiment 2.  
**Author Contributions:** Conceptualization, L.S. and C.Z.; methodology, L.S. and C.Z.; software, Y.Z. and G.X.; validation, L.S., C.Z., G.X. and X.H.; formal analysis, X.H.; resources, L.S.; data curation, C.Z.; writing--original draft preparation, C.Z.; writing--review and editing, L.S., X.Z., Y.Z. and G.X. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by Basic Public Welfare Research Program of Zhejiang (Yanjuan Qin: LGG19F010010).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** The research data used and/or analyzed during the current study are available from the corresponding author on reasonable request.  
**Conflicts of Interest:** The authors declare no conflict of interest.