## 3 Simulation and Experimental Analysis
### Experimental Results and Analysis
However, the jump amplitude of the q-axis current in Figure 17b is smaller when the speed changes. Figure 18a shows that the waveform jitter with internal interference (higher harmonics) will be very obvious. In high performance control occasions, such control performance is not allowed. The reference value of d-axis current is always 0. According to the time point selected in Table 2, the d-axis currents and electromagnetic torques are quantized in Table 3. Comparing the data of the two schemes, the d-axis current error and electromagnetic torque error of the control scheme based on the integral backstepping controller and the ELESO are 1-10% of the error of the comparison scheme. The control scheme based on the integral backstepping controller and the ELESO shows better control performance. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Time (s)** & \begin{tabular}{c} **Speed (a)** \\ **Act/Est** \\ \end{tabular} & \begin{tabular}{c} **Speed (a)** \\ **Error** \\ \end{tabular} & \begin{tabular}{c} **Speed (b)** \\ **Act/Est** \\ \end{tabular} & \begin{tabular}{c} **Speed (b)** \\ **Error** \\ \end{tabular} & \begin{tabular}{c} **Position (a)** \\ **Act/Est** \\ \end{tabular} & \begin{tabular}{c} **Position** \\ **(a) Error** \\ \end{tabular} & \
\begin{tabular}{c} **Position** \\ **(b) Act/Est** \\ \end{tabular} &
\begin{tabular}{c} **Position** \\ **(a) Error** \\ \end{tabular} \\ \hline
0.01 & 363.85/137.69 & 226.16 & 500.45/501.5 & \(-\)1.05 & 0.81/0.39 & 0.42 & 1.69/1.82 & \(-\)0.13 \\
0.05 & 470.00/462.84 & 7.16 & 506.67/505.13 & 1.54 & 2.16/1.48 & 0.68 & 4.52/4.61 & \(-\)0.09 \\
0.1 & 510.40/524.53 & \(-\)14.13 & 503.87/502.75 & 1.12 & 1.72/1.13 & 0.59 & 4.45/4.51 & \(-\)0.06 \\
0.3 & 500.58/497.83 & 2.75 & 500.15/499.03 & 1.12 & 3.38/2.75 & 0.63 & 6.17/6.23 & \(-\)0.06 \\ \hline
0.55 & 960.06/979.30 & \(-\)19.24 & 1015.57/1013.61 & 1.96 & 1.35/0.5 & 0.85 & 5.80/5.88 & \(-\)0.08 \\
0.6 & 1007.67/1005.30 & 2.37 & 1003.86/1002.66 & 1.2 & 5.99/4.68 & 1.31 & 6.14/6.19 & \(-\)0.05 \\
0.8 & 1001.32/1006.70 & \(-\)5.38 & 1000.29/999.41 & 0.88 & 5.28/4.09 & 1.19 & 4.14/4.18 & \(-\)0.04 \\ \hline
1.05 & 873.38/870.16 & 3.22 & 945.46/945.07 & 0.39 & 1.05/0.03 & 1.02 & 4.72/5.14 & \(-\)0.42 \\
1.1 & 926.43/921.41 & 5.02 & 995.04/994.04 & 1 & 1.43/0.3 & 1.13 & 2.05/2.44 & \(-\)0.39 \\
1.3 & 967.17/931.65 & 35.52 & 999.82/998.94 & 0.88 & 1.10/0.08 & 1.02 & 6.16/6.22 & \(-\)0.06 \\ \hline
1.55 & 1112.68/1140.04 & \(-\)27.36 & 1056.01/1053.08 & 2.93 & 5.98/4.58 & 1.4 & 1.14/1.21 & \(-\)0.07 \\
1.6 & 1110.35/1107.98 & 2.37 & 1011.21/1010.24 & 0.97 & 2.79/1.39 & 1.4 & 1.44/1.48 & \(-\)0.04 \\
1.8 & 1042.10/1036.18 & 5.92 & 1000.99/1000.23 & 0.76 & 2.71/1.45 & 1.26 & 3.51/3.55 & \(-\)0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Position and speed of experiment 1. Figure 16: Experiment 1 PMSM rotor position 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. The load startup and speed jump test of PMSM are also essential steps to verify its sensorless control performance. Experiment 2 is designed as PMSM load startup and speed jump test of PMSM are also essential steps to verify its sensorless control performance. Experiment 3 is designed as PMSM load startup and speed jump test. Figure 17: Experiment 1 PMSM d and q-axis currents 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.