## 3 Simulation and Experimental Analysis
### Experimental Results and Analysis  
The feasibility of the control scheme based on the combination of the integral backstepping controller and the ELESO is preliminarily verified through simulation. On this basis, the motor test bench shown in Figure 3 is used for experimental verification. The  
Figure 14: PMSM rotor speed under load startup 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. Figure 13: PMSM d and q-axis currents under load startup 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. magnetic particle brake and tension controller provide load to the PMSM. The dynamic torque sensor can display the change of dynamic parameters such as speed and torque of the PMSM. At zero speed and low speed, the back EMF is very small, and the rotor position cannot be accurately estimated. I-F open-loop startup is usually used to cover the startup from standstill through the low-speed area. After rotor pre-positioning, the method applies a constant q-axis current to drag the speed up to the desired speed, then switches to a medium-high speed angle observer [36]. According to the simulation results, two experiments are designed to verify the superiority of the control scheme based on the integral backstepping controller and the EESO. These experiments also use the control scheme based on the backstepping controller and the ESO as a comparison. Firstly, PMSM starts at no load and accelerates to 500 r/min. At 0.5 s, the PMSM accelerates to 1000 r/min. When the time reaches 1 s, the load jumps to 6 N-m. Finally, the load drops to 0 N-m at 1.5 s, and the PMSM keeps running at this state. Figure 15 shows the speed waveforms under this experiment. The total duration of the experiment is set to 2 s. The timeline of the experiment is marked in Figure 15, and all the following waveforms are based on this timeline. Figure 15 clearly shows that when the system state changes, the control scheme based on the integral backstepping controller and the ELESO has a faster response speed. Figure 16 shows the actual position and estimated position of the rotor after taking the remainder under the two schemes. In Figure 16, the errors of the two schemes are small, which will be difficult to show the superiority of the improved scheme. In this paper, the position and speed information are quantified in the table for a clearer comparison. Table 2 shows the estimated and actual values of position and speed under the two schemes. According to the design of experiment 1, the appropriate time points are selected for data acquisition. In experiment 1, after the PMSM is started, the system state changes three times at 0.5 s, 1 s and 1.5 s. Table 2 shows that the control scheme based on the integral backstepping controller and the ELESO has better tracking effect in the whole process of experiment 1. The rotor position tracking error is basically stable within 0.1 rad, which is greatly improved compared with the control scheme based on the backstepping controller and the ESO. When the system state changes, the rotor speed jump amplitude of the improved scheme is lower. Moreover, when the system operates stably, especially when the load value is rated, the steady-state error of the control scheme based on the integral backstepping controller and the ELESO is smaller, and its speed can converge to the set value faster. Figure 15: Experiment 1 PMSM rotor speed 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. Figure 17 is the current waveforms diagram of the d and q-axis. Figure 18 shows the electromagnetic torque waveforms. In Figure 17, both schemes have obtained stable current waveforms.