## 4 Simulation and Experimental Results Analysis
### Experimental Analysis  
Figure 6 shows the speed and current response waveforms of the three controllers. Figure 6a shows the no-load start waveform of the I-SMC. Figure 6b-d show the current and speed response for I-SMC, SMC, and NOD-SMC, respectively. From Figure 6, although the three controllers have different overshoots, it can be seen that all three controllers can achieve good speed tracking control under no-load conditions. However, after the motor is subjected to an impulse load torque of 10 Nm and an unknown disturbance in the mismatched channel, the three controllers show different responses. Although I-SMC still maintains speed tracking control for the motor, it produces almost the same amount of overshoot as at the no-load start up. In contrast, the dynamic characteristics of the latter two controllers are better. Figure 5 shows the response of the three controllers subjected to two disturbances. It can be seen from the figure species that the speed response of the SMC appears to have a constant static difference after being disturbed. The reason for this phenomenon is that the disturbance of the added mismatch channel is a constant. Therefore, although SMC has better dynamic performance than I-SMC, this steady-state static difference is fatal for high performance applications. In contrast, NOD-SMC combines the advantages of both controls, based on an observer, in order to identify unknown disturbances in the system, through the fast response time of a sliding mode controller. Ultimately, a PMSM high-performance speed control is achieved. This conclusion also matches well with the simulation in Figure 3. The transient response data for the three controllers are presented in Table 2.  
Figure 6: PMSM stator three phase current waveforms. (**a**,**b**) I-SMC, (**c**) SMC, and (**d**) NOD–SMC.  
Figure 7 shows the full operating response of the NOD-SMC. It consists of no-load starting of the motor to rated speed, followed by the sudden addition and reduction of the rated torque load, and no-load deceleration. Figure 7a,b shows that the rotor position angle does not fail or lose step even when the motor is disturbed by the rated torque, which also shows the robustness of the designed control system.  
Figure 8 shows the complete speed waveform of the proposed controller, and it includes starting, increasing the rated load, reducing the load, and decelerating. Figure 8b,c shows the speed response for loading and decreasing the load, respectively. Although the speed fluctuates between two transient state processes with load changes, there is no missing or incorrect rotor position angle information. These waveforms not only prove the effectiveness of the proposed control algorithm, but also illustrate the correctness of the experiment platform.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Controller** & **Mp (Start)** & **Mp (Load)** & **Rise Time (Tr/ms)** & **Settling Time (Ts/s)** \\ \hline I-SMC & +52\% & \(-\)53.0\% & 25.6 & _83.4_ \\ SMC & +32\% & \(-\)7.0\% & 24.2 & _30.0_ \\ NOD-SMC & +2\% & \(-\)3.5\% & _21.0_ & _22.0_ \\ \hline \hline \end{tabular}
\end{table}
Table 2: The transient response data for the three controllers.  
Figure 7: PMSM stator three phase current waveforms.