## 4 Simulation and Experimental Results Analysis
### Simulation Analysis  
Figure 3 shows the speed response waveform of PMSM. The simulation condition is that the 10 Nm load torque disturbance is added suddenly 0.5 s after a no-load start. From the figure, it can be seen that these three control algorithms perform very well in the PMSM speed tracking control. From the initial waveform within 0.2 s, it can be seen that although the integral sliding mode control algorithm has good steady-state characteristics, it brings a large overshoot to the system. This conclusion and the theoretical proof in Section 3 have a good match. In order to suppress this negative effect to the system due to insufficient control algorithms, this paper designs a sliding mode controller based on a nonlinear disturbance observer. It can be seen from the figure that the compound controller with a disturbance observer can compensate for the overshoot of the system to a certain extent. According to the detail drawings, it can be seen that when the system is disturbed by a sudden load, the traditional sliding mode algorithm has a constant steady-state bias. Although the integral sliding mode control brings a certain overshoot to the system, speed tracking control is the most basic requirement of the entire servo control system. In order to balance the dynamic performance of the system and the control target of the system at the same time, the sliding mode controller based on the nonlinear disturbance observer shows a more comprehensive and excellent performance.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Symbol** & **Value** & **Unit** \\ \hline Rated voltage & \(U\) & 200 & V \\ Rated current & \(I\) & 17.8 & A \\ Rated speed & \(\omega\) & 1000 & r/min \\ Rated power & \(p\) & 3 & kW \\ Rated torque & \(T_{L}\) & 14.3 & Nm \\ Rotor inertia & \(J\) & 0.003 & kg\(\cdot\)m\({}^{2}\) \\ Inductance & \(L\) & 5.25 & mH \\ Damping coefficient & \(B\) & 0.008 & Nms \\ Resistance & \(R\)s & 0.958 & \(\Omega\) \\ No. of poles & \(n_{p}\) & 4 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: The main parameters of the PMSM.  
Figure 2: The experimental test platform.  
Figure 4 is the electromagnetic torque waveform of PMSM under the action of the NDO-SMC algorithm and I-SMC algorithm. It can be seen in Figure 4a that the electromagnetic torque waveform jitter of the sliding mode controller with disturbance observer compensation is small. Compared with Figure 4b, the electromagnetic torque jitter of the integral sliding mode controller without a disturbance observer is larger. In the occasions where a high performance is required, such a control performance is not allowed.  
Figure 5 shows the PMSM stator three-phase current waveforms for both controllers. Comparing the current waveforms, it can be seen that the sliding mode controller based on the disturbance observer compensation has a higher sinusoidality for the three-phase currents and contains less harmonic currents, which in turn reduce the losses during PMSM operation [28].  
Figure 4: Electromagnetic torque of the (**a**) NOD-SMC controller and (**b**) I-SMC controller.  
Figure 5: PMSM stator three-phase current waveforms of the (**a**) NOD–SMC controller and (**b**) I-SMC controller.  
Figure 3: Speed response waveform of three controllers.