# High-Performance Speed Control of PMSM Using Fuzzy Sliding Mode with Load Torque Observer
## 4 Simulation and Experiment  
### Simulation Experiment Research  
To further prove the effectiveness of the control scheme proposed in this paper, the control strategy of the proposed and SMC + LO and PID + LO and ADRC simulation test are compared by using MATLAB/Simulink. The parameters of the PMSM are shown in Table 2. The reference is \(n^{*}=800\) r/min; a step load torque disturbance with an amplitude of 0.1 N\(\cdot\)m is added at \(t=0.25\) s. Speed response curves corresponding to the control strategies is shown in Figure 6; Figure 7 is \(d-q\) current response curves of the proposed control strategy in this paper; Figure 8 is the output curve of the load torque observer and load torque. The performance of four control methods under adding sudden load are summarized in Table 3. As can be seen from Table 3, when tracking the step signal, the regulation time of ISMC + LO is the same as that of SMC + LO. The regulation time of ISMC + LO is 29% and 23% of that of ADRC and PID + LO, respectively. When a step load is suddenly applied, the dynamic speed drop of ISMC + LO is 84.3%, 73%, and 66% of that of SMC + LO, ADRC, and PID + LO, respectively. The recovery time of ISMC + LO is 73.3%, 55%, and 36.7% of that of SMC + LO, ADRC, and PID + LO, respectively.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Stator Inductor** & **Nominal** & **Stator** & **Maximum** & **Moment of** & **Permanent Magnet** & **Polar** \\ \(L_{q},L_{q}\) & **Power** & **Resistance** & **Torque** & **Inertia** & **Flux Linkage** & **Logarithms** \\ \hline
0.000835 H & 200 W & 2.875 \(\Omega\) & 0.63 N\(\cdot\)m & 0.0003 kg\(\cdot\)m\({}^{2}\) & 0.3654 Wb & 4 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Parameters of permanent magnet synchronous motor.  
Figure 8: Torque observer output curves.  
Figure 6: Speed response curves under adding sudden load.  
Figure 7: \(d-q\) current response curves under adding sudden load.  
It can be seen from Figure 6 that the control strategy proposed in this paper has a smaller chattering amplitude compared to SMC + LO. As is shown in Figure 8, the load torque observer can quickly and accurately observe the external load torque.  
To verify the tracking of the controller, comparative simulation experiments with variable speed are conducted. Figure 9 shows the tracking response curves of the control strategy proposed in this paper, SMC + LO, ADRC, and PID + LO. Figure 10 is \(d-q\) current response curves of the proposed control strategy in this paper. The performance of four control methods under variable speed tracking is summarized in Table 4. As can be seen from Table 4, when \(n\) changes from 0 to 800, the regulation time of ISMC + LO is the same as that of SMC + LO. The regulation time of ISMC + LO is 29% and 23% of that of ADRC and PID + LO, respectively. When \(n\) changes from 800 to 1000, the regulation time of ISMC + LO is the same as that of SMC + LO. The regulation time of ISMC + LO is 29% and 13.8% of that of ADRC and PID + LO, respectively. When \(n\) changes from 1000 to 600, the regulation time of ISMC + LO is the same as that of SMC + LO, and the regulation time of ISMC + LO is 20% of that of ADRC and PID + LO.  
As can be seen from Figure 9, the proposed control strategy has no chattering compared to the SMC + LO, and its regulation time is shorter than those of the PID + LO and ADRC.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Property Index** & **PID + LO** & **ADRC** & **SMC + LO** & **ISMC + LO** \\ \hline Adjusting time (s) & 0.14 & 0.11 & 0.032 & 0.032 \\ Dynamic deceleration (r/min) & 4.1 & 3.7 & 3.2 & 2.7 \\ Recovery time (s) & 0.03 & 0.02 & 0.015 & 0.011 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Property index of four control methods under adding sudden load.  
Figure 9: Speed response curves under variable speed tracking.