# Super-Twisting Sliding Mode Control with SVR Disturbance Observer for PMSM Speed Regulation
## 4 Simulation  
The simulation of PMSM speed control system was conducted using MATLAB/Simulink. The PMSM simulation parameters are listed in Table 1. A traditional sliding mode controller,STRL-SMC and STRL-SMC with SVR-DOB were compared to the performance. In this simulation, we designed the reaching law of traditional SMC as \(-k_{1}\)sgn\((s)-k_{2}\)s [29]. With the discontinuous control input, we confirmed that there was chattering in proportion to the gain \(k_{1}\). The proposed STRL induces continuous control input which has the ability of the chattering reduction. Compared with the traditional SMC, STRL-SMC with SVR-DOB shows the reduced chattering effect as shown in Figure 3b.  
\begin{table}
\begin{tabular}{c c c} \hline
**Symbol** & **Parameter** & **Value** \\ \hline \(R\) & Stator phase resistance & 2.875 \(\Omega\) \\ L & Inductance & 153 mH \\ \(\psi_{f}\) & Flux linkage & 0.175 Wb \\ \(\int\) & Inertia & \(5.5\times 10^{-3}\) kg-m\({}^{2}\) \\ \(n_{p}\) & Pole pairs & 4 \\ \hline \end{tabular}
\end{table}
Table 1: Parameters of PMSM.  
Figure 3: Comparison between traditional SMC and STRL-SMC for disturbance suppression.  
The reference speed changes following the staircase waveform. Figure 3 shows the results of the traditional SMC and STRL-SMC. Moreover, quantitative results on performance index were compared in Table 2. Table 2 represents the performance difference between traditional SMC and STRL-SMC for maximum overshoot, settling time, and steady-state error according to the results in Figure 3. A comparison between traditional SMC and STRL-SMC for the speed tracking results is shown in Figure 4. The reference speed was set to 100 rad/s. The load torque was suddenly increased by 3 N \(\cdot\) m at 0.01 s.  
Figure 5 depicts the performance comparison between the traditional SMC and STRL-SMC. The gains of traditional SMC and STRL-SMC are optimized for the best performance, respectively. The load torque was suddenly increased by 3 N \(\cdot\) m at 0.008 s and decreased by 1 N \(\cdot\) m at 0.012 s, respectively. As shown in Figure 5, the chattering of the proposed STRL-SMC result is smaller than the traditional SMC result under the same simulation condition. The performance of SVR-DOB is represented in Figure 6.  
In the Figure 4, STRL-SMC shows rapid response to track the reference speed than the traditional SMC. For transient state driven by speed increment of 50 rad/s, STRL-SMC shows better performance than the traditional SMC with a fast response. The result proves the anti-disturbance ability of STRL-SMC. The difference from the simulation results of the two control methods demonstrated smaller speed fluctuations from STRL-SMC with SVR-DOB than those from STRL-SMC. Compared with STRL-SMC, which does not include SVR-DOB, STRL-SMC with SVR-DOB exhibits a better performance and robustness to disturbances. Therefore, the STRL method has the advantages of an improved dynamic performance and disturbance rejection properties compared with traditional SMC. The  
Figure 5: Comparison between STRL-SMC and STRL-SMC with SVR-DOB.  
proposed controller can lead the measurement speed to track successfully the reference speed of 100 rad/s.