## 5 Results Analysis
### Faulty Conditions  
Figures 12-14 show the FPPMSM responses of the speed, torque, and currents under the influence of an OCF in phase \"_a_\". This fault event occurred at time 1 s, while the motor was operating at a load torque of 20 Nm and a speed reference of 200 rpm. Fault detection occurred at time 1.5 s, prompting an immediate transition to the proposed FTC diagram under faulty conditions using the MCL control strategy. It is clear that the oscillations and ripples in speed and torque responses using the proposed control were significantly reduced compared to the traditional controllers. Figure 14 illustrates the notable irregularities in the currents between times 1 s and 1.5 s before fault detection. Following fault detection, the currents exhibited disparities in magnitude, with phases \"_d_\" and \"_c_\" increasing by 26.31% and phases \"_e_\" and \"_b_\" increasing by 46.78%. Figure 11: Torque response to speed changes in healthy conditions. Figure 12: Speed response using MCL under OCF. Figure 13: Torque response using MCL under OCF. To evaluate the MCL and MTO control criteria using controllers based on PI, TSMC, and SMC with NESO, the FPPMSM was operated with four phases under a load torque of 40 Nm and a speed reference of 300 rpm. As shown in Figures 15 and 16, the torque ripple peak was larger for the MTO strategy compared to the MCL strategy. Meanwhile, the proposed control (SMC with NESO) exhibited minimal and almost identical torque ripples for each control criterion (see Figure 17). In addition, as noted in Figure 18, the MTO strategy kept all phase currents equal in magnitude and increased by 38.2% compared to normal operation with five phases. According to (43), Table 1 presents the calculation of torque ripples and speed fluctuations for the MTO and MCL strategies based on the traditional controllers and the proposed control. It is evident that the SMC with NESO had the lowest ripples and fluctuations, which were approximately identical for both strategies. Figure 16: TSMC performance using MCL and MTO under OCF. Figure 14: Current response in _abcde_ frame using MCL under OCF. Figure 15: PI control performance using MCL and MTO under OCF. To validate the robustness of the proposed control under faulty operating conditions, we investigated the impact of parameter uncertainties, specifically by varying the stator resistance. The mismatched disturbances in (19) and (20) were modeled as follows: \(d_{1}(t)=-\frac{\Delta R_{s}}{L_{dp}}i_{dp}\), \(d_{2}(t)=-\frac{\Delta R_{s}}{L_{qp}}i_{qp}\), and \(d_{6}(t)=-\frac{\Delta R_{s}}{L_{s}}i_{\beta s}\). Two control scenarios were investigated: one employed the proposed control based on the NESO that incorporated the HTF, and the other used an ESO without the HTF. The load torque and speed reference were set to 20 Nm and 300 rpm, respectively, and the stator resistance was adjusted to +60% of \(R_{s}\) at time 0.5 s. Figures 19 and 20 show the FFT spectra of the phase \"\(d\)\" stator current in the steady state. As can be seen, the proposed control using the HTF had a lower THD of 24.08% compared to the control without HTF, which had a THD of 35.75%. Figures 21 and 22 illustrate the speed and torque responses. It is evident that when the stator resistance changed at time 0.5 s, the control without HTF showed more pronounced ripples in speed and torque compared to the proposed control with HTF. Nevertheless, when the speed reference was set to 100 rpm at time 2 s, the ripples in both scenarios were nearly identical. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Controllers** & **Strategy** & \(T_{e_{pip}}\)**\%** & \(\Omega_{\mu\text{a}}\)**\%** \\ \hline PI & MTO & 37.3153 & 1.9202 \\  & MCL & 30.8831 & 1.5769 \\ \hline TSMC & MTO & 19.4586 & 0.9958 \\  & MCL & 16.0544 & 0.814 \\ \hline SMC+NESO & MTO & 1.9396 & 0.0118 \\  & MCL & 1.8087 & 0.0094 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of MTO and MCL using PI, TSMC, and SMC with NESO. Figure 17: SMC+NESO performance using MCL and MTO under OCF.