## 5 Results and Discussions  
### Feasibility Analysis  
This section conducts feasibility simulation experiments to validate the performance of the super-helical sliding mode model reference adaptive control system proposed in this paper. The initial operating speed of the motor is set at 1000 r/min, while the initial load torque is 10 N-m. At 0.3 s into the simulation, the load torque abruptly transitions to 20 N-m. Similarly, at 0.5 s, another abrupt change occurs where the load torque shifts to 20 N-m. Additionally, at the 0.5 s mark, the motor speed undergoes an abrupt change to 1500 r/min. To validate the effectiveness and robustness of the proposed control strategy, a pulse disturbance module was introduced at the torque input, generating a pulse signal with an amplitude of 5 at 0.1 s intervals. Furthermore, the motor stator resistance was treated as an uncertain parameter, with a 10% increment at 0.5 s to emulate the effects of internal aging. These configurations were designed to rigorously assess the strategy's resilience under external disturbances and model uncertainties. Figure 6 presents the motor speed simulation waveforms corresponding to both the STSM-MRAS and traditional PI control systems when abrupt changes in motor speed and load occur. Figure 7 illustrates the speed error simulation waveforms corresponding to the STSM-MRAS and traditional PI control systems under similar conditions. Figure 8 exhibits the simulated waveforms of rotor position error for the STSM-MRAS and conventional PI control systems during abrupt changes in motor speed and load. Figure 9 illustrates the simulated motor speed error waveforms for the STSM-MARS and conventional PI-MARS control systems when subjected to external disturbances and model uncertainties. method is shown in Equation (49), where \(M_{N}\) represents the speed overshoot, \(N_{max}\) is the maximum speed, and \(N_{ss}\) is the steady-state speed. \[\mathbf{M}_{N}=\mathbf{N}_{\text{max}}-\mathbf{N}_{ss} \tag{49}\]  
As depicted in Figure 7, upon motor initialization, the STSM-MARS control system proposed in this paper exhibits an overshoot of 119 r/min, reaching a steady state in 0.036 s. Conversely, the conventional PI-MARS control system experiences an overshoot of 157 r/min, requiring 0.062 s to reach a steady state. The motor startup behavior aligns similarly with that of the conventional PI-MARS control system, attaining a steady state in 0.062 s. At 0.3 s, during the load surge of 20 N, the speed of the STSM-MARS control system decreases by 70 r/min, whereas the conventional PI-MARS control system registers a decrease of 82 r/min. Subsequently, at 0.5 s, during the speed surge, the overshoot of the STSM-MARS control system amounts to 77 r/min, while the conventional PI-MARS control system is a steady state. Figure 8: Motor speed error results. Figure 7: Motor speed results. Figure 9: Rotor position error results. control system exhibits an overshoot of 116 r/min. This formulation provides a comparative analysis of the performance of the STSM-MARS and conventional PI-MARS control systems during motor startup, load surge, and speed surge scenarios. As illustrated in Figure 8, during motor startup, the speed error of the STSM-MARS control system proposed in this paper is 31 r/min, whereas the speed error of the conventional PI-MARS control system is 45 r/min. At 0.3 s, during the load surge of 20 N, the speed error of the STSM-MARS control system is \(-\)0.002 rad, while that of the conventional PI-MARS control system is \(-\)0.006 rad. Subsequently, at 0.5 s, during the speed surge, the speed error of the STSM-MARS control system amounts to 20 r/min, reaching a steady state at 26 r/min, whereas the conventional PI-MARS control system takes additional time to achieve a steady state, with a speed error of 26 r/min.