## 5 Experimental Evaluation
### Experiment Results and Discussion  
The initial speed is set to 100 rpm in the experiment, and the motor starts in the unloading condition. It continues to accelerate until reaching the reference speed. The reference speed is immediately increased to 200 and 400 rpm at 0.25 and 0.5 s, respectively; it is reduced back to 100 rpm at 0.75 s. Figure 13 shows the experimental results. According to the experimental results, it takes 0.05 s for the motor to reach steady-state speed with the MPC control method during low-speed operation. However, it takes a longer time to reach a steady state during medium to high-speed operatio  
Figure 12: Experimental platform of hardware. Figure 13: (**a**) Variation curve of rotational speed \(Nr\); (**b**) Variation curve of electromagnetic torque \(Te\); (**c**) Variation curve of stator magnetic flux linkage \(\psi s\). approximately 9.7%. When the speed drops sharply, the MPC method exhibits a waveform where the speed cannot be tracked for approximately 0.13 s. It then waits for an additional 0.06 s before re-tracking the reference speed. On the other hand, regardless of the speed stage of the motor, it can reach the reference speed within 0.02 s without any overshoot under the MPTC method. Therefore, the MPTC designed in the work demonstrates faster and better speed-tracking performance compared to the traditional MPC control method. The MPC exhibits lower torque switching in terms of the torque response during speed transitions. The MPTC shows larger torque values at each speed-switching point, and the difference between peak torque and speed switching is truly correlated. However, MPTC can recover reference torque more rapidly than the MPC when the local torque waveform is observed. Additionally, the steady-state torque fluctuation in the MPTC is significantly smaller than that using the MPC, with an average reduction in ripples of approximately 58.4%. As for the stator flux, both methods maintain stability. MPTC exhibits higher peaks at speed switching points, but they remain within the allowable range of the motor. The dynamic and steady-state characteristics of the MPTC are similar to torque characteristics. Therefore, the MPTC designed in the work demonstrates better steady-state torque performance compared to the traditional MPC. Given an initial reference speed of 400 rpm, the motor is started without loads until the reference speed is reached. The load torque of 2 Nm is applied to the PMSM at 0.25 s after a period of no-load operation, and the reverse torque of \(-\)2 Nm is immediately loaded at 0.5 s. Load torque is withdrawn at 0.75 s to observe the performance of the motor. Figure 14 shows the experimental results. The experimental results indicate that, when the load is suddenly increased, the motor speed decreases by a maximum of 157 rpm with the MPC; however, it only decreases by 78 rpm with the MPTC. When torque suddenly transits from load torque to dragging torque, the speed increases by 316 rpm with the MPC, whereas the MPTC method shows an increase of only 107 rpm. The MPC experiences a period of speed drop after torque is removed, which lasts until approximately 0.04 s before it continues to track the reference speed. On the other hand, the speed tracking of the MPTC is similar to the curve of the first  
Figure 14: (**a**) Variation curve of rotational speed _Nr_; (**b**) Variation curve of electromagnetic torque _Te_; (**c**) Variation curve of stator magnetic flux linkage \(\psi\)s.  
sudden increase in torque. Therefore, the MPTC designed in the work exhibits stronger resistance to load disturbances compared to the traditional MPC. Although the MPC does not exhibit high peak torque from the torque-response perspective, it shows approximately 12% overshoot when torque is tracked during the load application. When torque reverses, the MPC maintains zero torque for approximately 0.2 s, which rapidly increases the speed. Approximate 0.07 s are taken for the MPC to track back to load torque. The same situation occurs when load torque is removed.