## 4 Experimental Verification
### Experimental Results with Rotor Speed Change  
The experimental results of the approach in [14] and the proposed 2 DOF IMC ADO method under a 2 N \(\cdot\) m load are presented, where the rotor speed step commands are 200 r/min, 500 r/min and 750 r/min, respectively. Figure 6 shows the comparative results of the \(dq0\)-axes currents, and Figure 7 shows the measured rotor speed, total torque and A-phase current of the two methods, where \(i_{d}^{*},i_{q}^{*},i_{0}^{*}\) are the reference current of \(i  
When the reference rotor speed steps from 200 rpm to 500 rpm at 0.86 s, the regulation time of [PERSON]'s method is 0.4 s (\(d\)-axis), 0.1s (\(q\)-axis) and 0.02 s (0-axis), respectively, as shown in Figure 5(a). However, it is improved to 0.2 s (\(d\)-axis), 0.06 s (\(q\)-axis) and 0.01 s (0-axis) by using the proposed method, as shown in Figure 5(b). When the reference rotor speed steps from 500 rpm to 750 rpm at 2.86 s, compared with [PERSON]'s method, the same conclusion can be drawn that the proposed 2 DOF IMC ADO method has a better dynamic response speed. In addition, it can also be observed from Figure 6 that, with the increase in the reference rotor speed, the d-axis current fluctuation becomes large. For the method in [14], the maximum overshoot and fluctuation of the d-axis current are up to 1.4 A  
Figure 6: Experimental results of the \(dq0\)-axes current when the speed changes. (**a**) Method in [14]. (**b**) 2 DOF IMC ADO method. Figure 7: Experimental results of the rotor speed, total torque and phase current when the speed changes. (**a**) Method in [14]. (**b**) 2 DOF IMC ADO method. and 1.6 A, respectively. By contrast, the smaller maximum overshoot and fluctuation of the \(d\)-axis current based on the proposed method can be observed in Figure 6b, which is only 1 A and 1.5 A. Furthermore, under the steady-state condition, it is clear that the 2 DOF IMC ADO scheme results in an improvement in tracking the performance of the \(dq0\)-axes current (Figure 6). This is because the SRM's non-linearity and coupling characteristic between different axes can be fully considered in the proposed 2 DOF IMC ADO method. Additionally, the introduction of the SRM model can also provide a quick response capability for the proposed method, which is not commonly found in the method in [14]. Due to the quick current response and good tracking capability of the proposed method, better torque ripple minimization performance can be also seen in Figure 7. As Figure 7 reveals, when the command speed changes at 0.86 s, the \(T_{e}\) regulation time of [PERSON]'s method is 0.3 s, and a large torque ripple up to 8.5 N \(\cdot\) m can be observed. However, under the same parameters of the speed-loop controller, the torque regulation time of the proposed method is only 0.2 s, and the torque ripple is reduced. After 2.85 s, the output torque has a shorter regulation time than the method in [14], and the good torque ripple suppressed performance is presented in Figure 7b. To further evaluate the torque ripple, a quantitative analysis is applied by introducing the percentages of the torque ripple \(T_{r}\). The \(T_{r}\) can be obtained by:  
\[T_{r}=\frac{T_{max}-T_{min}}{T_{avg}}\times 100\% \tag{33}\]  
where the \(T_{max}\), \(T_{min}\), \(T_{avg}\) are the maximum value, minimal value and average value of total torque in one electric angle period. The torque ripple percentages \(T_{r}\) of both methods are summarized in Table 2.  
The \(T_{r}\) findings in Table 2 show that, compared with the technique in [14], the torque ripple percentages of the suggested method are lower, decreasing by 4.9%, 10.35% and 6.7%, respectively. The results indicate that better \(dq0\)-axes current tracking performance brings a smoother output torque, which is consistent with (6). Based on the experimental results and analysis above, it can be found that, by using the proposed method, the dynamic and steady-state performance of the \(dq0\)-axes current controllers are improved at the different operating speeds.