## 4 Simulation Study
Figure 5: Comparison of \(q\)-axis current simulations of two methods with current variations (0 A to 3 A) and with simultaneous resistance, inductance, and flux linkage mismatches (\(R_{0}=2R_{s}\), \(L_{0}=2L_{s}\), and \(\psi_{f0}=2\psi_{f}\)): (**a**) DPCC with normal integral sliding mode compensation combined with weight factors; (**b**) DPCC with weakened integral sliding mode compensation combined with weight factors. Figure 6: Comparison of \(q\)-axis current simulations of two methods with current variations (0 A to 3 A) and with simultaneous resistance, inductance, and flux linkage mismatches (\(R_{0}=0.75R_{s}\), \(L_{0}=0.75L_{s}\), and \(\psi_{f0}=0.75\psi_{f}\)): (**a**) DPCC with normal integral sliding mode compensation combined with weight factors; (**b**) DPCC with weakened integral sliding mode compensation combined with weight factors. with weight factors in which the rotational speed is 450 rpm and the load torque increases from 0 to 1 Nm at 0.2 s and decreases from 1 to 0 Nm at 0.4 s, and with single parameter mismatches. Figure 7 shows the case of resistance mismatch, and we can see from Figure 7a,c that when \(R_{0}=2R_{s}\), the \(q\)-axis feedback value is slightly larger than the reference current for DPCC, with an error of about 4.4% of the \(q\)-axis reference when loaded, and that when \(R_{0}=0.5R_{s}\), it is slightly smaller than the reference current, with an error of about 2.1% of the \(q\)-axis reference when loaded. From Figure 7b,d, it is evident that the method proposed in this article can remove steady-state errors. Figure 8 represents the case of inductance mismatch. Figure 8a shows that the \(dq\)-axis feedback current fluctuates widely for DPCC when \(L_{0}=2L_{s}\), and that the range of fluctuation is about 0.3 A, which is about 12.7% of the \(q\)-axis reference when loaded. Figure 8b shows that the \(dq\)-axis current fluctuates very little after being optimized and compensated, i.e., about 2.6% of the \(q\)-axis reference when loaded. When \(L_{0}=0.5L_{s}\), as is shown in Figure 8c, it has a large impact on the \(d\)-axis of the DPCC, and its steady-state error is about 0.13 A when loaded. The steady-state error can be eliminated with compensation, as is shown in Figure 8d. Figure 9 represents a flux linkage mismatch, and from Figure 9a,c, it is clear that for DPCC the \(q\)-axis feedback value exceeds the reference when \(\psi_{f0}=2\psi_{f}\), and that the error of both is about 35% of the \(q\)-axis reference when loaded, whereas the \(q\)-axis feedback value is less than the reference when \(\psi_{f0}=0.5\psi_{f}\), and the error of both is about 11.4% of the \(q\)-axis reference when loaded. From Figure 9b,d, it is clear that the error can be eliminated after compensation. Figure 7: Comparison of \(dq\)-axis current simulations of two methods at 450 rpm with resistance mismatch under torque variation (1 Nm): (**a,b**) \(R_{0}=2R_{s}\); (**c,d**) \(R_{0}=0.5R_{s}\); (**a,c**) DPCC; (**b,d**) DPCC with weakened integral sliding mode compensation combined with weight factors. Figure 10 and 11 represent comparisons of simulations about \(dq\)-axis currents between DPCC and DPCC optimized with weakened integral sliding mode compensation combined with weight factors under a rotational speed of 450 rpm and a load torque that increases  
Figure 8: Comparison of \(dq\)-axis current simulations of two methods at 450 rpm with torque variation (1 Nm) for inductance mismatch: (**a,b**) \(L_{0}=2L_{s}\); (**c,d**) \(L_{0}=0.5L_{s}\); (**a,c**) DPCC; (**b,d**) DPCC with weakened integral sliding mode compensation combined with weight factors. Figure 9: Comparison of \(dq\)-axis current simulations of two methods at 450 rpm with torque variation (1 Nm) for flux linkage mismatch. (**a,b**) \(\psi_{f0}=2\psi_{f}\); (**c,d**) \(\psi_{f0}=0.5\psi_{f}\); (**a,c**) DPCC; (**b,d**) DPCC with weakened integral sliding mode compensation combined with weight factors.