## 5 Experimental Study
Figure 11:1 Experimental comparison of \(dq\)-axis currents at 450 rpm with torque variation (0.2 to 0.5 to 0.2 Nm) and simultaneous resistance, inductance, and flux linkage mismatches (\(R_{0}=2R_{s}\), \(\psi_{f0}=2\psi_{f}\), and \(L_{0}=2L_{s}\)): (**a**) DPCC; (**b**) DPCC with weakened integral sliding mode compensation combined with weight factors. Figure 11:2 Experimental comparison of \(dq\)-axis currents at 450 rpm with torque variation (0.2 to 0.5 to 0.2 Nm) and 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. Figure 17 shows the \(dq\)-axis currents with no parameter mismatches. As is shown in Figure 17, a slight error is produced between the \(dq\)-axis feedback and the reference current under DPCC due to the nonlinear characteristics of the practical control system as well as the influence of delayed effects, such as the inverter. This causes the \(d\)-axis feedback current to shift in the negative direction after the load is increased to a certain degree at this speed, owing to the voltage limitation of the DC supply in the experiment. Figure 17 shows that the improved method under the same conditions can overcome the factors mentioned above and can eliminate the effects of external factors, thus eliminating errors. Figures 18-20 indicate the \(dq\)-axis currents under single motor parameter mismatches. Figure 18 represents a resistance mismatch, while Figure 18,c show that the \(q\)-axis feedback current increases modestly when the model resistance value becomes larger (\(R_{0}=2R_{s}\)) and drops slightly when the model value is smaller than the practical resistance value (\(R_{0}=0.5R_{s}\)). Figure 18,d show that the optimized method can compensate for the error. Figure 19 shows an inductance mismatch in which the fluctuation of the \(dq\)-axis feedback current under DPCC is clearly shown to increase when the model value is larger than the actual motor inductance value (\(L_{0}=1.4L_{s}\)), as in Figure 19, while the model of the optimized method is shown to attenuate the current fluctuation in Figure 11:3 In Figure 19, when the model inductance changes to a smaller value (\(L_{0}=0.5L_{s}\)), the fluctuation of the \(d\)-axis feedback current under the DPCC method increases slightly, within a range of approximately 0.17 A from the negative direction, and it affects the \(q\)-axis error. In Figure 19, the range of the negative direction of the \(d\)-axis feedback current under the optimized method is approximately 0.12 A, and this method reduces the \(dq\)-axis error. Figure 20 shows a situation in which there is a flux linkage mismatch, and Figure 20,c show that a huge deviation is caused between the \(q\)-axis feedback and the reference current when the model flux linkage is 2, which is 0.5 times the actual motor value. Figure 20,d show that the optimized method can compensate for the error and reduce system sensitivity to this parameter. Figures 21 and 22 represent the \(dq\)-axis currents for a case in which the three motor parameters are simultaneously mismatched. Figure 21 shows the \(dq\)-axis current under DPCC when the model values are changed to 2 times the practical parameters (\(L_{0}=2L_{s}\), \(\psi_{f0}=2\psi_{f}\), and \(R_{0}=2R_{s}\)) simultaneously, and it can be seen that the waveform is obviously fluctuating and generating a fairly big steady-state error. The optimized method in shown in Figure 21 can effectively reduce the fluctuations and compensate for the error under the same conditions. Figure 22 shows the \(dq\)-axis current under DPCC when the predictive model parameters are changed to 0.5 times their actual values (\(L_{0}=0.5L_{s}\), \(\psi_{f0}=0.5\psi_{f}\), and \(R_{0}=2R_{s}\)) simultaneously.