# Model Predictive Control for Six-Phase Induction Machines with Insight into Past Current Errors
## 5 Experimental Results
### Experimental Tests
At a lower sampling frequency, RAE-MPC reduces by 7.65 times the value of the maximum squared current error measured at 500 rpm and by 11.38 times at 800 rpm. In the case of \(f_{s}=20\) kHz, this quality index is 7.74 times smaller at 500 rpm and 18.44 at 800 rpm. It must be noted that the achieved reduction in currents in the secondary plane does not come from increasing the number of switching states applied per control period, but from the correct minimization of the accumulative error. The tests performed at a sampling frequency of 20 kHz are illustrated in Figure 9 (500 rpm) and Figure 10 (800 rpm). Figure 9: Speed (**a**), \(\alpha\)-\(\beta\) currents (**b**), \(\alpha\)-\(\beta\) squared errors (**c**), \(x\)-\(y\) currents (**d**), \(x\)-\(y\) squared errors multiplied by their weighting factor (**e**), and phase currents (**f**) when \(f_{s}=20\) kHz and \(\omega=500\) rpm. In both cases, it can be appreciated how the reference values of speed (Figures 9a and 10a) and currents in the primary subspace (Figures 9b and 10b) are correctly followed by the two compared methods. As a consequence of the adequate tracking in the primary plane, its squared error (Figures 9c and 10c) is small in all the studied cases. However, different behavior is observed when studying the currents in the secondary plane (Figures 9d and 10d) and its squared error (Figures 9e and 10e). The accumulated error through time, manifesting in notable peaks present during the whole test at both speeds, is clearly compensated when using RAE-MPC. Furthermore, the graphs in both Figures 9e and 10e complement the information given by the quality index \(e_{xy}^{2 max}\). It is noticeable how considering the accumulated error in the cost function not only reduces the peak value registered of these errors, but it also diminishes the errors during the whole test, which translates into less distorted phase currents (Figures 9f and 10f). Once again, it should be noted that this improvement is achieved without compromising the tracking of primary currents, which  
Figure 10: Speed (**a**), \(\alpha\)-\(\beta\) currents (**b**), \(\alpha\)-\(\beta\) squared errors (**c**), \(x\)-\(y\) currents (**d**), \(x\)-\(y\) squared errors multiplied by their weighting factor (**e**), and phase currents (**f**) when \(f_{s}=20\) kHz and \(\omega=800\) rpm. is an attainment that cannot be accomplished by increasing the value of \(K_{xy}\) in standard FCS-MPC. Since the primary objective of including the accumulated error in the cost function is to enhance current quality, the study of current THD has been extended in Figure 11. The values of this quality index are presented for both MPC and RAE-MPC at three different speeds and control frequencies, with the proposed method displaying lower current distortion in all the tested conditions. A possible disadvantage to the proposed method is the increase in computational effort. The time that the microcontroller requires to perform all the operations that form the regulation scheme set a hard limit to the achievable control frequency. However, it should be remarked that RAE-MPC only requires the inclusion of low-cost mathematical operations. By experimentally measuring the benchmark FCS-MPC approach time in the test rig, the algorithm requires 28 \(\upmu\)s, while the proposed RAE-MPC needs 32 \(\upmu\)s. This increase, although measurable, can be considered acceptable when compared to the benefits that the proposed scheme provides. In summary, the performance shown by RAE-MPC at various sampling frequencies and points of operation demonstrates the value of compensating the accumulated current errors. While traditional FCS-MPC targets only the sum of all errors, the proposed method achieves significantly lower harmonic distortion and copper losses by including in the cost function a term that reflects the past evolution of the individual components.