# Model Predictive Control for Six-Phase Induction Machines with Insight into Past Current Errors
## 5 Experimental Results
### Weighting Factor Influence  
Traditional FCS-MPC in multi-phase machines requires the appropriate tuning of one weighting factor for every secondary subspace. In the cost function presented in (7), the value of \(K_{xy}\) must be adjusted to accommodate two control goals: tracking the reference values of \(\alpha\)-\(\beta\) currents and lowering the production of \(x\)-\(y\) currents. On the other hand, the implementation of RAE-MPC requires the adjustment of an additional parameter, \(K_{acc}\). As the weighting factors of the cost function tend to be adjusted heuristically, the proposed method adds a new degree of complexity. In principle, RAE-MPC presents the disadvantage of requiring more tuning tests in order to achieve the optimal performance. To approximate the importance of this disadvantage, multiple tests have been performed, maintaining the operating point (\(f_{s}=20\) kHz, \(\omega=800\) rpm) but modifying the value of \(K_{xy}\) and \(K_{acc}\) in (11). Both parameters have been adjusted individually, meaning that the results for the study of \(K_{xy}\) are obtained with \(K_{acc}=0\), and vice versa.  
Figure 11: Current THD values obtained by standard MPC and RAE-MPC across different control frequencies (10, 12.5, and 20 kHz) and speeds (200, 500, and 800 rpm).  
With the objective of displaying the effects of these weighting factors on harmonic injection and current reference tracking in the primary subspace, Figure 12 is presented. The left graph of Figure 12 shows the evolution of THD, which is related to current production in the secondary subspaces. As it can be seen, both factors are inversely proportional to this quality index. While a value of 0.05 in \(K_{xy}\) produces a THD of 24.53 %, increasing it up to 2 reduces it to 16.54 %. Similarly, these values applied to \(K_{acc}\) obtain 17.11 % and 12.69 %, respectively. However, low harmonic injection is not desirable if it comes at the cost of a poor tracking of the references. In order to monitor this tracking, the Root Mean Squared Error between the reference and the measured currents in the primary subspace (\(RMSE_{\alpha\beta}\)) has been plotted on the right graph of Figure 12. Here, the opposite tendency is observed: increasing the priority of secondary control goals worsens the quality index. However, the two studied factors increase the error at notably different rates. Both start with an \(RMSE_{\alpha\beta}\) of approximately 0.21 A when each weighting factor has a value of 0.05, but once \(K_{xy}\) is increased up to 2, \(RMSE_{\alpha\beta}\) reaches 0.52 A. On the other hand, raising \(K_{acc}\) only increases \(RMSE_{\alpha\beta}\) up to 0.27 A.  
Two conclusions can be derived from this analysis. Firstly, \(K_{acc}\) is more impactful than \(K_{xy}\) in the pursuit of low harmonic injection. Secondly, \(K_{acc}\) is more stable than \(K_{xy}\) and, thus, easier to tune. Notably, an increment of 40 times the original value of the weighting factor introduced by RAE-MPC only amounts to an increase 0.06 A in tracking error, while \(K_{xy}\) produces 0.31 A. In summary, although RAE-MPC requires the tuning of one more weighting factor than FCS-MPC, adjusting its value is more straightforward than tuning the standard \(K_{xy}\). This is due to the wide range of values of \(K_{acc}\) that provide similar performance quality.