# Model Predictive Control for Six-Phase Induction Machines with Insight into Past Current Errors
## 5 Experimental Results
### Experimental Tests  
The present section details the experimental tests carried out to demonstrate the suitable performance of the RAE-MPC when compared to an MPC based on the use of \(V_{l}\) vectors as active control actions. The improvements are presented in two manners. On the one hand, diverse quality indices are employed to compare both control solutions, such as the total harmonic distortion (THD) of phase currents, peak-to-peak currents in the secondary subspace (\(I_{xy}^{p2p}\)), the maximum squared error of the currents in the secondary subspace multiplied by its weighting factor (\(e_{xy}^{2 max}\)), and the obtained switching frequency (\(f_{sw}\)). These indices have been calculated for different operating points and sampling frequencies (\(f_{s}\)) in an effort to demonstrate the flexibility of the proposed method. On the other hand, the tracking of the different control variables are depicted. Its objective is to present visual proof of the enhanced performance provided by the RAE-MPC. Furthermore, since the proposed method requires the tuning of a new weighting factor, a study on the complexity of this adjustment has been performed. With the intention of obtaining the quality indices used to compare the MPC and the proposed RAE-MPC, tests have been performed at two different mechanical speeds (500 and 800 rpm) and two sampling frequencies (10 kHz in Table 2 and 20 kHz in Table 3). The improvements achieved by the presented method can be observed from various perspectives. First of all, RAE-MPC displays significantly lower values of THD in all speeds and values of \(f_{s}\). In the case of \(f_{s}=10\) kHz, current THD diminishes from 37.67% to 26.63% for a relative improvement of \(-29.31\%\) at 500 rpm, whereas at higher speeds (800 rpm) THD drops from 30.62% to 22.64%, a relative reduction of 26.06%. This enhancement in performance is also present at \(f_{s}=20\) kHz, where the relative reduction in harmonic content is 26.20% at 500 rpm and a remarkable 35.69% at 800 rpm. The improvement in the current harmonic content can be explained by the different performance of the MPC and RAE-MPC in controlling the secondary subspace. By observ \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & & **Value** \\ \hline \(V_{dc}\) (V) & dc-link voltage & 300 \\ \(T_{rated}\) (Nm) & Rated torque & 8 \\ \(R_{s}\) (\(\Omega\)) & stator resistance & 4.20 \\ \(R_{r}\) (\(\Omega\)) & Rotor resistance & 3 \\ \(L_{m}\) (mH) & Mutual inductance & 370 \\ \(L_{l_{8}}\) (mH) & stator leakage inductance & 4.5 \\ \(L_{l_{l}}\) (mH) & Rotor leakage inductance & 55.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Six-phase IM drive parameters. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \(\omega\) (**rpm**) & **Method** & **THD (\%)** & \(I_{xy}^{p2p}\) (**A**) & \(e_{xy}^{2 max}\) (**A\({}^{2}\)**) & \(f_{sw}\) (kHz) \\ \hline
500 & MPC & 37.67 & 4.34 & 4.36 & 2.79 \\
500 & RAE & 26.63 & 3.29 & 0.57 & 2.94 \\ \hline
800 & MPC & 30.62 & 4.62 & 6.60 & 2.34 \\
800 & RAE & 22.64 & 3.40 & 0.58 & 2.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Quality indices in a range for \(f_{s}=10\) kHz. \begin{table}
\begin{tabular}{l l l l l l} \hline \hline \(\omega\) (**rpm**) & **Method** & **THD (\%)** & \(I_{xy}^{p2p}\) (**A**) & \(e_{xy}^{2 max}\) (**A\({}^{2}\)**) & \(f_{sw}\) (kHz) \\ \hline
500 & MPC & 26.76 & 3.39 & 2.09 & 5.65 \\
500 & RAE & 19.75 & 2.24 & 0.27 & 5.94 \\ \hline
800 & MPC & 21.66 & 3.49 & 4.98 & 4.43 \\
800 & RAE & 15.11 & 2.42 & 0.27 & 4.38 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Quality indices in a range for \(f_{s}=20\) kHz. ing \(I_{xy}^{p2p}\) values, it is clear that the proposed method is successful at reducing peak currents when \(f_{s}=10\) kHz (going from 4.34 A to 3.29 A at 500 rpm and from 4.62 A to 3.40 A at 800 rpm) and also \(f_{s}=20\) kHz (going from 3.39 A to 2.24 A at 500 rpm and from 3.49 A to 2.42 A at 800 rpm). In all cases, a reduction of more than 24% is achieved, thus leading to lower copper losses.