## 5 Simulation Approach and Considerations
### Interpretation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & & \multicolumn{4}{c}{**GA-DTC**} & \multicolumn{2}{c}{**Classic DTC**} & \multicolumn{2}{c}{**Improvement (\%)**} \\ \hline  & **Characteristics** & **ITAE** & **IAE** & **ISE** & **Weighted** & **-** & **Classic DTC/Weighted GA-DTC** \\ \hline  & Response Time (ms) & 24.2 & 24.2 & 24.2 & 24.2 & 40.2 & 39.8 \\ \cline{2-7} \multirow{2}{*}{\(\omega\)} & Overshoot (rad/s) & 1.37 & 0.35 & 0 & 0 & 6.13 & 100 \\ \cline{2-7}  & Rejection Time (ms) & 1.04 & 1 & 30 & 1 & 1.17 & 14.53 \\ \cline{2-7}  & Undershoot (rad/s) & 3.6 & 3.9 & 3.5 & 3 & 3.2 & 6.25 \\ \hline  & Response Time (ms) & 0.76 & 0.75 & 0.71 & 0.68 & 0.69 & 1.45 \\ \cline{2-7} \multirow{2}{*}{\(\mathrm{T}_{\mathrm{em}}\)} & Overshoot (Nm) & 4.035 & 3.265 & 2.967 & 3.26 & 3.809 & 14.41 \\ \cline{2-7}  & Ripples (Nm) & 2.914 & 2.87 & 2.739 & 2.59 & 3.591 & 27.88 \\ \hline \(\overline{\mathrm{\mathrm{\mathrm{\mathrm{\Psi}}}_{\mathrm{s}}}}\) & Ripples (wb) & 0.0716 & 0.0715 & 0.0713 & 0.0617 & 0.0727 & 15.13 \\ \hline \(\overline{\mathrm{\mathrm{\mathrm{\Psi}}_{\mathrm{r}}}}\) & Ripples (wb) & 0.0159 & 0.0158 & 0.0156 & 0.0153 & 0.016 & 4.375 \\ \hline \(\mathrm{i}_{\mathrm{sa}}\) & THD (\%) & 6.21 & 6.74 & 5.8 & 5.6 & 8.29 & 32.45 \\ \hline \(\mathrm{I}_{\mathrm{ra}}\) & THD (\%) & 3.14 & 2.28 & 2.35 & 2.21 & 7.62 & 71 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Performance measures ofclassic DTC and GA-DTC. posed strategies. However, the GA-DTC control function with ISE and with a combination of objective functions allowed for perfect tracking, with a reduction in significant ripples compared to the conventional CDC approach and compared to other objective functions, which showed improvements of 27.88% (3.591 Nm in the case of the conventional CDC control and 2.59 Nm in the case of the weighted AG-CDC control), so it can be said that the ISE and weighted approaches present a tracking of the reference setpoint without any underruns, as is shown in the conventional CDC approach. On the other hand, the torque behaviors at the start and at the sudden changes of speed were similar for all the control strategies, which is normal, because it is difficult or impossible to have a control that allows to completely cancel the call to the currents during the moments mentioned above. However, they are limited through a saturation block, which is the torque band that is chosen between \(+15\) Nm and \(-15\) Nm in order not to exceed the recommended starting torque. Using a weighted combination, the stator and rotor flux waveforms for the proposed AG-CDC controls are demonstrated in Figures 6b-10b. The combined objective functions exhibited a good dynamic range, and the latter resulted in a reduction of the stator and rotor ripples by 15.13% and 4.375%, respectively (0.0727 Wb and 0.016 Wb, respectively, in terms of the conventional CDC control, and 0.0617 Wb and 0.0153 Wb, respectively, in terms of the weighted AG-CDC control). Because of these characteristics, the AG is well-suited for high-performance applications. Figures 6c,d-10c,d, illustrate the stator and rotor currents that are sinusoidal, with variable harmonics as a function of load variation, as well as the impact of the optimal gains of each strategy, using the weighted and separated objective functions. However, what interests us is the harmonic spectral analysis of the currents to measure the rate of harmonic distortion. It is well-known that the rates of THDs are the image of the torque ripples. With a high rate, further ripples would be created from the torque and vice versa. It can be observed in Figures 6e,f-10e,f that the THD of the strategy with the weighted objective functions, compared to the separate objective functions as is illustrated on the figures, allowed a reduction of the THD of 32.45% and 71% for the stator and rotor currents, respectively, (8.29% and 7.62%, respectively, in terms of the conventional CDC control, and 5.6% and 2.21%, respectively, in terms of the weighted AG-CDC control).