# Simulation Study of Two Torque Optimization Methods for Direct Torque-Controlled Induction Motors
## 3 Simulation Results and Discussion  
A Matlab/Simulink simulation package is utilized to simulate the IM speed-controlled drive with the conventional DTC and the two proposed methods. The drive system has an IM of a nameplate and circuit parameters shown in Table 1. Usually, the reference stator flux is the rated value of the IM, which is pre-calculated from the IM parameters. The speed controller is a simple Proportional Integral (PI) that is tuned using Nicola-Ziglar methodology. Figure 3 shows how the speed controller produces the reference torque for the system according to the speed error--as the reference values of the stator flux and torque are determined, the DTC algorithm starts. During this research, we compare three DTC algorithms, the conventional DTC, the proposed optimization Method (1), and the proposed optimization Method (2). The hysteresis tolerances of the flux and torque are 5% and 8%, respectively. A simulation for proposed system with optimization Method (2) was conducted to compare with the results of optimization Method (1). The simulation results indicate the same improvement in the transient performance as that of Method (1), but with perfect identification of the motor parameters. The simulation was conducted assuming that the motor parameters were constants during operation. When there was incorrect identification or parameter changes, Method (1) performance deteriorated while the performance of Method (2), which did not have parameters, remained unchanged. The torque step response of Method (2) and Method (1) compared to the conventional DTC is shown in Figure 5. It is noted that the response of Method (2) is similar to that of Method (1), except near the full load torque. This may be due to the approximations made in Equation (13). Method (2) possesses a significant advantage over Method (1) since Method (2) does not have any motor parameters except for \(R_{\mathrm{s}}\). The drive system gives the same performance and simulation results with Method (1) as with Method (2). The simulation results for Method (2) are typically the same as the results obtained with Method (1). These results have been omitted to avoid repetition. The speed step responses of the conventional DTC compared to proposed Method (1), are shown in Figure 6. The reference speed is 25% of the rated speed at full load conditions. It is concluded \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**IM Rating** & \multicolumn{4}{c}{**IM Equivalent Circuit Parameters**} \\ \hline
10 KW, 6 pole, 220V, 60 Hz & \(R_{s}\) = 0.294 \(\Omega\) & \(L_{m}\) = 0.041 H & \(L_{s}\) = 0.0424 H & \(\lambda_{s}\) = 0.454 Wb \\ \hline  & \(R_{r}\) = 0.156 \(\Omega\) & \(L_{r}\) = 0.0417 H & \(J\) = 0.4 kgm\({}^{2}\) & \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System Parameters. Figure 5: The step torque response of the proposed methods with the conventional DTC; at no load. from Figure 6 that the speed response of Method (1) is better than the traditional response due to a lower settling time (12% improvement). Figure 7 compares the tip trace of the stator flux vector of the traditional DTC and that of proposed optimization Method (1). The stator flux trace of Method (1) is better than the trace of the traditional DTC. Using the method of the least squares, the error in the stator flux value for the traditional DTC is greater than the error with Method (1) by 9%. Hence, proposed Method (1) has a better stator flux response, at steady-state, than the conventional DTC. Figure 8 shows the effect of changing the controller sampling period on the inverter switching frequency of proposed Method (1) at different operating speeds and full load conditions. It is clear that, as the sampling frequency increases, the switching frequency increases. However, the traditional DTC has a variable frequency. Its average value at full load conditions was nearly 200% of proposed Method (1). Hence, the switching losses and system efficiency of the proposed systems are better than the traditional DTC.