**3.2 Second scenario**

In this scenario we used the same simulation conditions of the first scenario, but the main deference consists in reducing the sampling period which is equal to 10 μs. In fact, when the control algorithm is implemented on software solutions like the


**Table 2.**

*Comparison between the both control strategies.*

*Robust Control Based on Input-Output Feedback Linearization for Induction Motor Drive… DOI: http://dx.doi.org/10.5772/intechopen.104645*

microcontrollers or the DSP, the sampling time increased due to the serial processing of these solutions, which consequently raises the control loop delay, the torque ripples and the stator current distortions. In order to overcome the limitations of these solutions in terms of execution time, the FPGA is proposed thanks to its parallel processing and short execution time. In order to show the effects of the execution time on the simulation results, a sampling period of 10 μs is chosen. The obtained results in this scenario demonstrate that when the sampling period decreases, the torque and the stator flux ripples, as well as the stator current harmonics, are reduced, as shown in **Tables 2** and **3**.

The IM starts with a reference speed equal to 100 rad/sec. At t = 1 sec, the reference speed falls slowly to reach 100 rad/sec at t = 2 sec. At t = 0.5 sec, a rated torque is applied.

**Figure 9** depicts the evolution of the rotor speed of the IM controlled by two control strategies. It can be noticed that the rotor speed converges to the reference speed for both control strategies. However, the suggested SVM-DTC-IOFL offers better performance in terms of ripples around the reference speed, as shown in **Figure 9(b)**. As given by **Figure 10(a)**, the proposed control strategy provides better performance in terms of ripples compared to the classical DTC (**Figure 10(b)**). **Figure 11** presents the three phase stator current consumed by the IM control by both control strategies. It can be seen that the suggested control strategy offers better performance in terms current distortions. In fact, for the proposed SVM-DTC-IOFL, the stator current has a smooth waveform (**Figure 11(a)**). **Figure 12** presents the evolution of the extremity of the stator flux vector in the Concordia reference. It can be noticed that when the motor is controlled by the classical DTC, the stator flux vector trajectory presents high deviations and ripples (as shown by **Figure 12(b)**). Contrariwise, in the case of the proposed SVM-DTC-IOFL a smooth circular trajectory is obtained as illustrated in **Figure 12(a)**. More details are given in **Table 3**.


### **Table 3.**

*Comparison between the both control strategies.*

**Figure 9.** *Speed response for: (a) proposed SVM-DTC-IOFL, (b) classical DTC.*

**Figure 10.**

*Torque response for: (a) proposed SVM-DTC-IOFL, (b) classical DTC.*

**Figure 11.** *Three phase stator current for: (a) proposed SVM-DTC-IOFL, (b) classical DTC.*

**Figure 12.** *Three phase stator flux for: (a) proposed SVM-DTC-IOFL, (b) classical DTC.*

### **3.3 Third scenario**

This section consists in testing the robustness of the proposed SVM-DTC-IOFL under stator resistance variations at a low speed region. In this study, the IM starts with a reference speed equal to 20 rad/sec. The sampling period is equal to 10 μs. At t = 4 sec, the stator resistance increases to reach 1.5 Rsn. **Figure 13**(**a**, **b**), presents the evolution of the rotor speed for both control strategies. As shown in **Figure 13(a)**, it can be seen that the suggested SVM-DTC-IOFL offers better performance with a small deviation when the stator resistance goes up.

**Figure 14**(**a**, **b**) illustrates the evolution of the stator flux module for both control strategies. Referring to **Figure 14(a)**, it can be noticed that when the stator resistance rises, the stator flux curve presents small deviations and then it converges quickly to its reference value. However, when the IM is controlled by the classical DTC, the actual stator flux diverges from its reference value due to the variation in the stator resistance.

*Robust Control Based on Input-Output Feedback Linearization for Induction Motor Drive… DOI: http://dx.doi.org/10.5772/intechopen.104645*

**Figure 13.** *Speed response for: (a) proposed SVM-DTC-IOFL, (b) classical DTC.*

**Figure 14.** *Speed response for: (a) proposed SVM-DTC-IOFL, (b) classical DTC.*
