# Induction Machine-Based EV Vector Control Model Using Mamdani Fuzzy Logic Controller
## 4 Discussion  
The P-I speed controller and proposed fuzzy MFLC controller's performance to track reference speed is compared in \"Figures 12 and 13\". This shows variation in the three-phase current, rotor speed, and torque from rest to small, medium, and high-speed transitions for the time duration (8 s). First and foremost, a speed transition of 40 km/h was applied at a time of 0 s in both figures. Following, the second transition of 60 km/h was applied at times of 2.0 s and 1.0 s, respectively. A final speed transition of 80 km/h was applied at times of 4.0 s and 2.0 s, respectively. As it can be concluded that while the P-I speed controller produces higher control effort and steady-state error, the fuzzy MFLC generates a lower control effort and steady-state error, which enriches its performance. Figure 11: Mamdani fuzzy logic controller Simulink environment: (**a**) fuzzy logic designer; (**b**) input membership function; (**c**) output membership function; (**d**) rule viewer; and (**e**) output surface of MFLC. Figure 12: Overall P–I speed controller performance comparison (0–40, 40–60, 60–80) representing the induction machine application in the EV model for different speed modes to compare its effects on torque, current, and voltage, respectively. Tables 2-4 summarize the performance parameters of P-I and the proposed fuzzy MFLC speed controller for predefined speed transitions. Time-domain factors such as the rise time, settling time peak time, and overshoot are compared for both controllers. In terms of reference speed tracking, both controllers track the reference speed. However, after critically watching the pattern of waveforms, the proposed Mamdani-FLC controller was much better than the P-I controller with higher accuracy, zero overshoot, and negligible steady-state error. The response time of the P-I controller and Mamdani-FLC for a speed transition 40 km/h was: 1.6 s and 0.7 s; for a speed transition of 60 km/h was: 1.3 s and 0.7 s; and for a speed transition of 80 km/h was: 1.2 s and 1.1 s, respectively. The total response time taken by the P-I speed controller was 4.1 s as compared to Mamdani-FLC which is 2.5 s. Hence, a fuzzy MFLC controller requires a lesser settling time compared to a P-I controller. The overshoot for the P-I controller is observed as 14%, 7%, and 5% for small, medium, and large speed transitions. The Mamdani-FLC completely removes the overshoot which indicates the suitability of a later model for speed control application in EVs. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Speed Controller Type** & **Rise Time (\(T_{r}\))** & **Settling Time (\(T_{s}\))** & **Peak Time** & **Overshoot Percentage** \\ \hline P-I controller & 0.25 s & 1.6 s & 0.55 s & 14 \\ Mamdani FLC & 0.5 s & 0.7 s & 0.7 s & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Performance comparison between P-I controller and Mamdani fuzzy logic controller (low-speed transition). Figure 13: Overall MFLC speed controller performance comparison (0–40, 40–60, 60–80) representing the induction machine application in the EV model for different speed modes, respectively, to compare its effects on torque, current, and voltage, respectively. Figure 13 displays the superior performance of the fuzzy MFLC controller for a speed transition of 40 km/h. The waveform shows a convergence of speed as per the agreed speed transition. Moreover, it reaches a step-change in speed within minimum time and tracks the reference speed via the fuzzy closed-loop feedback control system. This further indicates the speed controller performance for a speed transition of 60 km/h. Finally, a speed transition of 80 km/h was observed for the high-speed operation of EV. The fuzzy MFLC model was tested for multiple speed scenarios for understanding driving requirements. From rest to motion torque of IM reaches the highest value of 300 N.m initially but it drops to the minimum value as reference speed is achieved. The three-phase current follows the torque trend.