## 3 The Proposed PI-Tuned Speed Controller  
The model under consideration is based on a Li-ion DC battery with the scope to check the performance of the supply voltage. DC voltage is converted into a three-phase AC supply by using an IGBT inverter. The IGBT inverter gate pulses are fed by the speed control loop of the vector control. The output of the IGBT inverter is applied to IM to the drive for the applied speed commands. The output of the IM speed control model is measured to analyze the performance of the EV. The proposed multimodal EV is applicable for the desired speed modes, based on the current situation and road signals, to ensure a smooth and efficient drive. The user-defined speed mode works as a reference for the speed controller, and after the control action of the PI controller, the gate pulses for inverter operation are generated. The battery is initially charged at 770 V, while temperature and aging effects (due to the battery's lifecycle) are not considered. In terms of indirect vector control, two current components are used to change the value of flux and torque, as per the speed command. Figure 2 presents a block diagram of P-I controller-based indirect vector control. The required angle \(\theta_{\mathrm{e}}\) is calculated using the vector control currents \(\mathrm{i}_{\mathrm{qs}}^{*}\) and \(\mathrm{i}_{\mathrm{ds}}^{*}\), further transformed from a synchronously rotating frame to a stationary vector frame with the help of angle \(\theta_{\mathrm{e}}\), and produced from the flux value. Stationary vector frame current signals are converted into phase current signals to compare the measured phase currents and generate gating pulses for the IGBT inverter. The gate pulses are used to get a 3-phase supply from an IGBT-based inverter, fed by a Li-ion DC battery. The inverter-based supply is directly fed to an IM for suitable output. The input and output parameters are displayed to analyze model performance for the various speed modes (40, 60, and 80 km/h). The model operation starts with a user-defined reference speed to implement an automatic car model. Reference speed and torque are applied as separate inputs to IM, using a manually operated switch block. The respective reference speeds of 40, 60, and 80 km/h, with torque at (0 and 100 N m), are applied on IM. These three-speed modes are defined to summarize the model's behavior for user-defined drive patterns. IM speed \(\omega\) is compared with the reference speed provided by the user \(\omega^{*}\) for the tuning of FM-PI  
Figure 2: An indirect vector controller, based on a P-I controller and the hysteresis band current regulator. controller gains. Feedback on measured speed is continuously monitored for closed-loop control action. A discrete (P-I) controller processes (as a speed difference) an error signal without automatic tuning, followed by a saturator to maintain the torque command \(\mathrm{T_{e}^{*}}\) within an upper and lower limit, as shown in Figure 3. The role of the speed controller is to monitor the speed at a steady state as well as for transients. The gain of the P-I controllers is tuned to achieve an optimum damping ratio (less than unity), kept at \(\mathrm{K_{p}}\) = 15 and \(\mathrm{K_{i}}\) = 30 for a maximum upper torque limit of 300 N m.  
The stator direct-axis current \(\mathrm{i_{ds}}\) forming the rotor flux and torque is directly linked to the quadrature-axis current, \(\mathrm{i_{qs}}\), whereas the reference quadrature axis current \(\mathrm{i_{qs}^{*}}\) is computed from the reference torque \(\mathrm{T_{e}^{*}}\) as an input variable in Equation (3), while \(\left|\Psi\mathrm{r}\right|_{\mathrm{est}}\) and \(\mathrm{T_{r}}\) are calculated from Equations (4) and (5), respectively.