## 3 Components Modeling of Proposed Design  
A BLDC motor, also known as a synchronous DC motor, consists of a permanent magnet rotor while the stator is wound. BLDC motors are used in EVs and HEVs due to their long lifetime, high efficiency, and low maintenance. BLDC motors can deliver greater torque as compared to other motors. Different types of motor show various qualities that can be used in EVs with a particular control mechanism to operate the motor [37]. In [38], the researchers verify the advantage and use of a BLDC motor and three-phase induction motor for EVs due to extreme fidelity, productivity, efficiency, reliability, and average acceleration. It has a permanent magnet for excitation and high flux density, which is responsible for giving the high efficiency. It also has advanced power density, high productivity, and a small size, which is why it is used for HEVs and EVs [39]. In [40], the BLDC motor is used for HEV application for restoring the braking energy into the battery. In this paper, two types of mechanisms were discussed for obtaining the rotor position by using the Hall sensor and the zero cross detection method. Since the BLDC motor has no carbon brushes, there is no issue of sparking which gives the motor more durability and a long life. It has a long life and the power-to-weight ratio is also high. This motor gives torque ripples at commutation and uses trapezoidal back electromotive force (EMF). A comparison between the PID controller and FLC for the speed controlling of different motors has been studied [41]. Comparison of different types of motors [37; 38] which are extensively used in EV application is shown in Table 1. The performance of the BLDC motor is also better than its other alternatives. The Hall sensor measures the angular speed and angular position. The angular position from the Hall sensor is used in the commutation logic circuit, which computes the switching pattern for the three-phase inverter. The following Equations (1)-(3) can be used for the calculation of three-phase terminal voltages of armature winding:  
\[V_{a}=\ Ri_{a}+L\frac{di_{a}}{dt} \tag{1}\]  
\[V_{b}=\ Ri_{b}+L\frac{di_{b}}{dt} \tag{2}\]  
\[V_{c}=\ Ri_{c}+L\frac{di_{c}}{dt} \tag{3}\]  
Figure 2: MATLAB simulation of overall proposed system. where \(L\) is the armature self-inductance, \(V_{a}\), \(V_{b}\), \(V_{c}\) are the three-phase terminal voltages, \(e_{a}\), \(e_{b}\), \(e_{c}\) are the three-phase motor's back emf, \(R\) is the armature resistance, and \(i_{a}\), \(i_{b}\), \(i_{c}\) are the three-phase motor's input current. The motor's back EMF three-phase voltages can be calculated by using Equations (4)-(6) respectively. \[e_{a}=\ K_{w}f(\theta_{e})\omega \tag{4}\]  
\[e_{b}=\ K_{w}f\bigg{(}\theta_{e}-\frac{2\pi}{3}\bigg{)}\omega \tag{5}\]  
\[e_{c}=\ K_{w}f\bigg{(}\theta_{e}+\frac{2\pi}{3}\bigg{)}\omega \tag{6}\]  
The relation between the electrical (\(\theta_{e}\)) and mechanical rotor (\(\theta_{m}\)) angle is shown in Equation (7), given below:  
\[\theta_{e}=\frac{p}{2}\theta_{m} \tag{7}\]  
where \(p\) represents the number of poles on the rotor, \(\theta_{e}\) is the electrical rotor angle, \(\theta_{m}\) is the mechanical rotor angle, and \(\omega\) is the angular speed of the motor. The total electromagnetic torque (\(T_{e}\)) for modeling the BLDC motor can be calculated using Equation (8). The Simulink model of the BLDC motor is shown in Figure 3.  
\[V_{a}=\ Ri_{a}+L\frac{di_{a}}{dt} \tag{1}\]0  
where, \(T_{e}\) represents the total electromagnetic torque of the motor, \(e\) is the back EMF of the motor, and \(i\) is the input current of the motor.