# DDC Control Techniques for Three-Phase BLDC Motor Position Control
## 2 System Modelling and Preliminaries  
### General Theory of BLDC Motor  
In this section, the general description of a brushless DC motor is given, followed by the concept of controlling a brushless DC motor. There are two major parts of a brushless DC motor, namely the rotor and the stator, as shown in Figure 1. The inner part is named as the stator and outer circular part is called the rotor. The rotor has permanent magnets and the stator consists of three electromagnets. These electromagnets have different polarity due to alternating current. That is why it is called the three-phase rotor. Usually, there is a 120-phase difference between the three electromagnets. Figure 1 shows the phenomenon of rotation of the rotor in a clockwise direction, whereas the polarity of the electromagnets keeps changing. In order to turn the rotor with a constant speed, the polarities are changed at a constant frequency. A careful look shows that a single electrical rotation \(\theta_{e,r}\) causes a half-mechanical rotation \(\theta_{\text{m},r}\). It is determined based on the number of poles, as specified in the following Equation (1). \[\theta_{\text{m},r}=\frac{2}{number\ of\ poles}\times\theta_{e,r} \tag{1}\]  
The motor under consideration consists of 14 poles. Hence, one electrical rotation is equal to one seventh of a mechanical rotation. In Figure 2, only low and high signals are shown, which means that each electrical rotation consists of six steps. By using Pulse Width Modulation (PWM) signals, the number of steps can be increased. A PWM signal value varies from 0 to 255. Using these signal values, voltage can be sent from zero percent to hundred percent as depicted in the Figure 2.  
These basic concepts of a BLDC motor help to understand the control structure. The alternating electromagnets producing a rotating space vector. This vector is calculated by following the method proposed as follows. This method reduces the computational time. Figure 3 shows that one electrical rotation is equal to six parts, where A, B, and C are voltage vectors. If both B and C are zero, and voltage A has a value of 255, the resultant vector points in the direction of A. In order to operate in an area, the maximum PWM value is assigned to voltage A, while C is turned off and B can be varied. Table 1 shows the phases used to operate in a particular area. This method shows that every electrical rotation is divided into six parts, and every part can be further divided into 255 steps. Therefore, every electrical rotation consists of 1524 steps (eliminating double scenarios). Hence, a mechanical rotation consists of approximately 10.660 steps. Each step covers nearly 0.03 mechanical degrees. Figure 1: Schematic of the operation of a brushless direct current (DC) motor. Figure 2: Visualization of a PWM signal having 255 steps to rotate a DC motor to 360 electrical degrees. Table 1 shows the PWM values used to determine the area of the vector in Figure 3, where X means \"to be calculated\". With the knowledge of the operating area, the exact value of PWM can be calculated for a certain resultant vector. Note that for each operating area in Equations (2)-(7), the PWM value in the second part of the equation is at its maximum value of 255, but this is left out to make the equations universal.