Brushless DC motors (bldcm) replace conventional mechanical commutators with electronic commutators, relying on position signals to control the electronic commutators. Position signals play a very important role in the normal operation of the entire system, directly affecting whether the motor can commutate normally and whether it can reach maximum output. Currently, there are various detection elements for detecting the rotor position of permanent magnet motors[1][2][3], including electromagnetic, photoelectric, magnetic, and proximity switch types, among which the most commonly used are rotary transformers, photoelectric encoders, magnetic encoders, and Hall elements[4][5]. However, regardless of the type of position sensor, there are some drawbacks. First, position sensors are difficult to install in the limited internal space of the motor and are difficult to maintain; second, installing position sensors increases the size and cost of the motor; at the same time, it increases the inertia of the shaft; the number of system wiring increases, reducing the system's anti-interference ability; in some high-temperature, vibration, or highly corrosive environments, position sensors will reduce the reliability of the system or may not be able to be installed at all. [align=center] Figure 1 Back EMF zero-crossing point and commutation time diagram[/align] The sensorless method does not directly detect the rotor position, but indirectly obtains the rotor position by processing the physical quantities such as the motor flux linkage, current and voltage. The sensorless control technology of BLDCM has emerged rapidly and has become the future development trend of BLDCM control. Especially under small and light load starting conditions, sensorless brushless DC motors have become an ideal choice and have broad development prospects. The key technology of sensorless control of BLDCM lies in the method of obtaining and estimating rotor position information. In recent years, the positionless detection methods introduced in domestic and foreign literature mainly include the back EMF zero-crossing point detection method, the back EMF third harmonic integral detection method, the freewheeling diode monitoring method, the back EMF integral method, the flux linkage estimation method, the extended Kalman filter method, the inductance measurement method, the current method, the eddy current effect detection method, etc. [6][7][8][9]. This paper discusses the commutation strategy and starting control scheme of the sensorless BLDCM system that uses the back EMF zero-crossing point to detect the rotor position, and conducts simulation research. The back EMF zero-crossing method for rotor position detection (bldcm) generally uses a concentrated stator winding to obtain a good trapezoidal back EMF. This back EMF has two zero-crossing points within one cycle, and each zero-crossing point leads the next commutation point by 30° electrical angle. As long as the zero-crossing point of the back EMF can be detected, the position of the motor rotor and the time of the next commutation can be determined. This is the basic principle of the back EMF zero-crossing detection method. It can be seen that detecting the back EMF of the open-circuit phase (as shown in Figure 2, phase u) can obtain the appropriate commutation time of the stator winding. [align=center] Figure 2 Schematic diagram of terminal voltage back EMF zero-crossing detection[/align] However, the back EMF of the stator winding is difficult to detect directly. In practical applications, alternative methods are usually used to detect the back EMF zero-crossing point. The "phase voltage method" and the "terminal voltage method" are used, that is, the zero-crossing point information of the back EMF is indirectly obtained by measuring the phase voltage or terminal voltage. In Figure 2, the stator windings are fed by phases v and w, and phase u is an open circuit phase. Its phase voltage vun is equal to the back EMF eu of phase u. Therefore, as long as the phase voltage zero-crossing point of phase u is detected, the zero-crossing point of the back EMF of phase u can be obtained. This is the so-called "phase voltage method". However, measuring phase voltage requires the motor to have its center line drawn, which is quite limited in practice [10]. Assuming that the impedances of the three phase windings of the stator are equal, i.e.: zu=zv=zw=z (1) Then the potential of the center point n is: Therefore, as long as the zero-crossing time of vx-vs/2 is measured, the zero-crossing time of eu can be obtained indirectly. This is the "terminal voltage method". Similarly, another zero-crossing point of eu and all zero-crossing points of ev and ew can be obtained. The "terminal voltage method" requires the motor to have its center line drawn. It is simple and flexible. However, the motor terminal voltage signal not only contains the back EMF signal of the motor, but also contains the chopping signal. The chopping signal will seriously interfere with the back EMF waveform, making the zero-crossing point unclear. Therefore, a suitable low-pass filter must be selected for filtering. The actual position detection signal is obtained after RC filtering. Its zero-crossing point will inevitably produce a phase shift, making the position detection inaccurate. Appropriate phase correction must be performed in the application. The back EMF zero-crossing point detection method will produce a certain error when the motor is stationary or running at low speed. It is generally used for speeds above 10% of the rated speed. When the speed is below this, other detection measures need to be adopted [11]. In this paper, the "terminal voltage method" is used to obtain the back EMF zero-crossing point. Commutation strategy without position sensor In the BLDCM control without position sensor, the rotor position is detected by the back EMF zero-crossing point method. Therefore, when controlling the motor commutation, the commutation time of the motor must be determined according to the information of the back EMF zero-crossing point [11]. As shown in Figure 1, the commutation time is 30° electrical angle after the back EMF zero-crossing point is delayed. However, the "terminal voltage method" is generally used to detect the back EMF zero-crossing point. In order to suppress the influence of interference signals on the zero-crossing point when detecting the terminal voltage, a passive filter is usually used to filter the terminal voltage. However, the filtered signal lags behind the actual terminal voltage signal by 90° electrical angle. In this way, the detected zero-crossing signal can be used as the commutation signal of the motor. This method is relatively simple, but the determination of the commutation time is greatly affected by the speed. Only within a certain speed range can the zero-crossing delay be accurate. Exceeding the range will lead to increased electromagnetic torque pulsation, and in severe cases, the motor will lose synchronization. Therefore, complex compensation methods are required when using this method. If software is used to suppress interference at the terminal voltage, the determination of the commutation time can be directly detected by detecting a zero-crossing delay of 30° (i.e., t/12). The specific control method is: use the controller's timer to time the interval between two back EMF zero-crossings (i.e., 60°t/6) to calculate the inverter cycle. This method requires software compensation during acceleration and deceleration to obtain the optimal commutation time. Sensorless Pre-positioning Start When a brushless DC motor is stationary or at very low speed, the back EMF is zero or very small and cannot be used to determine the rotor position. Therefore, motors controlled by the back EMF method require special starting technology. In the past, a "three-stage" start was often used, which involves three stages: pre-positioning, acceleration, and running state switching. First, the initial position of the rotor is determined, then the holding time of each trigger state of the inverter power transistor is gradually reduced, and the applied voltage is continuously increased so that the motor accelerates according to the predetermined optimized acceleration curve, and then switches to the self-controlled state. This method requires that: the timing of the power transistor trigger signal determined according to the detected back electromotive force must correspond to the determined logic conduction timing to ensure that the position detection signal is reliable and accurately reflects the actual position of the rotor; the switching conditions are designed reasonably so that the motor switches to the self-synchronous operation state as early as possible. The disadvantage of this method is that the acceleration curve needs to be optimized and the start-up control is relatively complicated[12]. Currently, pre-positioning start-up is commonly used. The specific control process for starting is as follows: Forced pre-positioning: Regardless of the rotor's position, the motor is given a specific energizing state. The stator's composite magnetomotive force has a definite direction in space. As long as the energizing time is long enough, the rotor's magnetic poles can be pulled to a position coinciding with the axis of the stator's composite magnetomotive force. Starting: The inverter's power transistors are sequentially switched according to the set rotation direction. Simultaneously, the zero-crossing point of the back EMF of the open-circuit phase is detected using the "terminal voltage method," and the applied voltage to the motor is gradually increased by increasing the motor's PWM duty cycle. During pre-positioning start-up, the maximum conduction time of the power transistors remains constant, denoted as t0, which is determined by the minimum starting speed. A timer is used for timing, with commutation fixed at t0/2. After commutation, the zero-crossing point of the back EMF of the open-circuit phase is detected. As soon as the zero-crossing point of the back EMF of the open-circuit phase is detected, or the counter reaches its countdown, the counter is reset and the timing restarts. Commutation resumes at t0/2. The commutation is performed sequentially. If the back EMF of the open phase is detected to be zero-crossing n times consecutively, the system can switch to automatic control mode. The timing diagram of the starting process is shown in Figure 3. [align=center] Figure 4: Simulation system of brushless DC motor without position sensor Figure 5: Relationship between back EMF and quantized data[/align] This control method requires switching from external control mode to automatic control mode only after the back EMF of the open phase is detected to be zero-crossing n times consecutively. This is to prevent false detections caused by interference and to stabilize the motor speed, ensuring a smooth start-up process. This method has good starting reliability, simple control method, and does not require an external dedicated starting circuit. When using this method, the following should be noted: The external voltage should not be too high at the beginning of the start-up, otherwise it may cause the rotor to be subjected to excessive force and rotate past the predetermined position, making it difficult to detect the zero-crossing point, thus prolonging the start-up process or even causing start-up failure; During the start-up process, the external voltage should be increased steadily to ensure stable speed. Simulation of sensorless BLDCM Currently, most simulations of BLDCM systems are for those with position sensors. In order to facilitate the study of the sensorless control strategy of brushless DC motor, this paper designs a simulation research platform for brushless DC motor to detect rotor position by the back EMF zero-crossing method. In this system, the design method is to quantize each back EMF into three specific values, which represent the different stages of the back EMF. The relationship between the back EMF and the quantized data is shown in Figure 5. The six codes of the three back EMF quantization correspond to the six positions of the rotor and are used to control the inverter commutation [13]. [align=center] Figure 6 Sensorless rotor position detection module [/align] The back EMF detection module is shown in Figure 6. The three back EMF input module first quantizes the values ​​and then converts them into -1, 0, and 1. Then, it inputs them together with the reference current signal output by the speed regulator into the s-function. The s-function controls the commutation by setting the reference current of the three phases according to the back EMF code, thus realizing the sensorless control function [14][15]. Since the back EMF has not been established when the bldcm starts, the commutation of the motor cannot be controlled by detecting the back EMF. Therefore, this system uses a position sensor to control motor commutation during startup. Once the system reaches steady-state back EMF formation, it switches to a sensorless control mode. Currently, this switching is achieved by controlling the simulation time, which needs further improvement. This paper simulates a rotor position detection model using back EMF. Detecting back EMF allows for correct motor commutation control, and the system exhibits ideal responses to disturbances and speed regulation. In the simulation, the BLDCM motor parameters were set as follows: stator phase winding resistance r = 1 Ω, stator phase winding self-inductance l = 0.03 h, mutual inductance m = -0.0065 h, moment of inertia j = 0.007 kg·m², rated speed ne = 2500 r/min, and number of pole pairs pn = 1. The system switches to sensorless control at 0.2 s. At startup, the load torque tl = 1 nm, and the speed setpoint is 80 rad/s. When the simulation reaches t = 0.5 s, the speed setpoint is suddenly increased to 140 rad/s. The simulated waveforms of back EMF and phase current are shown in Figures 7 and 8. The system speed response and torque response waveforms are shown in Figures 9 and 10. Simulation results show that the proposed model for determining rotor position and controlling motor commutation by detecting the back EMF is feasible. The motor can follow a given speed, achieving sensorless control and providing a simulation model for further research on sensorless control strategies. However, the torque response curves show that the motor's rotor pulsation is relatively large under sensorless control, requiring further investigation. [align=center] Figure 7 a Back EMF Waveform Figure 8 a Phase Current Waveform Figure 9 Speed ​​Response Curve[/align] Conclusion This paper uses the widely used method of detecting the zero-crossing point of the back EMF to discuss the commutation strategy, PWM modulation control method, and starting control scheme of this sensorless BLDCM system, and establishes a simulation research platform. The results show that this platform facilitates further research on sensorless control strategies, but further improvements are needed in starting control.