1. Overview

The basic principle of BLDC without hall is similar to that of BLDC with hall. The so-called “six step commutation method” is used. According to the current position of rotor, the stator winding is electrified in certain order to make BLDC motor rotate. The difference is that Hall effect sensor is not needed for Hall effect BLDC, and the current position of rotor can be determined by detecting the zero crossing point of back EMF of stator winding. Compared with the scheme with hall, the most obvious advantage is to reduce the cost and volume. And the motor leads are changed from 8 to 3, so that the wiring debugging is greatly simplified. In addition, Hall sensor is easy to be affected by external environment such as temperature and magnetic field. Therefore, hall free BLDC has been applied more and more, and hall BLDC is gradually replaced by hall BLDC in many fields. This paper introduces the hall free control theory of three-phase BLDC motor. According to the specific application situation, the specific implementation method will be different.

2. Introduction of BLDC motor structure and driving mode

The structure of a simple BLDC is shown in Figure 1. The outer layer of the motor is the stator, which contains the motor winding. Most bldcs have three Y-connected windings, each of which is made up of a number of coils interconnected. Inside the motor is the rotor, which is composed of magnetic opposite poles around the circumference of the motor. Figure 1 shows a rotor with only two poles (North and south poles). In practice, most motors have multiple pairs of poles.

Principle of BLDC motor controlled by back EMF

Figure 1blcd basic structure

The basic model of BLDC motor drive circuit is shown in Figure 2. The switch tube Q0 ~ Q5 is used to control the power on state of the motor three-phase winding. The switch tube can be IGBT or power MOS tube. Among them, the switch tube at the top, which is connected with the positive end of the power supply, is called the “upper bridge”, and the lower switch tube connected with the negative end of the power supply is called the “lower bridge”.

Figure 2 basic model of BLCD motor drive circuit

For example, if Q1 and Q4 are opened and other switches are closed, the current flows from the positive end of the power supply through Q1, phase a winding, c-phase winding and Q4 back to the negative end of the power supply. The current flowing through phase A and phase C stator windings will produce a magnetic field. According to the right hand rule, the direction of the current is parallel to the phase B winding. Because the rotor is a permanent magnet, under the action of magnetic field force, it will rotate in the direction parallel to the stator magnetic field, that is, to the position parallel to phase B winding, so that the north pole of the rotor is aligned with the south pole of the stator magnetic field. Similarly, by opening different MOSFET combinations of upper and lower arms, the current flow direction can be controlled, and the magnetic field in different directions can be generated to make the permanent magnet rotor turn to the specified position. In order to make BLDC motor rotate continuously in the specified direction, the stator winding must be electrified in a certain order. Switching from one power on state to another is called “commutation”, for example, from AB to AC. Commutation causes the rotor to rotate to the next position. There are three switch tubes in the upper and lower bridge arms respectively, and there are six combinations in total. Therefore, the motor can rotate for one electrical cycle after six steps of commutation. This is the so-called “six step commutation method”. To make the rotor have the maximum torque, the ideal situation is to make the stator magnetic field perpendicular to the rotor magnetic field direction. But in fact, because the stator magnetic field direction only changes once every 60 ° and the rotor is always rotating, it is impossible to keep the phase difference of 90 ° at all times. The optimization method is to make the stator magnetic field ahead of the rotor magnetic field direction by 120 ° electric angle during each commutation. In this way, the angle between the stator magnetic field and the rotor magnetic field direction changes from 120 ° to 60 ° in the next 60 ° rotation process, and the torque utilization rate is the highest. In order to determine which winding will be energized according to the power on sequence, the current position of the rotor must be known. In BLDC with hall, the position of rotor is detected by Hall effect sensor embedded in stator. Hall free BLDC motor does not rely on the position sensor, but uses the characteristic signal of the motor itself to achieve the similar effect as the position sensor, and the most widely used method is back EMF method introduced in the next section of this paper.

3. The principle of BLDC motor controlled by back EMF

When a BLDC motor rotates, the rotation of the permanent magnet rotor produces a variable magnetic field in the motor. According to the law of electromagnetic induction, each phase winding will induce back electromotive force (BEMF). The BEMF waveform of BLDC motor changes with the position and speed of the rotor, and presents a trapezoidal shape as a whole. Figure 3 shows the waveform of current and back EMF in an electric cycle of motor rotation, in which the solid line represents the current, the dotted line represents the back EMF, and the abscissa represents the electrical angle of motor rotation. According to the “six step commutation” control theory of BLDC, we know that at any time, only two phases of three-phase BLDC are connected to each other, the other phase is open, and three-phase two-phase is electrified In this way, a rotating magnetic field is generated, which pulls the permanent magnet rotor to rotate. The 60 ° here refers to the electrical angle. An electrical cycle may not correspond to a complete mechanical rotation cycle of the rotor. The number of electrical cycles to be repeated for a mechanical turn depends on the number of magnetic poles of the rotor. Each pair of rotor poles needs to complete one electrical cycle, so the number of electrical cycles / revolutions is equal to the number of rotor poles.

Figure 3lcd motor current and back EMF waveform

The key to control BLDC is to determine the commutation time. It can be seen from Fig. 3 that in the middle of each two commutation points, there is a point where the polarity of the back EMF changes, that is, the point where the back EMF changes from positive to negative or from negative to positive, which is called zero crossing point. Using this characteristic of back EMF, as long as we can accurately detect the zero crossing point of back EMF and delay it by 30 ° is the time of phase change.

4. Detection method of back EMF

As can be seen from Fig. 3, each zero crossing of back EMF occurs in the non electrified phase. For example, in the first 60 ° in Fig. 3, the phase a current is positive, the phase B current is negative, and the phase C current is zero. This indicates that the motor AB is energized, and the current flows from phase a to phase B, and phase C is open circuit. The zero crossing point of back EMF occurs in phase C. Moreover, since phase C is not electrified and has no current, its phase voltage has a direct corresponding relationship with the back EMF. Therefore, as long as the voltage of the non electrified phase is detected within each 60 °, the back EMF can be detected.

4.1 reconstruction of virtual neutral point

Due to the Y-shaped connection of BLDC motor, three phases are connected to the common neutral point, so the phase voltage cannot be measured directly. Only the terminal voltage of each phase can be measured, that is, the voltage of each phase to ground. Compared with the neutral point voltage, when the terminal voltage changes from greater than the neutral point voltage to less than the neutral point voltage, or from less than the neutral point voltage to greater than the neutral point voltage, it is the zero crossing point. The schematic diagram is shown in Fig. 4 (a).

Figure 4 detecting zero crossing point of back EMF

But the general BLDC motor does not have the external lead of neutral point, so it is impossible to measure the neutral point voltage directly. The most direct way to solve this problem is to reconstruct a “virtual neutral point”, which is formed by connecting the three-phase windings to a common point through the voltage with equal resistance, which is the virtual neutral point, as shown in Fig. 4 (b). The method of reconstructing virtual neutral point has certain practicability, but it also has great shortcomings. Because BLDC motor is driven by PWM mode, PWM outputs “on” first and then “off” in a cycle; when PWM is “on”, motor winding is energized, and when “off” is turned off. Therefore, the voltage applied to both ends of the motor winding is continuously switched between the high level and the low level, and the voltage at the neutral point contains a lot of switching noise. If the neutral point voltage is filtered, on the one hand, it will increase the complexity of the circuit, on the other hand, the filter circuit will cause the signal phase shift, so that the detected zero crossing point will move backward than the actual time, which can not accurately guide the commutation.

4.2 sample back EMF in PWM on range

In fact, if we only sample the back EMF in the PWM “on” range, we can use half of the total terminal voltage instead of directly detecting the neutral point voltage. The derivation process is as follows.

Principle of BLDC motor controlled by back EMF

Fig. 5 neutral point voltage of pwmon interval

Suppose the h-pwm-l-om modulation mode is adopted (see Section 5.2: PWM modulation mode for details), that is, the upper bridge arm adopts PWM modulation, and the lower bridge arm is Hengtong. Figure 5 shows the simplified equivalent circuit of BLDC motor when PWM is “on”. Each phase of the motor is equivalent to a series of resistance, inductance and back EMF. Assume that AB is currently energized, current flows from phase a to phase B, and phase C is open. DC is DC bus voltage, VA, VB and VC are terminal voltage of a, B and C phase respectively, VN is neutral point voltage, EA, EB and EC are back EMF of a, B and C phases respectively.

For the voltage loop equation of phase A:

Vn=Vdc−Vmos−ri−Ldidt−eaVn=Vdc−Vmos−ri−Ldidt−ea

(4.2.1)

For B-phase voltage loop equation:

Vn=Vmos+ri+Ldidt−ebVn=Vmos+ri+Ldidt−eb

(4.2.2)

VMOS is the voltage drop on the MOS transistor. The sum of the above two formulas is as follows:

Vn=Vdc2+ea+eb2Vn=Vdc2+ea+eb2

(4.2.3)

For a three-phase balanced system, if the third harmonic is ignored, there is a

ea+eb+ec=0ea+eb+ec=0

(4.2.4)

Replace (5.2.4) with (5.2.3) to obtain

Vn=Vdc2+ec2Vn=Vdc2+ec2

(4.2.5)

Thus, the c-phase terminal voltage is obtained

Vc=Vn+ec=Vdc2+32ecVc=Vn+ec=Vdc2+32ec

(4.2.6)

It can be seen from the above formula that the terminal voltage of the dead phase is formed by the superposition of the back EMF of the phase on the VDC / 2. Therefore, the zero crossing point of the back EMF can be detected by comparing the end voltage of the dead phase with that of the VDC / 2. This method avoids the influence of switching noise, so there is no need to add filter circuit.

In order to avoid the peak voltage when PWM just changes from “off” to “on”, back EMF sampling is usually conducted after PWM enters “on” state for a period of time, as shown in Fig. 6. This function can be easily realized with the center alignment mode of PWM of sh79f168. In the center alignment mode, the periodic interruption of PWM occurs in the middle of “on” state. So we can set the PWM to the center alignment mode, and then sample the back EMF in the period interrupt.

Figure 6 sampling when PWM is “on”

However, this method has a disadvantage, that is, the duty cycle of PWM can not be too small, otherwise the time when PWM is “on” is too short to carry out AD sampling, so it is unable to accurately judge the zero crossing point and make the commutation of motor disordered and unable to operate normally. After the motor enters the closed-loop control, the smaller the PWM duty cycle is, the lower the speed is. Therefore, this method is not suitable for the situation that requires very low speed. In reality, there are few occasions that require the motor to operate at very low speed, so this method can also be applied to most applications.

Another problem to be noted is that in a period of time after the commutation, if the current disconnected phase winding is connected to the positive terminal of the power supply before commutation, the terminal voltage will rapidly drop to the negative terminal voltage of the power supply at the moment of commutation, forming a downward spike; if the current disconnected phase winding group is connected to the negative terminal of the power supply before commutation, the terminal voltage will rapidly rise to the power supply at the moment of commutation The positive terminal voltage of the source forms an upward spike. This phenomenon is more obvious when the PWM duty cycle is larger, and the duration is longer, as shown in Fig. 7.

Figure 7 voltage spike at commutation time

The reason for this phenomenon is that, at the moment of commutation, due to the inductance effect of the motor winding, the current in the disconnected phase winding will not disappear immediately. According to the direction of the current, it will continue to flow through the body diode of the switch tube of the upper or lower bridge arm, and it will disappear for a period of time. The greater the current, the longer the duration. Take Figure 5 as an example, if the motor is switched from AB Power on to AC power on, phase B winding will be disconnected and the switch tubes of upper and lower bridge arms will be closed. At that time, the current flowing from the neutral point in the B-phase winding would not disappear immediately. Therefore, the current flowing through the body diode of the upper bridge arm would be short circuited with the positive end of the power supply, and a positive peak would appear. Similarly, if the motor was switched from the status shown in the figure to the CB, the switches of the upper and lower bridge arms of group A were closed. According to the direction of the current, only the current could be continued through the diode of the lower bridge arm and the negative end of the power supply Short circuit, and a negative spike appears. The larger the current, the longer the free current time and the wider the peak.

Obviously, when sampling in the PWM period just commutation, it is likely to be affected by the peak voltage, which can not reflect the correct back EMF. Therefore, according to the duty cycle of PWM, the sampling can be avoided in one or two PWM cycles just commutation, so as to avoid the peak voltage.

4.3 sample back EMF in PWM off range

If it is required that the motor can operate at very low speed, the back EMF sampling method can be used in PWM off range.

To understand the following content, we must first have a basic understanding of the structure of the switch tube. Whether IGBT or power MOS transistor, there is a diode in reverse parallel between c-pole and e-pole (or d-pole and S-pole), which is called bulk diode, as shown in Fig. 2.

Figure 8 neutral point voltage in PWM off range

When the PWM of the drive end is switched from on state shown in Fig. 5 to off state as shown in Fig. 8, the current in the winding will not disappear immediately due to the inductance effect of the motor winding, so the body diode of the lower arm MOS transistor will form a circuit, as shown in Fig. 8. If the voltage drop of diode is ignored,

For phase a, the loop equations are as follows:

Vn=0−ri−Ldidt−eaVn=0−ri−Ldidt−ea

(4.3.1)

For the B-phase loop equation:

Vn=ri+Ldidt−ebVn=ri+Ldidt−eb

(4.3.2)

For a three-phase balanced system, if the high-order harmonics are ignored, the above three equations can be obtained

ea+eb+ec=0ea+eb+ec=0

(4.3.3)

I want to add the following three formulas:

Vn=ec2Vn=ec2

(4.3.4)

So the c-phase terminal voltage is

Vc=Vn+ec=32ecVc=Vn+ec=32ec

(4.3.5)

Therefore, the end voltage of the winding is sampled in PWM off range, and the voltage value is proportional to the size of the reverse electromotive force, and its zero crossing also directly reflects the zero crossing of the reverse electromotive force. Because this method needs a certain PWM off range to sample, it can not be implemented when PWM duty is 100%, that is, the motor can not reach full speed. In addition, when PWM is just off, the voltage of the off phase will be clamped at -0.7v due to the continuous current of the body diode of the lower bridge arm MOS tube, so it is necessary to delay for a while before sampling, which increases the difficulty of software implementation. In order to have sufficient sampling time, generally, when PWM duty cycle is relatively large, sampling is conducted in PWM on section, and in PWM off interval when PWM duty cycle is very small. But when PWM duty cycle is very small, the motor speed is low, and the emf will be very small, so the accuracy of detection will be limited.

Closed loop speed regulation 5

As long as the zero crossing point of back EMF can be detected accurately, the closed-loop speed regulation can be carried out conveniently.

5.1 establishment of closed loop

The back EMF of each phase has two zero crossing cases: from positive to negative and from negative to positive. There are six zero crossing conditions in three phases, corresponding to six commutation states, and the corresponding relationship is fixed. Therefore, we can first write the corresponding relationship into a table. When a zero crossing point is detected in the program, the corresponding IO output is determined by looking up the table to control which two are connected to each other in the next step; then switch to the current open phase and continue to detect the zero crossing point of back EMF, such as this cycle, until a stable closed loop is established.

Theoretically, the zero crossing point is always 30 ° ahead of the commutation point, as shown in Fig. 3. Therefore, after the zero crossing is detected, it is necessary to delay the electrical angle by 30 ° before commutation. However, in the process of closed-loop speed regulation, the motor rotation time of an electrical cycle is not fixed, we can not predict how long the next 30 ° electrical angle will be after the detection of zero crossing. How to determine the delay time after zero crossing is detected? Although we can’t predict the length of the next 30 ° electrical angle, the length of the 60 ° electrical angle between two commutation points can be measured. The timer is cleared at each commutation, and the timer value read in the next commutation is the length of the commutation period. Therefore, we can adopt an approximate method and use the last commutation period, that is, the time of 60 ° electrical angle is halved as the next 30 ° electrical angle delay time. This method is feasible because the speed of the motor is gradual, and the time difference between two adjacent commutation cycles is not very big.

5.2 PWM modulation mode

After the motor enters the closed loop, the speed can be adjusted as long as the duty cycle of PWM is adjusted. When the PWM duty cycle is large, the current flowing through the motor winding is large, the stator magnetic field is strong, and the speed is high; on the contrary, when the PWM duty cycle is small, the motor speed is low.

There are two PWM modulation methods: full bridge modulation and half bridge modulation. During the 120 ° conduction period, the upper and lower bridges of the power inverter bridge are driven by PWM mode, that is, “full bridge modulation”; during the 120 ° conduction period, only the upper bridge (or lower bridge) of the power inverter bridge is driven by PWM mode, and the lower bridge (or upper bridge) is always on, which is called “half bridge modulation”.

The switching frequency of MOSFET under full bridge modulation is about twice as high as that of half bridge modulation, so it is rarely used. Half bridge modulation modes include h-pwm-l-on (in the 120 ° conduction range (the same below), the upper bridge arm MOS tube is PWM modulation, the lower bridge arm MOS tube is constant on), h-on-l-pwm (upper bridge arm MOS tube is constant on, lower bridge arm MOS tube is PWM modulation), pwm-on (front 60 ° PWM, rear 60 ° constant on), on-pwm (front 60 ° constant on, last 60 ° PWM), etc., each has its own characteristics, which can be according to the specific circuit and application situation The selection of specific modulation mode is not detailed in this paper. One of the most commonly used is the first two, which are relatively simple to implement and can meet the general application.

Starting mode of BLDC motor

The most difficult point of BLDC motor control is not position detection and commutation, but starting mode. Due to the positive correlation between the back EMF and the speed of the motor winding, when the speed is very low, the BEMF is also very small, so it is difficult to accurately detect. Therefore, when the motor starts from zero speed, the back EMF method is often not applicable. The motor must be pulled to a certain speed by other methods to make BEMF reach the level that can be detected before switching to the back EMF method.

6.1 positioning

Only when the position of the rotor at standstill is determined, which two switches should be triggered for the first time can be determined. The process of determining the initial position of the rotor is called positioning.

6.1.1 positioning by two connected electrical method

The simplest and commonly used method is to power on any two motors and control the motor current not to be too large. After a period of power on, the rotor will turn to the predicted position corresponding to the power on state to complete the rotor positioning. Taking Fig. 9 as an example, if AB and ab are electrified, the position of stator magnetic potential FA is as shown in the figure. At this time, if the rotor magnetic potential FF is at the position shown in the figure, the rotor will rotate clockwise by 120 ° electric angle and align with the stator magnetic field direction.

Figure 9 rotor positioning

In order to avoid this problem, AC and BC can be electrified first, and the direction of the magnetic field formed is perpendicular to FA, then the rotor must turn to the position perpendicular to fa (even if there is deadlock at this time, the rotor is still perpendicular to FA at the position with 180 ° angle to the specified direction), and then power on AB to ensure that the rotor turns to the FA direction.

6.1.2 positioning with the method of strain detection

A more effective method is to detect the initial position of the rotor by changing the inductance of the motor winding. This method does not depend on any characteristics of the motor, so it is applicable to any motor. Even if the starting load of the motor is changed, the positioning can be effectively realized. The method is based on the following principle: a voltage is applied to the coil in the magnetic field of the permanent magnet. According to the direction of the magnetic field, the generated current will enhance or weaken the strength of the magnetic field, thus reducing or increasing the coil inductance.

Fig. 10 positioning with variable sensitivity detection method

The specific implementation method is shown in FIG. 10. First connect one phase winding to the high level, and the other two phases are grounded. At this time, the direction of stator magnetic field generated is shown in the figure. Then, the two-phase winding connected to the high-level is changed to the high-level winding, and the original high-level winding is grounded, resulting in a magnetic field in the opposite direction. In both cases, the power on time is very short, the rotor does not rotate, and a current pulse is generated in the winding. By comparing the current pulse in these two cases, the inductance of the two windings can be compared, so that the rotor can be positioned in the range of 180 degrees. Then change another phase of the motor winding and repeat the previous process, positioning the rotor in the other 180 ° range. When the three-phase windings are tested once, the 60 ° range of the rotor can be determined by the coincidence of the three ranges.

Since the time of winding energizing is very short in this method, the problem of over-current will not be worried. In addition, since the rotor position will not be changed, this method can also be used to detect the rotor position in the rotor running clearance.

6.2 acceleration

After defining the initial position of the rotor, it can be determined which switch tubes should be opened for the first time to make the two connected to each other, and control the rotor to rotate forward or reverse to the next position, that is, the first commutation. If the back electromotive force generated during the first commutation is enough to detect the zero crossing point, it can directly enter the closed-loop control. However, the actual situation is often not so ideal. Under the speed of motor commutation for the first time from static state, it is often not enough to generate enough back EMF to realize zero crossing detection. Therefore, we can only accelerate the open-loop motor to a certain speed, so that the back EMF can detect zero crossing level, and then switch to closed-loop speed regulation.

Because the open-loop acceleration is very unstable, a reasonable acceleration curve must be designed in advance. One method is to determine three or four key points on the acceleration curve through experiments, and then fit the expression of the whole curve.

The successful implementation of this method is affected by many factors such as load torque, applied voltage, acceleration curve and moment of inertia. By optimizing the acceleration curve, this method can ensure the smooth starting of the motor, but for different motors and different loads, the corresponding optimized acceleration curve is not the same, which leads to the lack of universality.

Another acceleration method is to use the variable inductance detection method introduced in the previous section “positioning”. After a certain period of acceleration, this method is used to detect the rotor position, and then adjust the phase sequence to be energized according to the rotor position to continue accelerating. Repeat the test acceleration test acceleration until the motor runs at high speed to the required speed.

6.3 switching to closed loop

If you don’t want to spend too much energy on developing the acceleration curve, you can switch to the closed loop in another way. This method does not require the phase difference between the rotor and the stator magnetic field. As long as the motor can accelerate to a sufficient speed and open the three-phase windings, the rotor will be in an uncontrolled state and continue to rotate by virtue of inertia. At this time, there is no current in the three-phase winding, so the back EMF zero crossing detection can be carried out, and there is no need to worry about the situation that the zero crossing point of back EMF occurs in the energized phase and cannot be detected. After several times of zero crossing are detected continuously, it can be switched to the closed loop. After all three phases are cut off, the motor will rotate for at least dozens of electrical cycles under the action of inertia, and there are at least ten cycles when the speed is above the level that the back EMF can detect, which is enough to detect the rotor position. Therefore, this method is feasible. The disadvantage is that this method is not applicable when the load torque is large.

7 Summary

This paper assumes that readers already have a certain basis of BLDC control with hall, so the sequence of description is from hall with to no hall, from easy to difficult. Finally, according to the actual execution sequence, the control process of hall free BLDC is summarized as follows:

1. Positioning. This paper mainly introduces the two connected electrical method and the variable inductance detection method. Theoretically speaking, the latter is a better method, but I have not verified it in practice.

2. Speed up. In my practical projects, for the motor we use, we can directly enter the closed loop without accelerating. However, the several acceleration methods mentioned in this paper, in addition to the one combined with the sense of change detection method, have also been tested in practice.

3. Switch to closed loop. In the open-loop phase, the back EMF of the open phase is continuously detected. If the detection is stable, it can be switched to the closed-loop.

4. The back EMF method is used for closed-loop control. In the PWM on range, the zero crossing point can be obtained by sampling the terminal voltage of the disconnected phase winding and comparing it with half of the DC bus voltage. Through the zero crossing point of back EMF, the current position of the rotor can be determined, and then which two should be connected to each other in the next step. Due to the peak voltage generated during commutation, the back EMF detected during the period of commutation may not be accurate. Therefore, the voltage sampling value of the previous one or two PWM cycles should be abandoned according to the actual situation. If the ultra-low speed closed-loop control is required, the open phase voltage can be sampled in the PWM off range, and the zero crossing point of the sampling value is the zero crossing point of the back EMF.

5. The higher the speed of the PWM, the higher the duty cycle of the motor.

The most difficult point of BLDC control without hall is the starting problem. All the methods introduced in this paper have their limitations. Up to now, there is no reliable and universal method to realize the reliable starting of hall free BLDC with different characteristics under different application conditions. We can only choose a certain starting method according to the actual conditions. However, with the development of motor technology, more and more Hall free BLDC can realize the back EMF with higher intensity and sensitivity in the future, which can directly enter the closed loop and simplify the control process greatly.

reference

[1] AN1083: Sensorless BLDC Control With Back-EMF Filtering, Reston Condit, Microchip Technology Inc., 2007.

[2] AN885: Brushless BLDC Motor Fundamentals, Padmaraja Yedamale, Microchip Technology Inc., 2003.

[3] Advances in Sensorless Control of BLDC Motors, Agile Systems, 2005.

[4] Direct Back EMF DetecTIon Method for Sensorless Brushless DC Motor Dives, Jianwei Shao, Virginia Polytechnic InsTItute and the State University, 2003.

[5] AN1946: Sensorless BLDC Motor Control and BEMF Sampling Methods with ST7MC, STMicroelectronics, 2007.

[6] AN857: Brushless DC Motor Control Made Easy, Ward Brown, Microchip Technology Inc., 2002.

[7] control of permanent magnet brushless DC motor, Zhou Xuwei, sinowalth, 2008

[8] AP08018: Start-up Control Algorithm for Sensorless and Variable Load BLDC Control Using Variable Inductance Sensing Method, Infineon Technologies AG. 2006.

Leave a Reply

Your email address will not be published. Required fields are marked *