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Home » BLDC Motor FAQ » How to Control Sensorless BLDC Motor Based on Back EMF?

# How to Control Sensorless BLDC Motor Based on Back EMF?

**Reconstruction of virtual neutral points**

Because of Y-shaped connection of BLDC motor, three phases are connected to the public neutral points, resulting in failure of the phase voltage to be directly measured. As a result, only the terminal voltage of various phases can be measured, namely the voltage of various phases on the ground. Then, the voltage is compared with the voltage of neutral points. When the terminal voltage changes from the voltage which is larger than that of neutral points to voltage which is smaller than that of neutral points, or the other way around, it is the zero-crossing point. The schematic diagram is shown in Fig. 1 (A).

**Sampling of the back electromotive force when the PWM is "On"**

In fact, if we sample the back electromotive force within the "On" section of PWM, then there is no need to directly detect the neutral point voltage, which can be represented by half of the total terminal voltage. Below is the deduction process:

Assume that the H-PWM-L-OM regulating method is adopted. The upper bridge arm adopts the PWM regulation, and the lower bridge arm is constantly on. Fig. 2 shows the simplified BLDC motor equivalent circuit when PWM is " On." Every phase of the electric motor is equal to the series of resistance, inductance and back electromotive force. Assume that A and B are connected with power. The current flows from A phase to B phase, and C phase is in an open circuit. V

_{dc}features the direct current busbar voltage. V

_{a}, V

_{b}and V

_{c}denote the terminal voltage of A phase, B phase and C phase. V

_{n}denotes the central point voltage. ea, eb and ec represent the back electromotive force of A, B and C phase.

For the voltage loop equation of A phase series:

V_{n}=V_{dc}- V_{mos}- ri - L*(di/dt) - e_{a (1)}

V_{n}=V_{mos}+ri+L*(di/dt) -e_{b}(2)

Where Vmos is the pressure drop on the MOS tube. Add the above two formulas to get:

V_{n}=V_{dc}/2 + (e_{b}+e_{a})/2 (3)

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

e_{a}+ e_{b}+ e_{c}= 0 (4)

Substitute (4) into (3) to get:

V_{n}=V_{dc}/2 + e_{c}/2 (5)

Therefore, the voltage at the C phase terminal can be obtained as

V_{c}=V_{n}+e_{c}=V_{dc}/2+ (3/2) *e_{c (6)}

From the above equation, it can be seen that the terminal voltage not connected with the phase is formed through superposition of the back electromotive force of this phase onto V

_{dc}/2. Therefore, by comparing the terminal voltage not electrified with the phase with the voltage value on V

_{dc}/2, the zero-crossing-point of the back electromotive force is detected. This method can avoid the influence of the switch noise, so there is no need to increase the filtering circuit.

In order to avoid the peak voltage appearing when PWM changes from "Off" to "On" the back electromotive force is sampled after PWM enters the "On" status and lasts for a period of time. See Fig. 3. This function can be easily realized via the central alignment of PWM of SH79F168. Under the central alignment model, interruption of PWM happens on the central position under the "On" status in one cycle. Therefore, we can set PWM to be the central alignment model, and then conduct the back electromotive force sampling during the cycle interruption.

However, this method has one defect, that is, the duty cycle of PWM cannot be too small. Otherwise, the "On" time of PWM is too short, making it too late to conduct AD sampling. As a result, it is impossible to correctly judge the zero-crossing-point, and the phase-change of the motor will be in a chaos, impeding normal operation. After the motor enters the close-loop control, the smaller the duty ratio of PWM is, the slower the rotating speed is. Therefore, this method is not applicable to occasions requiring an ultralow rotating speed. In the real world, there are just a few occasions in which the electric motor is required to operate at an ultralow rotating speed. Hence, this method is also applicable to most situations.

Another issue requiring attention is that, if the phase winding which is disconnected at present is the plus end of the power connection source before phase-switching for a period to come after phase-switching, the terminal voltage will quickly drop to the negative terminal at one instant to form a downward PEAK. If the phase winding which is disconnected is the minus end of the power connection, its terminal voltage will quickly rise to become the positive voltage of the power source at the moment of phase-switching, thus forming an upward peak. The higher the PWM duty ratio is, the more significant the phenomenon is, and the longer the phenomenon lasts. See Fig. 4.

A main cause of the phenomenon is that, the moment the phase is switching, affected by the inductance effect of the motor’s winding, the current within the disconnected phase winding will not disappear immediately. According to different directions of the current, the follow current continues via the parasite diode of the switch tube of the upper bridge arm or the lower bridge arm. It disappears after continuing for a period of time. The larger the current is, the longer it persists. Take Fig. 4 for example. if the electric motor switches from the AB connection to AC connection, the B-phase winding is disconnected, and the switch tube of the upper and lower bridge arm will all be turned off. At the moment, the current in the B-phase winding flowing from the neutral point will not disappear immediately, but constitutes the short circuit with the plus end of the power source via the follow current of the parasite diode of the upper bridge arm. Then, a positive peak will appear. Similarly, if the electric motor switches from the status in the drawing to CB connection, the switch tube of the A-phase upper and lower bridge arm will all be turned off. According to the current direction, it can only form the short circuit with the minus end of the power source via the follow current of the lower bridge arm’s parasite diode. Then, a negative peak will appear. The larger the current is, the lower the follow current will be, and the wider the peak will be.

Obviously, if the sampling is conducted within the phase-switching PWM cycle, it is highly likely to be influenced by the peak voltage, thus being unable to reflect the actual back electromotive force. In the first to two PWM periods, we can avoid sampling so as to avoid the peak voltage according to the value of the PWM duty ratio.

**Sampling of the back electromotive force in the "Off" section of PWM**

If the motor can function at an ultra-low speed, the method to sample the back electromotive force in the "Off" section of PWM.

Before reading the following part, you should first have a basic understanding of the switch tube structure. Either in terms of IGBT or in terms of power MOS tube, there is an anti-parallel diode between C-pole and E-pole (or D-pole and S-pole), which is known as the parasite diode.

V_{n}=0 - ri - L*(di/dt) - e_{a (7) }For the loop equation of phase B column:

V_{n}= ri + L * (di/dt) - eb (8)

For a three-phase equilibrium system, if the higher harmonics are ignored, the above three equations are added

e_{a}+ e_{b}+ e_{c}= 0 (9)

The above three formulas would like to add:

V_{n}= e_{c }/ 2 (10)

So we get C phase voltage is equal to

V_{c}=V_{n}+e_{c}=(3/2) *e_{c }(11)

Therefore, terminal voltage of the disconnected phase winding is sampled in the "Off" section of PWM. The voltage value thus obtained is proportional to the value of the back electromotive force. The zero-passing-point can also directly reflect the zero-passing-point of the back electromotive force. This method requires sampling in the " Off" section of PWM. When PWM duty is 100%, the sampling cannot be implemented, for the electric motor cannot achieve the full gear. Besides, when PWM enters the " Off" state, because of the follow current of the parasite diode of the lower bridge arm MOS tube, the disconnected phase voltage will stay at -0.7V. That is why sampling should come after a period of time, which will increase the difficulty of software realization. In order to ensure ample time for sampling, when PWM duty is large, sampling is conducted in the "On" section of PWM. When PWM duty is small, the sampling is conducted within the " Off" section of PWM. However, when PWM duty is small, the motor rotation speed will be slow, and the back electromotive force will be small, thus impeding the detection precision.