Brushless rotor position estimation

How to estimate rotor position of brushless dc motor having trapezoidal shaped air gap flux distribution using flux-linkage based technique? The commonly used equation given in books and other technical resources to estimate the flux is given as Ψ = Ψp + Ψpm = ∫(U - Ri)dt , where Ψ denotes total flux linkage of the phase (consisting of self and mutual flux Ψp; and Ψpm due to permanent magnet rotor), U denotes phase voltage; R and i denote phase resistance and current. But how does this relation translate into rotor position? What electrical quantity do we actually measure to control the motor in this method?

Thank you.

Try turning the armature without power. Hook up a scope to a coil. Watch the waveform generated by a passing magnet. I believe the goal is to detect this waveform while the motor is running under power.

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No doubt this is difficult for the simple reason that every coil near a magnet is supposed to get current while it is near the magnet.

using flux linkage, that sounds like you are looking for the signal from a hall sensor.
As you know, the other ways to sense rotor position are sensorless bldc control, and encoder based techniques.

Thanks for your replies. I am not having any scopes but I do know the waveform generated when the motor is hand cranked. The question is what is being measured? Is it the flux? Or the flux is being inferred from some other electrical measurement? I don't understand if the goal is to calculate flux by measuring the terminal voltage and instantaneous current through the energized phases and then doing the math using above equation. Can it be so?

treez said:

using flux linkage, that sounds like you are looking for the signal from a hall sensor.

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Stator flux-linkage based technique is one of the many ways to control BLDC motor without using any sensors; including hall effect sensor.

Thank you.

Actually When you say "flux linkage" method, I think that is also known as the "sensorless BLDC control".
I think it looks for the voltage across the stator coils as the rotor turns, and it infers from that what is the position of the rotor.
So its sensorless because there is no added sensor, well, the "sensor" is the stator coil itself, and you look at the voltage across it....it must peak at a certain time, which gives away the rotor position.

Thanks again for your quick response.

treez said:

and you look at the voltage across it....it must peak at a certain time, which gives away the rotor position.

Click to expand...

I also think that measuring the stator phase voltage and inferring the flux from this can give way the rotor position. However, I don't know if this is the ONLY way to use the above given equation. I have not been able to find much detail regarding this method of BLDC motor control. So, it is proving to be very difficult to grasp this technique.

The reason you don't understand is not because you lack intelligence, it is indeed because of the shrowd of secrecy that exists over the world of electric motors and drives.......to many engineers, this is their bread and butter, their mortgage, their everything, they don't want to see it being explained clearly to a potential job competitor such as yourself.
But yes, the voltage across a stator coil will likely have a peak or something that can be detected at a certain instant of time, as the rotor rotates, and that gives away the rotor position.
As you know, a BLDC's stator coils can only be correctly pulsed if the rotors exact position is known.

I think that sensing the position of the rotor by "looking" at the stator coil voltage waveform as the rotor rotates within it, is called "back-EMF sensing".
It has problems at low speed because there is not much build up of back-EMF...So if using this method it is difficult to sense the position of the rotor at low speed...something like that anyway

Yes, I understand this is an age of an intellectual property and a very few are really willing to share their information. I am preparing for an interview for which I am asked to study in detail the various ways to control BLDC motor. I have been reading a book titled "Permanent Magnet Brushless DC Motor Drives and Controls". A nice book for a beginner in BLDC. However, I need some details. I will try to look up the Google once again to see if I can find anything on this. Anyway, thank you for your help.

As far as I can tell, with a bldc, you have “commutation PWM”, where you jump from one stator coil to the next, and within that you also have “high frequency PWM”……..the HF PWM is like kind of using the stator coil as a buck inductor so you can control the current in it to a certain value. Ideally you would like steady flat DC in the stator coil, but you cant have that , so you switch the coil on and off very quickly, and the zig zag shape of the resulting current in the bldc coil kind of approximates DC current……I mean, its going up and down, but not that badly up and down…..so its effectively a dc current in the coil.

Your Back EMF sensing pulses, are what tell your micro when to shift along to the next stator coil (commutation PWM).

Interesting that you call it “IP”……its common knowledge in the industry, and not patented by anybody, but indeed , individual companys consider it their IP.

I believe that the HF PWM is basically using the stator coil as like an inductor in a constant off time buck converter…so as to control current in it. You control the peak current level, and this inadvertently oviously controls the average coil current.

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here is simulation of 3 ph bldc...all txt files must be in same folder as sim file else it wont work