# How are real-time speed and torque of a brushless DC motor computed?

Let's suppose I need to work with a three-phase brushless DC motor. The DC motor has only three wires to control its 3 phases, there is no other wires (no Hall effect sensor return for example). Usually one uses a driver (like an ESC) to control the speed of the motor: the MCU sends a PWM signal to the driver which in return controls the 3 phases of the motor.

I know that controlling the duty cycle controls the speed of the motor. But are drivers capable of computing the real-time speed (in rpm) of the motor when the motor does not have feedback wires? If so, how do they do?

Can they compute the real-time torque as well?

Typically back EMF sensing is used to commutate and get speed information for sensorless drive schemes.

It doesn't work well at no or low RPMs so for startup the motor can be driven open loop, or a salient pole permanent magnet machine can use inductance saturation sensing to position the rotor and start commutation.

For torque estimation the motor current is often good enough.

The best control of 3 phase Delta Sensorless BLDC technology is very mature now with Field Oriented Control (FOC BLDC) Infineon is one source of such a solution with an ARM based SOC, system on a chip. THe current is sensed , harmonics filtered without fundamental phase shift , digitized and transformed from 3D to a rotating 2D vector space as torque can only be used with positive currents in 2 rotating phase currents.

The 3D to 2D is called the Clarke Transform following by the rotating 2D vectors called the Park Transform.

• actual flux is thus computed and expected vs actual are compared with input controls for full range frequency control with V/f controls normal for variable speed and current regulated with PWM to match the desired rotating flux.

There is also a feedback loop for comparing the rotating 2D currents with a PI controls for frequency and phase.

https://www.infineon.com/dgdl/Infineon-TLE987x-Sensorless-Field-Oriented-Control-ApplicationNotes-v01_00-EN.pdf

TI, Allegro and many others also have various solutions for FOC.