Electronic – Back EMF in sensored BLDC motor

Brushless DC means exactly that - a DC motor with brushless commutation. The controller's job is to switch the phases in and out at the correct rotor angles (not frequency) just like the commutator in a brushed motor. The motor spins at whatever speed it wants to, depending on supply voltage and load.

If the motor has sensors then the controller can be very simple, since it just has to read the sensors and turn on the appropriate phases depending on rotor angle. It has no direct control over commutation frequency, but it can 'control' motor speed indirectly by varying the effective supply voltage (using either a regulator or PWM).

Sensorless controllers have a harder job because they must monitor the back-emf waveform for zero crossings. At startup there is no back-emf so the ESC cannot detect the rotor's position. To get the rotor spinning it pulses the phases at low power like a stepper motor, gradually increasing speed until it gets a strong enough back-emf to switch into synchronous operation.

During this startup period only, the sensorless ESC controls motor speed by varying commutation frequency. However since it is basically dragging the rotor up to speed, any sudden change in load can cause it to loose sync. Also the motor may start in reverse, then it has to stop and try again. This may result in the rotor jumping back and forth a few times until the ESC sees a good back-emf.

can FOC even work for BLDC without an encoder but just with Hall sensors?

You have an encoder, it just doesn't have very high resolution. But how to increase it?

Once you know how fast the rotor is spinning (time between Hall sensor signal changes) you can predict intermediate angles. If motor speed is changing then the prediction will be off, but you can compensate for this too by measuring the acceleration and factoring it in.