Can FOC be done with only one PID controller and a lookup-table that determines phase-offset?

Normally two PIDs are used to do torque-control with FOC -- one for the direct torque and one for quadrature torque.

The reason for this is described here:

Why are two PID controllers needed for FOC (Field Oriented Control)?

Assume that I characterised a particular motor so that for any given speed and torque (as measured by current and speed sensors) the ideal phase-offset was known (or interpolated) by a lookup table.

If I used this lookup table combined with sensors for rotor-position, torque, and speed, would I be able to dispense with the second PID loop and only use one for determining the quadrature (torque) force?

I believe this question is equivalent to asking whether the phase-offset depends on anything other than the speed and measured current. If there's no other forces that might affect the phase-angle, then the PID for direct torque can be removed.

• I guess, in theory, you can put any function in a lookup table even if the lookup table might be many, many dimensions. Then you have to search through it and cross-interpolate across all those dimensions Commented Sep 20, 2020 at 18:37
• I realize that this is an old question. But it seems to me that the answer is no. You need to control the D-axis current even if you want to set it to zero (which you will want to do any time you are running below base speed). In order to implement field weakening, you will need to set the D-axis current to a negative value. But you can't just not control the current. Commented Oct 10, 2022 at 4:05
• I guess maybe you could have a single PID to control the magnitude of the current by outputing the amplitude of the voltage. And you could use your lookup table to maintain the phase angle between voltage and flux as estimated by the observer. That angle would probably only be based on speed, unless you do field weakening. But I also don't see why you wouldn't just follow the path of least resistance and use two PIDs. Commented Oct 10, 2022 at 4:08