Modeling FOC motor control with State Space mathematics.

[narmstro2020]

I'd like to know what the mathematics would be for modeling a motor with Field Oriented Control (like the one CTRE uses in their Phoenix 6 framework) for torque-current control.

I'm wanting to play around with making a sim class that works in a way similar to CTRE's setup from a mathematical standpoint.

The way I see it the only thing that would change would be the input parameter would be voltage instead of current, but I'm a little stuck on the math and any assistance would be appreciated.

EDIT: Would there be any equivalent kS, kV, kA constants like in the standard way of doing it with voltage control

[calcmogul]

The first-order approximation for a DC motor with angular velocity state and torque input is just A = [0], B = [1/J] where J is the moment of inertia.

torque = J * angular acceleration
angular acceleration = 1/J * torque
angular acceleration = 0 * angular velocity + 1/J * torque

The input limits will be device and mode-specific. Brushless motors with a flat torque vs angular velocity response will have a constant limit. Brushed motors and brushless motors mimicking the response of a brushed motor will have an input limit that decreases linearly with angular velocity.

You can also do current input with torque = Kₜ * current -> angular acceleration = 0 * angular velocity + Kₜ/J * current.

[calcmogul]

Yes, I just said that.

[narmstro2020]

I think I answered my question on this.

Could you setup a sysIdRoutine with torque determined from current, motor kt and gearing and pass that in as input instead of voltage?

[narmstro2020]

Sorry for the confusion on my part.

If we wanted to do position control would we have another row of zeroes in our matrix making it 3x3 at that point?
EDIT: The A matrix that is. B matrix would be 3x1?

[narmstro2020]

Actually nevermind. I forgot the dot was there in the state variable x-dot.
so a 2x2 and 2x1 for A and B.

[narmstro2020]

Thank you for the mathematics help @calcmogul. This fully answers my question.