Field Oriented Control 2-Phase Motor

I try to derive FOC for a 2-phase motor, but I'm struggling with the right formulas and I can't find any paper explaining it. The phases of the motor are 90° apart, such that I assume the Clark Transformation is not necessary:

$$I_{alpha} = Ia$$ $$I_{beta} = Ib$$

I'm not sure if this really is true, but the currents are 90° appart, as needed for the Park Transformation, which is only applying the rotation matrix with theta, the electrical angle:

$$Iq = cos(\theta) I_{alpha} + sin(\theta) I_{beta}$$ $$Id = cos(\theta) I_{beta} - sin(\theta) I_{alpha}$$

Now I use the standart double PI controller as for 3-Phase FOC and the inverse Park Transformation, such that I get Valpha and Vbeta, which I can apply to SVM.

$$V_q = (I_{qdes}-I_q) K_p + SumErrQ$$ $$V_d = -I_d K_p + SummErrD$$

So I implemented everything, but it works not as needed. I can control a 2-phase motor this way, but Id becomes large for one direction, so something seems to be missed here? Is anyone experience with 2-phase FOC?

Edit: Ok, I think that this should works as I implemented, but for larger Reference Currents Iq, Id becomes an offest in average different from 0, also when no higher velocities are reached. Is it possible, that this is due to flux saturation? I think high pole-pair motors (50-100 pp) are pretty sensitive to flux saturation, right? Is there a way to overcome this?

• You are aware Iq resembles the active current, Id the reactive current? – Janka Nov 30 '18 at 12:51
• Yes, why do you mean? – HansPeterLoft Nov 30 '18 at 13:15