Shown as below,how to deduce the id_frac_est = (ud_frac*K1_n + w_n*iq_frac*K2_n + ed_frac*K3_n + id_frac_est*K4_n)?

I don't know how to deduce it,and the id_frac_est is deduced form EMF?

**Original Attachment has been moved to: S12ZVM_FOC_Sensorless.slx.zip**

Hi Eden Li,

Please allow me to begin by saying that i understand your doubts about this. I also had some hard time to understand it, just to realize that sometimes the comments and notations within a model may be misleading you. I think in this case that is the root cause.

Let us start from the observer equation highlighted below. This equation is written in a synchronous reference system gamma/delta.

The Simulink model is used Id_est/Id_obs and Iq_est/Iq_obs but if you go over this inconvenient and replace with gamma/delta the d/q quantities you will reach to the conclusion that the blocks id_frac_est and iq_frac_est implements the equation in the red box above.

The maths behind is a bit more complex - i do not pretend to be an expert - but for an easy explanation you can start from the the non-salient motor model - where you can express as:

For the salient use case where Ld!=Lq the model becomes:

Now, if you take this equation and solve it in current observing frame you will end up with a similar model as the one implemented in the Simulink example.

The K1,K2,K3,K4 are just the coefficients of i = f(u,i,w,e) of the derived equations that are basically f(Lq,Lq,Rs,K). Unfortunately, i do not have the original values used to derived the K1---4 coefficients used in the model but all that i can say those are strongly dependent on the motor you are going to use.

If you search on the web about salience observers you will find a lot of literature that will cover this subject.

Hope this will clarify some of your doubts.

Best regards,

Daniel