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.
Thank you for your reply,i wanna confrim some parameters such as ud_frac,id_frac_est,ed_frac,
I do not know if is right?
Hi Eden Li,
Sorry i did not had a chance to compute it by myself but your math looks about right.
Anyhow, keep in mind that the exact coefficient might need to be adjusted/tuned for the final model since it's pretty hard to guess all those motor parameters exactly. You also have measurements error that you need to consider.
From my past experience - and i think that is the reason why those K1-4 factors are hardcoded in the model - you need to adjust those parameters manually via Freemaster in real time until you reach a proper stable system.
It's quite difficult to compute those based on the motor manufacturer datasheet - just think about the inverter transfer function that is not accounted for the math model.
Thank you for your reply!
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