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LAUNCHXL-F28069M: How TI's Instaspin address the angle error between Id and Vd?

Part Number: LAUNCHXL-F28069M

at Instaspin userguide Page27, here displays an overview of InstaSPIN-FOC and FAST,

The module of "Id PI" convert Id into Vd;

as i know, in a motor, U=I * (R+Ls),since the influence of inductance of coil , Vd and Id exists a certain phase angle θ,

HOW instaspin gain the phase error between Vd and Id ?

  • The InstaSPIN-FOC implements FOC theory to control the d-axis and q-axis reference current directly by transforming the motor three-phase current to d/q-axis frame and using PI regualtor. The FOC doesn't control the Vd and Vq directly and doesn't matter the phase error between Vd and Id, just need to know the rotor angle for the park and -park transformation.

    You may take a look at some textbooks that should have the detailed introduction about FOC theory.