I have been reading the document<MC9S12ZVMMCLUG> recently, it's not particulayly clear about the AMCLIB_BemfObsrvDQ.I hope I can get your help, Thanks！！！
The BEMF observer fits the input voltages and currents to a mathematical model of the
motor. The model mirrors the behavior of the PMSM; see the following equation:
But,The mathematical model of the motor should be the following equation:
The red mark is different.The document explains it as follow:
But I still dont't know why,I hope to get a detailed explanation. Thank you very much!!!
The model introduced in the AppNote uses "extended back-EMF", which is different from the actual EMF. Please refer to the following picture. Full explanation would basically do the same as set of articles on IEEE (https://ieeexplore.ieee.org/search/searchresult.jsp?newsearch=true&queryText=extended%20back%20emf%2...)
I hope it helps,