This paper proposes new mathematical models of an induction motor that generates torque precisely under vector control. The proposed models for the controlled motor have desirable features in respect to preciseness and compactness. They guarantee the same relation between the stator voltage and current signals as does the conventional T-type model consisting of five parameters. The number of parameters forming the new models is reduced to four, such as stator resistance, inverse of rotor time constant, stator inductance, and stator total leakage inductance, or another set of four related uniquely to them. The parameters are uniquely determined by the stator signals, in terms of which all controller parameters of the vector control system can be designed. ©1998 Scripta Technica, Electr Eng Jpn, 126(2): 4855, 1999