Extended complex Kalman filter for sensorless control of an induction motor

This paper deals with the design of an extended complex Kalman filter (ECKF) for estimating the state of an induction motor (IM) model, and for sensorless control of systems employing this type of motor as an actuator. A complex-valued model is adopted that simultaneously allows a simpler observability analysis of the system and a more effective state estimation. The observability analysis of this model is first performed by assuming that a third order ECKF has to be designed, by neglecting the mechanical equation of the IM model, which is a valid hypothesis when the motor is operated at constant rotor speed. It is shown that this analysis is more effective and easier than the one performed on the corresponding real-valued model, as it allows the observability conditions to be directly obtained in terms of stator current and rotor flux complex-valued vectors. Necessary observability conditions are also obtained along with the well-known sufficient ones. It is also shown that the complex-valued implementation allows a reduction of 35% in the computation time w.r.t. the standard real-valued one, which is obtained thanks to the lower dimensions of the matrices of the ECKF w.r.t. the ones of the real-valued implementation and the fact that no matrix inversion is required. The effectiveness of the proposed ECKF is shown by means of simulation in Matlab/Simulink environment and through experiments on a real low-power drive.