Observability conditions of induction motors at low frequencies

The paper studies the observability conditions for the induction motor. We first review the sufficient condition derived by from the classical geometrical analysis, then we present some particular case where these conditions turn out to be also necessary. The purpose of the paper is to clarify observability problems found in particular when the machine is operating at low frequencies without angular velocity sensor. The observability analysis also clarifies the fact that the observability problems are physically due to low frequency operation conditions, rather than to low rotational speed operation (even if these two cases coincide in absence of torque load).