In this paper we analyze the asymptotic stability of a vector control system for an induction motor with short-circuited rotor that contains in its loop a Gopinath observer. The studied control system is based on the direct rotor flux orientation method (DFOC) and the stability study is based upon the linearization theorem around the equilibrium points of the control system, emphasizing the estimated variation domain of the rotor resistance for which the control system remains asymptotically stable when the prescribed speed of the control system is close to zero. The stability study is made in both the continual and discrete cases. The mathematical model of the vector regulating system is made using a value dle–qle linked to stator current. In order to mathematically describe the DFOC control system we will consider the following hypotheses: the static frequency converter (CSF) is assumed to contain a tension inverter; the static frequency converter is considered ideal so that the vector of the command measures is considered to be the entry vector of the induction motor; the dynamic measure transducers are considered ideal; the system and axis transformation blocks are considered dynamically ideal; the mathematical model of the vector control system will be written in an dle–qle axis reference bounded to the stator current.
