In this paper we analyze the asymptotic
stability of a vector control system for a squirrel-cage
induction motor 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 dλe − qλe 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 dλe − qλe axis reference bounded to the
stator current.