In the paper we present the stability study of the Kalman estimator used in a vectorial drive system of an induction motor with short-circuited rotor. We consider that the control system for speed is a vectorial system with direct orientation after the rotor flux (DFOC). Although there are suggestive experimental results, the implementation of such a system containing a Kalman filter generates serious problems because of the tuning of the covariant matrixes of the measurement noise and the process noise. Also the solving of the Riccati equations in real time is difficult. These problems, as well as the simplifier hypothesis from the determination of the mathematical model on the states space of the induction motor and the modification of the rotor resistance by temperature lead to the decrease of the estimator and control system performances. Therefore you must implement an algorithm for research of the estimator stability. This algorithm has to hold count of the sampling step of sundries processors used in the drives command. The stability study is done by the determination of the transition matrix poles.
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.
