Sufficient global stability condition for a model of the synchronous electric motor under nonlinear load moment

Abstract

Systems of differential equations describing the dynamics of synchronous electric machines are periodic in the angular variable, and so they have a denumerable set of steady solutions corresponding to the operating mode of steady rotation of the rotor. Such system is called to be of gradient type if any solution of this system tends with time to one of these steady rotations (equilibrium states). The gradient type system is said to be globally stable when it has only one locally asymptotically stable equilibrium state on the period of the angular variable. In the article the subject of investigation is the Leonov Zaretskiy model of the synchronous electric motor (Vestnik St.Petersburg University. Mathematics, 45(4), 2012), which includes differential equations for electric currents in the damper and excitation windings of the rotor. The authors of this model proved that it is globally stable in the case of zero load moment. In the present paper the load moment is assumed to be a nonlinear function of the angular velocity of the rotor, having a linear estimate. Easily verifiable sufficient condition of global stability is obtained for this case.