Vibration Stability of the Impulse System of the Electric Drive Control

Abstract

Purpose of reseach is Study of vibration stability of the impulse system of direct current electric drive in order to ensure operating modes with specified dynamic characteristics. Methods. The stability analysis of periodic solutions of differential equations with discontinuous right-hand side is reduced to the problem of studying local stability of fixed map points. Results. The analysis of stability is carried out depending on the supply voltage of the electric drive and the gain of the correcting link in the feedback circuit. It is revealed that the boundary of the stability region on the plane of the variable parameters has a pronounced extremum in the form of a maximum at the bifurcation point of codimension two, also called the resonance point 1: 2. On one side of this point, the stability region is bounded by the NeimarkSacker bifurcation line, and on the other, by the period-doubling bifurcation line. This means that with a change in the parameters, the radius of the stability region first increases, reaching a maximum at the resonance point 1: 2, and then decreases. This important conclusion can be used in optimization calculations. Conclusion. The analysis of the vibration stability of the impulse system of direct current electric drive, the behavior of which is described by differential equations of the discontinuous right-hand side, is carried out. The problem of finding periodic solutions to differential equations is reduced to the problem of finding fixed points of the map. The fixed points of the map satisfy a system of nonlinear equations, which was solved numerically by the NewtonRaphson method. The stability of periodic solutions of differential equations corresponds to the stability of fixed points of the corresponding map. The studies were carried out with variation of the gain in the feedback circuit and the supply voltage. It is revealed that the loss of a fixed point occurs through the supercritical Neimark-Sacker bifurcation, when the complex-conjugate pair of multipliers leaves the unit circle when the parameters change. However, with an increase in the supply voltage, the Neimark-Saker bifurcation boundary passes into the perioddoubling bifurcation boundary at the 1: 2 resonance point.