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Border-Collision Bifurcations in Automatic Control Systems with Two-Side Sinusoidal Unipolar Reversible Pulse-Width Modulation

Andriyanov, A.I.

Abstract. This paper considers nonlinear dynamics of automatic control system based on two-side sinusoidal unipolar reversible modulation. Mathematical simulation of the considered system is carried out. The first bifurcation borders in two-parameter state space has been analyzed, that is relevant to the practical side. The paper demonstrates, that in the considered system the first bifurcation borders are critical, as they are related to hard bifurcations. A bifurcation, which corresponds to the variation of the widely-known border-collision bifurcation, was detected at large control signal values. Being characterized by its unique features this bifurcation variation is of great theoretical interest.

Keywords: automatic control system, sinusoidal pulse-width modulation, power inverter, bifurcation, nonlinear dynamics

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