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RESEARCH PRODUCT

Nonlinear Analysis of Phase-Locked Loop (PLL): Global Stability Analysis, Hidden Oscillations and Simulation Problems

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In the middle of last century the problem of analyzing hidden oscillations arose in automatic control. In 1956 M. Kapranov considered a two-dimensional dynamical model of phase locked-loop (PLL) and investigated its qualitative behavior. In these investigations Kapranov assumed that oscillations in PLL systems can be self-excited oscillations only. However, in 1961, N. Gubar’ revealed a gap in Kapranov’s work and showed analytically the possibility of the existence of another type of oscillations, called later by the authors hidden oscillations, in a phase-locked loop model: from a computational point of view the system considered was globally stable (all the trajectories tend to equilibria), but, in fact, there was only a bounded domain of attraction. In this review, following ideas of N. Gubar’, the qualitative analysis of hidden oscillation bifurcation in a two-dimensional model of phase-locked loop is considered.