Y.А. Gelozhe, A.V. Semenov, D.S Tokarev, А.А. Krechetov

Phase-locked loop system (PLL) functioning under complex conditions, when frequency shifts of the controlled active oscillator exceed the capture range bounds, state of rest requirement becomes a stochastic event, and occurrence of significant short-term disturbance interrupts, breaking off the synchronization even for a short time, is considered. The aim of the present work is to develop complementary control of transient processes, providing with probability equal to «1», sync mode establishment at initial detuning similar to capture range bounds in PLL with saw-tooth waveform of the pulse-phase discriminator (PPD) and high persistence of the low-pass filter (LPF). Problem statement. Nonlinear differential equation of PLL is given. The solution of this equation for the phase plane at initial detuning, similar to capture range bounds, is well known. There is an invariant manifold of phase portrait, interior point of which is the pinpoint target attractor. The problem is to transfer the representation point from random initial conditions to the domain of attraction of the target attractor and provide the sync mode establishment with probability equal to «1» by means of complementary control. The task of bringing the system into the state of rest is solved in the phase plane. With the aim of common control laws realization the domain of attraction of the target attractor as a segment of a vertical straight line is introduced. Alignment of the representation points on this line is executed by complementary relay control.