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UDC 621.01.512

FORCED SYNCHRONIZATION OF PHASE SYSTEMS AUTOMOTIVE EQUIPMENT WITH LANDING

S. S. Mamonov, PhD (physics and mathematics sciences), full professor of the department of mathematics and methods of teaching mathematical disciplines, RSU named after S.A. Yesenin, Ryazan; This email address is being protected from spambots. You need JavaScript enabled to view it.
A. O. Kharlamova, graduate student of the department of mathematics and methods of teaching mathematical disciplines, RSU named after S.A. Yesenin, Ryazan; This email address is being protected from spambots. You need JavaScript enabled to view it.

We consider a mathematical model of phase-locked loop (PLL) with delay, in the case of a second-order fractional-rational integrating filter. For the PLL system, conditions for the existence of several quasisynchronous regimes that determine phase-locking regimes have been obtained. The effect of delay on phase multistability of the system is analyzed. A comparative analysis of quasisynchronous regimes obtained is shown on the basis of their multiplicative characteristics. The aim of the paper is to develop a numerical-analytical approach for determining the conditions for the existence of quasisynchronous regimes of phase systems corresponding to the first-order limiting cycles of a system of third-order differential equations with a cylindrical phase space, developing an algorithm for finding unstable limit cycles, determining the lowpass filter and delay coefficients for realization in the system of PLL phase-locked loop.

Key words: phase systems, phase-locked loop, dynamic modes, quasi-synchronous modes, synchronization, limit cycles, rotation of a vector field, multipliers.

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