Русская версия
ISSN 1817-2172, рег. Эл. № ФС77-39410, ВАК

Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

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Nonlinear Dynamics of the Primary Oscillation Circuit of a Mems Gyroscope Under the Action of Phase-locked Loop and Automatic Gain Control Systems

Author(s):

Vasilisa Sergeevna Igumnova

postgraduate student of the Higher School of Mechanics and Control Processes,
Institute of Physics and Mechanics, SPbPU

igumnovavs@mail.ru

Alexey Vyacheslavovich Lukin

PhD, Associate Professor of the Higher School of Mechanics and Control Processes,
Institute of Physics and Mechanics, SPbPU

lukin_av@spbstu.ru

Ivan Alekseevich Popov

Leading Engineer of the Advanced Engineering School "Digital Engineering"

popov_ia@spbstu.ru

Nikolay Vladimirovich Kuznetsov

Doctor of physico-mathematical sciences, Head of the Department of Applied Cybernetics, St. Petersburg State University,
Head of the Laboratory of Information and Control Systems of the Institute for Problems in
Mechanical Engineering of the Russian Academy of Sciences (IPMash RAS)

nkuznetsov239@mail.ru

Mikhail Yurievich Lobachev

postgraduate student, Department of Applied Cybernetics,
Faculty of Mathematics and Mechanics, St. Petersburg State University

Yakov Valerievich Belyaev

PhD, Head of department, Concern "CSRI Elektropribor"

ybelyaev@eprib.ru

Abstract:

In this work, we study the dynamics of primary oscillations of a high-Q micromechanical resonator - a sensitive element of an RR-type MEMS gyroscope - under the action of various implementations of a phase-locked loop system operating in conjunction with an automatic gain control system for an electrostatic drive. The study of the dynamics of the object is carried out both numerically and analytically - using the averaging method. Conditions for the stability of a stationary regime in a linear approximation are obtained. The questions of accuracy of various methods of numerical solution of differential equations of the circuit of primary oscillations are considered. The influence of the mechanical nonlinearity of the resonator on the dynamics of the resonator and the control system has been studied. An implementation of a low-order PLL circuit that does not contain a double-frequency spurious signal at the output of the phase detector is proposed. The output characteristics of control systems (speed, capture bandwidth, etc.) are analyzed and qualitative conclusions are drawn about the features of the interaction between the dynamics of a mechanical oscillatory link and the PLL-ARC circuit.

Keywords

References:

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