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The pull-in range and a counterexample to the Egan conjecture for the fourth-order type 2 analog PLL. / Kuznetsov, N. V.; Lobachev, M. Y.; Yuldashev, M. V.; Yuldashev, R. V.; Kuznetsov, V. O.; Kolumbán, G.; Chechurin, L. S.

In: IFAC-PapersOnLine, Vol. 54, No. 21, 01.12.2021, p. 73-78.

Research output: Contribution to journal › Conference article › peer-review

Harvard

Kuznetsov, NV, Lobachev, MY, Yuldashev, MV, Yuldashev, RV, Kuznetsov, VO, Kolumbán, G & Chechurin, LS 2021, 'The pull-in range and a counterexample to the Egan conjecture for the fourth-order type 2 analog PLL', IFAC-PapersOnLine, vol. 54, no. 21, pp. 73-78. https://doi.org/10.1016/j.ifacol.2021.12.013

APA

Kuznetsov, N. V., Lobachev, M. Y., Yuldashev, M. V., Yuldashev, R. V., Kuznetsov, V. O., Kolumbán, G., & Chechurin, L. S. (2021). The pull-in range and a counterexample to the Egan conjecture for the fourth-order type 2 analog PLL. IFAC-PapersOnLine, 54(21), 73-78. https://doi.org/10.1016/j.ifacol.2021.12.013

Vancouver

Kuznetsov NV, Lobachev MY, Yuldashev MV, Yuldashev RV, Kuznetsov VO, Kolumbán G et al. The pull-in range and a counterexample to the Egan conjecture for the fourth-order type 2 analog PLL. IFAC-PapersOnLine. 2021 Dec 1;54(21):73-78. https://doi.org/10.1016/j.ifacol.2021.12.013

Author

Kuznetsov, N. V. ; Lobachev, M. Y. ; Yuldashev, M. V. ; Yuldashev, R. V. ; Kuznetsov, V. O. ; Kolumbán, G. ; Chechurin, L. S. / The pull-in range and a counterexample to the Egan conjecture for the fourth-order type 2 analog PLL. In: IFAC-PapersOnLine. 2021 ; Vol. 54, No. 21. pp. 73-78.

BibTeX

@article{f944e9debbc84e9b98ccab365538053c,
title = "The pull-in range and a counterexample to the Egan conjecture for the fourth-order type 2 analog PLL",
abstract = "Phase-locked loop is classical nonlinear control system for frequency and phase synchronization in electrical circuits. According to the Egan conjecture, the type 2 loops have an infinitely large pull-in range. This article reconsider the pull-in problem for the fourth order type 2 PLLs. The global stability domain is estimated by applying Lyapunov direct method for the cylindrical phase space. An analytical estimate of the pull-in range of the fourth-order PLL is presented for the first time in the literature. Parameters violating the pull-in conditions are determined by computer simulation. The results have revealed that stable oscillations may develop in the higher-order type 2 PLL in steady-state which is a clear counterexample to the Egan's conjecture.",
keywords = "analog PLL, cylindrical phase space, Egan conjecture, Egan problem on the pull-in range, global stability, harmonic balance method, Lyapunov functions, nonlinear analysis, Phase-locked loop, phase-locked loop, PLL, pull-in range, type 2, type II",
author = "Kuznetsov, {N. V.} and Lobachev, {M. Y.} and Yuldashev, {M. V.} and Yuldashev, {R. V.} and Kuznetsov, {V. O.} and G. Kolumb{\'a}n and Chechurin, {L. S.}",
note = "Publisher Copyright: Copyright {\textcopyright} 2021 The Authors.; 2021 Control Conference Africa, CCA 2021 ; Conference date: 07-12-2021 Through 08-12-2021",
year = "2021",
month = dec,
day = "1",
doi = "10.1016/j.ifacol.2021.12.013",
language = "English",
volume = "54",
pages = "73--78",
journal = "IFAC-PapersOnLine",
issn = "2405-8963",
publisher = "Elsevier",
number = "21",

}

RIS

TY - JOUR

T1 - The pull-in range and a counterexample to the Egan conjecture for the fourth-order type 2 analog PLL

AU - Kuznetsov, N. V.

AU - Lobachev, M. Y.

AU - Yuldashev, M. V.

AU - Yuldashev, R. V.

AU - Kuznetsov, V. O.

AU - Kolumbán, G.

AU - Chechurin, L. S.

N1 - Publisher Copyright: Copyright © 2021 The Authors.

PY - 2021/12/1

Y1 - 2021/12/1

N2 - Phase-locked loop is classical nonlinear control system for frequency and phase synchronization in electrical circuits. According to the Egan conjecture, the type 2 loops have an infinitely large pull-in range. This article reconsider the pull-in problem for the fourth order type 2 PLLs. The global stability domain is estimated by applying Lyapunov direct method for the cylindrical phase space. An analytical estimate of the pull-in range of the fourth-order PLL is presented for the first time in the literature. Parameters violating the pull-in conditions are determined by computer simulation. The results have revealed that stable oscillations may develop in the higher-order type 2 PLL in steady-state which is a clear counterexample to the Egan's conjecture.

AB - Phase-locked loop is classical nonlinear control system for frequency and phase synchronization in electrical circuits. According to the Egan conjecture, the type 2 loops have an infinitely large pull-in range. This article reconsider the pull-in problem for the fourth order type 2 PLLs. The global stability domain is estimated by applying Lyapunov direct method for the cylindrical phase space. An analytical estimate of the pull-in range of the fourth-order PLL is presented for the first time in the literature. Parameters violating the pull-in conditions are determined by computer simulation. The results have revealed that stable oscillations may develop in the higher-order type 2 PLL in steady-state which is a clear counterexample to the Egan's conjecture.

KW - analog PLL

KW - cylindrical phase space

KW - Egan conjecture

KW - Egan problem on the pull-in range

KW - global stability

KW - harmonic balance method

KW - Lyapunov functions

KW - nonlinear analysis

KW - Phase-locked loop

KW - phase-locked loop

KW - PLL

KW - pull-in range

KW - type 2

KW - type II

UR - http://www.scopus.com/inward/record.url?scp=85133739835&partnerID=8YFLogxK

U2 - 10.1016/j.ifacol.2021.12.013

DO - 10.1016/j.ifacol.2021.12.013

M3 - Conference article

AN - SCOPUS:85133739835

VL - 54

SP - 73

EP - 78

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 21

T2 - 2021 Control Conference Africa, CCA 2021

Y2 - 7 December 2021 through 8 December 2021

ER -

ID: 87582565