Stability and Hopf bifurcation in an hexagonal governor system

被引：21

作者：

Sotomayor, Jorge ^{[2
]}

Mello, Luis Fernando ^{[1
]}

Braga, Denis de Carvalho ^{[3
]}

机构：

[1] Univ Fed Itajuba, Inst Ciencias Exatas, BR-37500903 Itajuba, MG, Brazil

[2] Univ Sao Paulo, Inst Matemat & Estatist, BR-05508090 Sao Paulo, SP, Brazil

[3] Univ Fed Itajuba, Inst Sistemas Eletr & Energia, BR-37500903 Itajuba, MG, Brazil

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2008年 / 9卷 / 03期

关键词：

hexagonal governor; Watt governor; Hopf bifurcation; stability; periodic orbit;

D O I：

10.1016/j.nonrwa.2007.01.007

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study the Lyapunov stability and the Hopf bifurcation in a system coupling an hexagonal centrifugal governor with a steam engine. Here are given sufficient conditions for the stability of the equilibrium state and of the bifurcating periodic orbit. These conditions are expressed in terms of the physical parameters of the system, and hold for parameters outside a variety of codimension two. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：889 / 898

页数：10

共 16 条

[1]

ALHUMADI A, 1985, I MATH APPL, V21, P133

[2]

Andronov A.A., 1973, Theory of bifurcations of dynamic systems on a plane

[3] Watt steam governor stability [J].

Denny, M .

EUROPEAN JOURNAL OF PHYSICS, 2002, 23 (03) :339-351

[4] DEGENERATE HOPF-BIFURCATION FORMULAS AND HILBERTS 16TH PROBLEM [J].

FARR, WW ;

LI, CZ ;

LABOURIAU, IS ;

LANGFORD, WF .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (01) :13-30

[5] A short history of hydropower control [J].

Fasol, KH .

IEEE CONTROL SYSTEMS MAGAZINE, 2002, 22 (04) :68-76

[6]

Gasull A, 2001, COMPUT APPL MATH, V20, P149

[7]

Hassard B., 1981, Theory and Applications of Hopf Bifurcation

[8]

Kuznetsov Y. A., 2004, ELEMENTS APPL BIFURC

[9] DEVELOPMENT OF FREQUENCY-RESPONSE METHODS IN AUTOMATIC-CONTROL [J].

MACFARLANE, AGJ .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1979, 24 (02) :250-265

[10]

Maxwell JC, 1868, P R SOC LONDON, V16

← 1 2 →