A frequency method for predicting limit cycle bifurcations

被引：60

作者：

Basso, M

Genesio, R

Tesi, A

机构：

[1] Dipto. di Sistemi e Information, Università di Firenze, 50139 Firenze, Via di S. Marta

来源：

NONLINEAR DYNAMICS | 1997年 / 13卷 / 04期

关键词：

nonlinear systems; feedback systems; bifurcations; limit cycles; harmonic balance;

D O I：

10.1023/A:1008298205786

中图分类号：

TH [机械、仪表工业];

学科分类号：

0802 ;

摘要：

The paper studies the bifurcations of limit cycles in a rather general class of nonlinear dynamic systems. Relying on the classical harmonic balance approach as applied in control engineering neat frequency conditions for such bifurcations are derived. These results, approximate in nature, make clear the structural mechanism of the considered phenomena and can be applied to predict the occurrence of bifurcations as a function of system parameters. The application to several examples of different complexity shows the simplicity and accuracy of the proposed method for solving complicated problems of nonlinear dynamics.

引用

页码：339 / 360

页数：22

共 20 条

[1] [Anonymous], INT J BIFURCATION CH
[2] Arnol'd VI, 1983, GEOMETRICAL METHODS
[3] Atherton D. P., 1975, NONLINEAR CONTROL EN
[4] Gelb A, 1968, Multiple-input describing functions and nonlinear system design
[5] GENESIO R, 1993, PROCEEDINGS OF THE 32ND IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, P492, DOI 10.1109/CDC.1993.325099
[6] Genesio R, 1995, PROCEEDINGS OF THE 34TH IEEE CONFERENCE ON DECISION AND CONTROL, VOLS 1-4, P2904, DOI 10.1109/CDC.1995.478583
[7] A HARMONIC BALANCE APPROACH FOR CHAOS PREDICTION: CHUA'S CIRCUIT
Genesio, R.
Tesi, A.
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 1992, 2 (01): : 61 - 79
[8] A FREQUENCY APPROACH FOR ANALYZING AND CONTROLLING CHAOS IN NONLINEAR CIRCUITS
GENESIO, R
TESI, A
VILLORESI, F
[J]. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-FUNDAMENTAL THEORY AND APPLICATIONS, 1993, 40 (11): : 819 - 828
[9] HARMONIC-BALANCE METHODS FOR THE ANALYSIS OF CHAOTIC DYNAMICS IN NONLINEAR-SYSTEMS
GENESIO, R
TESI, A
[J]. AUTOMATICA, 1992, 28 (03) : 531 - 548
[10] Genesio R., 1995, Proceedings of the Third European Control Conference. ECC 95, P3035

← 1 2 →