Nonlinear influence in the frequency domain: Alternating series

被引：42

作者：

Jing, Xing Jian ^{[1
]}

Lang, Zi Qiang ^{[2
]}

Billings, Stephen A. ^{[2
]}

机构：

[1] Hong Kong Polytech Univ, Dept Mech Engn, Kowloon, Hong Kong, Peoples R China

[2] Univ Sheffield, Dept Automat Control & Syst Engn, Sheffield S1 3JD, S Yorkshire, England

来源：

SYSTEMS & CONTROL LETTERS | 2011年 / 60卷 / 05期

基金：

英国工程与自然科学研究理事会;

关键词：

Nonlinear systems; Volterra series; Alternating series; Output spectrum; RESPONSE FUNCTIONS; VIBRATION; SYSTEMS;

D O I：

10.1016/j.sysconle.2011.01.003

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

The nonlinear influence on system output spectrum is studied for a class of nonlinear systems which have Volterra series expansion. It is shown that under certain conditions the system output spectrum can be expressed in an alternating series with respect to some model parameters which define system nonlinearities. The magnitude of the system output spectrum can therefore be suppressed by exploiting the properties of alternating series. Sufficient (and necessary) conditions in which the output spectrum can be cast into an alternating series are studied. These results reveal a novel frequency-domain insight into the nonlinear influence on a system, and provide a new method for the analysis and design of nonlinear systems in the frequency domain. Examples are given to illustrate the results. (c) 2011 Elsevier B.V. All rights reserved.

引用

页码：295 / 309

页数：15

共 26 条

[1]

[Anonymous], 1991, INTRO THEORY INFINIT

[2]

[Anonymous], 1999, SYSTEM IDENTIFICATIO

[3]

[Anonymous], 1996, Frequency-Domain Methods for Nonlinear Analysis

[4] MAPPING NONLINEAR INTEGRODIFFERENTIAL EQUATIONS INTO THE FREQUENCY-DOMAIN [J].

BILLINGS, SA ;

JONES, JCP .

INTERNATIONAL JOURNAL OF CONTROL, 1990, 52 (04) :863-879

[5] FADING MEMORY AND THE PROBLEM OF APPROXIMATING NONLINEAR OPERATORS WITH VOLTERRA SERIES [J].

BOYD, S ;

CHUA, LO .

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS, 1985, 32 (11) :1150-1161

[6]

George D.A., 1959, 355 MIT RES LAB EL

[7]

Graham D., 1961, ANAL NONLINEAR CONTR

[8] Recent advances in nonlinear passive vibration isolators [J].

Ibrahim, R. A. .

JOURNAL OF SOUND AND VIBRATION, 2008, 314 (3-5) :371-452

[9] Mapping from parametric characteristics to generalized frequency response functions of non-linear systems [J].

Jing, Xing Jian ;

Lang, Zi Qiang ;

Billings, Stephen A. .

INTERNATIONAL JOURNAL OF CONTROL, 2008, 81 (07) :1071-1088

[10] Frequency domain analysis for suppression of output vibration from periodic disturbance using nonlinearities [J].

Jing, Xing Jian ;

Lang, Zi Qiang ;

Billings, Stephen A. ;

Tomlinson, Geofrey R. .

JOURNAL OF SOUND AND VIBRATION, 2008, 314 (3-5) :536-557

← 1 2 3 →