CONTROL-BASED CONTINUATION OF UNSTABLE PERIODIC ORBITS

被引：0

作者：

Sieber, Jan ^{[1
]}

Krauskopf, Bernd ^{[1
]}

Wagg, David ^{[1
]}

Neild, Simon ^{[1
]}

Gonzalez-Buelga, Alicia ^{[1
]}

机构：

[1] Univ Portsmouth, Dept Math, Portsmouth PO1 3HF, Hants, England

来源：

PROCEEDINGS OF ASME INTERNATIONAL DESIGN ENGINEERING TECHNICAL CONFERENCES AND COMPUTERS AND INFORMATION IN ENGINEERING CONFERENCE, VOL 4, PTS A-C | 2010年

关键词：

BIFURCATION-ANALYSIS; PENDULUM; SYSTEMS; CHAOS;

D O I：

暂无

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We present an experimental procedure to track periodic orbits through a fold (saddle-node) bifurcation, and demonstrate it with a parametrically excited pendulum experiment where the control parameter is the amplitude of the excitation. Specifically we track the initially stable period-one rotation of the pendulum through its fold bifurcation and along the unstable branch. The fold bifurcation itself corresponds physically to the minimal amplitude that is able to support sustained rotation. Our scheme is based on a modification of time-delayed feedback in a continuation setting, and we show for an idealized model that it converges with the same efficiency as classical proportional-plus-derivative control.

引用

页码：331 / 340

页数：10

共 50 条

[1] Control-Based Continuation of Unstable Periodic Orbits
Sieber, Jan
Krauskopf, Bernd
Wagg, David
Neild, Simon
Gonzalez-Buelga, Alicia
[J]. JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS, 2011, 6 (01):
[2] Large basins of attraction for control-based continuation of unstable periodic states
Kruse, Niklas
Wallner, Hannes
Dittus, Anna
Boettcher, Lukas
Barke, Ingo
Speller, Sylvia
Starke, Jens
Just, Wolfram
[J]. NONLINEAR DYNAMICS, 2024,
[3] Control-based continuation of periodic orbits with a time-delayed difference scheme
Sieber, J.
Krauskopf, B.
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2007, 17 (08): : 2579 - 2593
[4] Adaptive control designs for control-based continuation of periodic orbits in a class of uncertain linear systems
Li, Yang
Dankowicz, Harry
[J]. NONLINEAR DYNAMICS, 2021, 103 (03) : 2563 - 2579
[5] Adaptive control designs for control-based continuation of periodic orbits in a class of uncertain linear systems
Yang Li
Harry Dankowicz
[J]. Nonlinear Dynamics, 2021, 103 : 2563 - 2579
[6] Chaos control based on stability Transformation method for unstable periodic orbits
Kawai, Yuki
Tsubone, Tadashi
[J]. IEICE NONLINEAR THEORY AND ITS APPLICATIONS, 2012, 3 (02): : 246 - 256
[7] Control-based continuation for investigating nonlinear experiments
Barton, David A. W.
Mann, Brian P.
Burrow, Stephen G.
[J]. JOURNAL OF VIBRATION AND CONTROL, 2012, 18 (04) : 509 - 520
[8] Entrainment control of chaos near unstable periodic orbits
Mettin, R
[J]. IUTAM SYMPOSIUM ON INTERACTION BETWEEN DYNAMICS AND CONTROL IN ADVANCED MECHANICAL SYSTEMS, 1997, 52 : 231 - 238
[9] ISOLATED UNSTABLE PERIODIC ORBITS
CHURCHIL.RC
PECELLI, G
ROD, DL
[J]. NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1974, 21 (01): : A134 - A134
[10] ISOLATED UNSTABLE PERIODIC ORBITS
CHURCHILL, RC
PECELLI, G
ROD, DL
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1975, 17 (02) : 329 - 348

← 1 2 3 4 5 →