Reconfiguring smart structures using approximate heteroclinic connections

Jiaying Zhang, Colin R McInnes

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

A new method is investigated to reconfigure smart structures using the technique of polynomial series to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to first approximate the heteroclinic connection between two equal-energy, unstable equilibrium points, and then develop an inverse method to control the dynamics of the system to track the reference polynomial trajectory. It is found that high-order polynomials can provide a good approximation to heteroclinic connections and provide an efficient means of generating such trajectories. The method is used first in a simple smart structure model to illustrate the method and is then extended to a more complex model where the numerical generation of true heteroclinic connections is difficult. It is envisaged that being computationally efficient, the method could form the basis for real-time reconfiguration of smart structures using heteroclinic connections between equal-energy, unstable configurations.

LanguageEnglish
Article number105034
Number of pages16
JournalSmart Materials and Structures
Volume24
Issue number10
DOIs
Publication statusPublished - 23 Sep 2015

Fingerprint

smart structures
Intelligent structures
polynomials
Polynomials
Trajectories
trajectories
energy
configurations
approximation

Keywords

  • feedback linearization
  • heteroclinic connection
  • inverse method
  • polynomial series
  • reconfiguring smart structures

Cite this

@article{2f078ebf09df46ad814c54ac6c11d18e,
title = "Reconfiguring smart structures using approximate heteroclinic connections",
abstract = "A new method is investigated to reconfigure smart structures using the technique of polynomial series to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to first approximate the heteroclinic connection between two equal-energy, unstable equilibrium points, and then develop an inverse method to control the dynamics of the system to track the reference polynomial trajectory. It is found that high-order polynomials can provide a good approximation to heteroclinic connections and provide an efficient means of generating such trajectories. The method is used first in a simple smart structure model to illustrate the method and is then extended to a more complex model where the numerical generation of true heteroclinic connections is difficult. It is envisaged that being computationally efficient, the method could form the basis for real-time reconfiguration of smart structures using heteroclinic connections between equal-energy, unstable configurations.",
keywords = "feedback linearization, heteroclinic connection, inverse method, polynomial series, reconfiguring smart structures",
author = "Jiaying Zhang and McInnes, {Colin R}",
year = "2015",
month = "9",
day = "23",
doi = "10.1088/0964-1726/24/10/105034",
language = "English",
volume = "24",
journal = "Smart Materials and Structures",
issn = "0964-1726",
number = "10",

}

Reconfiguring smart structures using approximate heteroclinic connections. / Zhang, Jiaying; McInnes, Colin R.

In: Smart Materials and Structures, Vol. 24, No. 10, 105034, 23.09.2015.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Reconfiguring smart structures using approximate heteroclinic connections

AU - Zhang, Jiaying

AU - McInnes, Colin R

PY - 2015/9/23

Y1 - 2015/9/23

N2 - A new method is investigated to reconfigure smart structures using the technique of polynomial series to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to first approximate the heteroclinic connection between two equal-energy, unstable equilibrium points, and then develop an inverse method to control the dynamics of the system to track the reference polynomial trajectory. It is found that high-order polynomials can provide a good approximation to heteroclinic connections and provide an efficient means of generating such trajectories. The method is used first in a simple smart structure model to illustrate the method and is then extended to a more complex model where the numerical generation of true heteroclinic connections is difficult. It is envisaged that being computationally efficient, the method could form the basis for real-time reconfiguration of smart structures using heteroclinic connections between equal-energy, unstable configurations.

AB - A new method is investigated to reconfigure smart structures using the technique of polynomial series to approximate a true heteroclinic connection between unstable equilibria in a smart structure model. We explore the use of polynomials of varying order to first approximate the heteroclinic connection between two equal-energy, unstable equilibrium points, and then develop an inverse method to control the dynamics of the system to track the reference polynomial trajectory. It is found that high-order polynomials can provide a good approximation to heteroclinic connections and provide an efficient means of generating such trajectories. The method is used first in a simple smart structure model to illustrate the method and is then extended to a more complex model where the numerical generation of true heteroclinic connections is difficult. It is envisaged that being computationally efficient, the method could form the basis for real-time reconfiguration of smart structures using heteroclinic connections between equal-energy, unstable configurations.

KW - feedback linearization

KW - heteroclinic connection

KW - inverse method

KW - polynomial series

KW - reconfiguring smart structures

UR - http://www.scopus.com/inward/record.url?scp=84942884241&partnerID=8YFLogxK

UR - http://iopscience.iop.org/0964-1726

U2 - 10.1088/0964-1726/24/10/105034

DO - 10.1088/0964-1726/24/10/105034

M3 - Article

VL - 24

JO - Smart Materials and Structures

T2 - Smart Materials and Structures

JF - Smart Materials and Structures

SN - 0964-1726

IS - 10

M1 - 105034

ER -