Chaos control of an SMA–pendulum system using thermal actuation with extended time-delayed feedback approach

Dimitri Danulussi Alves Costa; Marcelo A. Savi

doi:10.1007/s11071-018-4210-5

Chaos control of an SMA–pendulum system using thermal actuation with extended time-delayed feedback approach

Dimitri Danulussi Alves Costa, Marcelo A. Savi (Corresponding Author)

Engineering

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

Abstract

Chaos control has been applied to a variety of systems exploiting system dynamics characteristics that present advantages of low energy consumption when compared with regular controllers. This work deals with the chaos control of a smart system composed of a pendulum coupled with shape memory alloy (SMA) elements. SMAs belong to smart material class being employed in several applications due to their adaptive behavior. The basic idea is to apply the extended time-delayed feedback control on an SMA–pendulum system by exploring the SMA temperature-dependent behavior. Actuation constraints are considered based on heat transfer equations. Controller parameters are estimated using Floquet theory employed to analyze controlled unstable periodic orbits (UPOs). Results show the capability of the thermal controller to perform UPO stabilization. Energy consumption and stabilization time are discussed establishing a comparison with an ideal controller, without heat transfer constraints.

Original language	English
Pages (from-to)	571–583
Number of pages	13
Journal	Nonlinear Dynamics
Volume	93
Issue number	2
Early online date	24 Mar 2018
DOIs	https://doi.org/10.1007/s11071-018-4210-5
Publication status	Published - Jul 2018

Keywords

nonlinear dynamics
chaos
shape memory alloys
pendulum
control

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Cite this

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title = "Chaos control of an SMA–pendulum system using thermal actuation with extended time-delayed feedback approach",

abstract = "Chaos control has been applied to a variety of systems exploiting system dynamics characteristics that present advantages of low energy consumption when compared with regular controllers. This work deals with the chaos control of a smart system composed of a pendulum coupled with shape memory alloy (SMA) elements. SMAs belong to smart material class being employed in several applications due to their adaptive behavior. The basic idea is to apply the extended time-delayed feedback control on an SMA–pendulum system by exploring the SMA temperature-dependent behavior. Actuation constraints are considered based on heat transfer equations. Controller parameters are estimated using Floquet theory employed to analyze controlled unstable periodic orbits (UPOs). Results show the capability of the thermal controller to perform UPO stabilization. Energy consumption and stabilization time are discussed establishing a comparison with an ideal controller, without heat transfer constraints.",

keywords = "nonlinear dynamics, chaos, shape memory alloys, pendulum, control",

author = "{Danulussi Alves Costa}, Dimitri and Savi, {Marcelo A.}",

note = "The authors would like to acknowledge the support of the Brazilian Research Agencies CNPq, CAPES and FAPERJ. The Air Force Office of Scientific Research (AFOSR) is also acknowledged. ",

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T1 - Chaos control of an SMA–pendulum system using thermal actuation with extended time-delayed feedback approach

AU - Danulussi Alves Costa, Dimitri

AU - Savi, Marcelo A.

N1 - The authors would like to acknowledge the support of the Brazilian Research Agencies CNPq, CAPES and FAPERJ. The Air Force Office of Scientific Research (AFOSR) is also acknowledged.

PY - 2018/7

Y1 - 2018/7

N2 - Chaos control has been applied to a variety of systems exploiting system dynamics characteristics that present advantages of low energy consumption when compared with regular controllers. This work deals with the chaos control of a smart system composed of a pendulum coupled with shape memory alloy (SMA) elements. SMAs belong to smart material class being employed in several applications due to their adaptive behavior. The basic idea is to apply the extended time-delayed feedback control on an SMA–pendulum system by exploring the SMA temperature-dependent behavior. Actuation constraints are considered based on heat transfer equations. Controller parameters are estimated using Floquet theory employed to analyze controlled unstable periodic orbits (UPOs). Results show the capability of the thermal controller to perform UPO stabilization. Energy consumption and stabilization time are discussed establishing a comparison with an ideal controller, without heat transfer constraints.

AB - Chaos control has been applied to a variety of systems exploiting system dynamics characteristics that present advantages of low energy consumption when compared with regular controllers. This work deals with the chaos control of a smart system composed of a pendulum coupled with shape memory alloy (SMA) elements. SMAs belong to smart material class being employed in several applications due to their adaptive behavior. The basic idea is to apply the extended time-delayed feedback control on an SMA–pendulum system by exploring the SMA temperature-dependent behavior. Actuation constraints are considered based on heat transfer equations. Controller parameters are estimated using Floquet theory employed to analyze controlled unstable periodic orbits (UPOs). Results show the capability of the thermal controller to perform UPO stabilization. Energy consumption and stabilization time are discussed establishing a comparison with an ideal controller, without heat transfer constraints.

KW - nonlinear dynamics

KW - chaos

KW - shape memory alloys

KW - pendulum

KW - control

U2 - 10.1007/s11071-018-4210-5

DO - 10.1007/s11071-018-4210-5

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JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

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ER -

Chaos control of an SMA–pendulum system using thermal actuation with extended time-delayed feedback approach

Abstract

Keywords

UN SDGs

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