Nonlinear Dynamics

, Volume 93, Issue 2, pp 571–583 | Cite as

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

  • Dimitri D. A. Costa
  • Marcelo A. Savi
Original Paper


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.


Nonlinear dynamics Chaos Shape memory alloys Pendulum Control 



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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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Center for Nonlinear Mechanics, COPPE – Department of Mechanical EngineeringUniversidade Federal do Rio de JaneiroRio de JaneiroBrazil

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