, Volume 49, Issue 8, pp 1859–1867 | Cite as

Nonlinear control in an electromechanical transducer with chaotic behaviour

  • José Manoel Balthazar
  • Dailhane Grabowski Bassinello
  • Angelo Marcelo Tusset
  • Átila Madureira Bueno
  • Bento Rodrigues de Pontes Junior
Nonlinear Dynamics and Control of Composites for Smart Engi design


The electromechanical transducer considered in this work is composed of a mechanical oscillator linked to an electronic circuit. Simulations results have determined that for some combination of parameters the electromechanical system is subject to chaotic motion with resonant transient behavior, and after the resonant transient the mechanical system (MS) synchronizes with the electrical system (ES). In order to improve the transient response, avoiding both the chaotic and resonant behaviors, a nonlinear control system is designed, a feedback control strategy is used to drive the system into the desired periodic orbit, and a nonlinear feedforward strategy is used to keep the system into the periodic orbit, obtained by the Fourier series. Two control techniques are used and compared, namely: the state dependent Ricatti equation and the optimal linear feedback control. Numerical simulations results are shown in order to compare the results, considering parametric uncertainties. Additionally, the energy transfer “pumping” between the ES and the MS is also analysed.


Electromechanical transducer Chaos, SDRE control OLFC, control Energy transfer 



The authors acknowledge financial support by FUNDUNESP-GRANT 021/13-DFP, São Paulo Research Foundation—FAPESP (grant: 13/04101-6) and CNPq-both Brazilian research funding agencies.


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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • José Manoel Balthazar
    • 1
  • Dailhane Grabowski Bassinello
    • 2
  • Angelo Marcelo Tusset
    • 3
  • Átila Madureira Bueno
    • 4
  • Bento Rodrigues de Pontes Junior
    • 5
  1. 1.Universidade Estadual Paulista—UNESPRio ClaroBrazil
  2. 2.Instituto Federal de EducaçãoCiência e Tecnologia do Paraná—IFPRParanavaíBrazil
  3. 3.Universidade Tecnológica Federal do Paraná—UTFPRPonta GrossaBrazil
  4. 4.Universidade Estadual Paulista—UNESPSorocabaBrazil
  5. 5.Universidade Estadual Paulista—UNESPBauruBrazil

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