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Nonlinear control in an electromechanical transducer with chaotic behaviour

  • Nonlinear Dynamics and Control of Composites for Smart Engi design
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Abstract

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.

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Acknowledgments

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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Authors and Affiliations

  1. Universidade Estadual Paulista—UNESP, Rio Claro, SP, Brazil

    José Manoel Balthazar

  2. Instituto Federal de Educação, Ciência e Tecnologia do Paraná—IFPR, Paranavaí, PR, Brazil

    Dailhane Grabowski Bassinello

  3. Universidade Tecnológica Federal do Paraná—UTFPR, Ponta Grossa, PR, Brazil

    Angelo Marcelo Tusset

  4. Universidade Estadual Paulista—UNESP, Sorocaba, SP, Brazil

    Átila Madureira Bueno

  5. Universidade Estadual Paulista—UNESP, Bauru, SP, Brazil

    Bento Rodrigues de Pontes Junior

Authors
  1. José Manoel Balthazar
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  2. Dailhane Grabowski Bassinello
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  3. Angelo Marcelo Tusset
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  4. Átila Madureira Bueno
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  5. Bento Rodrigues de Pontes Junior
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Correspondence to José Manoel Balthazar.

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Balthazar, J.M., Bassinello, D.G., Tusset, A.M. et al. Nonlinear control in an electromechanical transducer with chaotic behaviour. Meccanica 49, 1859–1867 (2014). https://doi.org/10.1007/s11012-014-9910-4

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  • DOI: https://doi.org/10.1007/s11012-014-9910-4

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