Nonlinear control in an electromechanical transducer with chaotic behaviour
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.
KeywordsElectromechanical 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.
- 3.Bishop RH (2006) Mechatronics: an introduction. CRC Press, New YorkGoogle Scholar
- 7.Tusset AM, Balthazar JM, Felix JLP (2012) On elimination of chaotic behavior in a non-ideal portal frame structural system, using both passive and active controls. J Vib Control 1–11. doi: 10.1177/1077546311435518
- 9.Rafikov M, Balthazar JM, Tusset AM (2008) An optimal linear control design for nonlinear systems. J Braz Soc Mech Sci Eng XXX(4):279–284Google Scholar
- 11.Rao S (2010) Mechanical vibrations, 5th edn. Prentice Hall, Upper Saddle RiverGoogle Scholar
- 14.Gendelman O (2007) Targeted energy transfer in systems with non-polynomial nonlinearity. J Sound Vib 315:723–745Google Scholar
- 15.Vakakis AF, Gendelman OV, Bergman LA, McFarland DM, Kerschen G, Lee YS (2008) Nonlinear targeted energy transfer in mechanical and structural systems, solid mechanics and its applications. Springer, DordrechtGoogle Scholar
- 18.Balthazar JM, Tusset AM, de Souza SLT, Bueno AM (2013) Microcantilever chaotic motion suppression in tapping mode atomic force microscope. Proc Inst Mech Eng 227:1730–1741Google Scholar