Abstract
This paper deals with a (MEMS) Gyroscope nonlinear dynamical system, modeled with a proof mass constrained to move in a plane with two resonant modes, which are nominally orthogonal. We present some modifications to the governing equations of the considered system, taking into account the nonlinear interactions between the parts of the systems. We also develop a linear optimal control design, for reducing the oscillatory movement of the nonlinear system to a stable point.
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Chavarette, F.R., Balthazar, J.M., Felix, J.L.P., Rafikov, M.: Reducing a chaotic movement to a periodic orbit, in of a micro-electro-mechanical system, by using an optimal linear control design. Commun. Nonlinear Sci. Numer. Simul. 14(5), 1844–1853 (2009a)
Chavarette, F.R., Balthazar, J.M., Rafikov, M.: On an energy pumping levels in a MEMS gyroscope vibrating problem, by using of an optimal (global and local) linear control design. In: Proceedings of the ASME 2009 IDETC/CIE, San Diego (2009b)
Chavarette, F.R., Balthazar, J.M., Felix, J.L.P.: Remarks on an optimal linear control design applied to a nonideal and an ideal structure coupled to an essentially nonlinear oscillator. J. Comput. Nonlinear Dyn. 5, 24501–24508 (2010)
Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical System, and Bifurcation of Vector Fields. Springer, New York (1983)
Lee, Y., Pai, P.F., Feng, Z.C.: Nonlinear complex response of a parametrically excited tuning fork. Mech. Syst. Signal Process. 22, 1146–1156 (2008)
Luo, A.C.J., Wang Fei-Yue: Chaotic motion in a micro-electro-mechanical system with non-linearity from capacitors. Commun. Nonlinear Sci. Numer. Simul. 7, 31–49 (2002)
Luo, A.C.J., Wang Fei-Yue: Nonlinear dynamics of a micro-electro-mechanical system with time-varying capacitors. J. Vib. Acoust. 126, 77–83 (2004)
Miller, N.J., Shaw, S.W., Oropeza-Ramos, L.A., Turner, K.L.: Analysis of a novel MEMS gyroscope actuated by parametric resonance. In: Proceedings of the Sixth EUROMECH Nonlinear Dynamics Conference (ENOC 2008), Saint Petersburg, Russia, June 30–July 4 2008 (2008)
Ogata, K.: Engenharia de Controle Moderno, vol. 4, p. 788. Pearson Prentice Hall, São Paulo (2003)
Oropeza-Ramos, L., Burgner, C.B., Olroyd, C., Turner, K.: Characterization of a novel MEMGyroscope actuated by parametric resonance. In: Proceedings of the ASME 2007, IDETC/CIE 2007, pp. 1–6, Las Vegas, Nevada, 4–7 September 2007
Oropeza-Ramos, L., Burgner, C.B., Olroyd, C., Turner, K.: Inherently robust micro gyroscope actuated by parametric resonance. In: IEEE International Conference on Micro Electro Mechanical Systems, pp. 872–875, Tucson, AZ (2008)
Ott, B., Grebogi, C., Yorke, J.A.: Controlling chaos. Phys. Rev. Lett. 66, 1196 (1990)
Rafikov, M., Balthazar, J.M.: On control and synchronization in chaotic and hyperchaotic systems via linear feedback control. Commun. Nonlinear Sci. Numer. Simul. 13(7), 1246–1255 (2008)
Sinhá, S.C., Henrichs, J.T., Ravindra, B.A.: A general approach in the design of active controllers for nonlinear systems exhibiting chaos. Int. J. Bifur. Chaos 10(1), 165 (2000)
Wauer, J.: On the dynamics of electrostatic transducer with distributed parameters. In: 9th Conference on Dynamical Systems Theory and Applications, pp. 1009–1016, Lódz, Poland, 17–20 December 2007
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Chavarette, F.R., Balthazar, J.M., Felix, J.L.P. (2013). On Nonlinear Dynamics and Control Design in a “MEMS” Gyroscope System. In: Wiercigroch, M., Rega, G. (eds) IUTAM Symposium on Nonlinear Dynamics for Advanced Technologies and Engineering Design. IUTAM Bookseries (closed), vol 32. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5742-4_32
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DOI: https://doi.org/10.1007/978-94-007-5742-4_32
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