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Nonlinear dynamics of MEMS resonator in PLL-AGC self-oscillation loop

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Abstract

The work is devoted to the study of a MEMS resonator dynamics under the action of phase-locked and automatic gain control loops. Particular attention is directed to the study of the nonlinearity factor of the resonator elastic restoring force. It was found that the determination of control system parameters based on the stability analysis of the operating resonant mode, in the general case, does not provide the required phase adjustment and stabilization of the oscillation amplitude. Stable multifrequency modes of oscillations are found, and an analytical study of the mechanisms of their appearance and evolution is carried out under variation of the key parameters of the system. The real regions of the control system stable operation are determined (which do not coincide, as was found, with the regions of stability of the operating resonant mode, due to the presence of hidden attractors in the phase space of the system). A methodology has been developed for identifying such areas of stable operation. A significant complication of the structure of possible motions in the system with an increase in the Q-factor of the resonator is revealed.

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Funding

The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation as part of World-class Research Center program: Advanced Digital Technologies (contract No. 075-15-2020-934 dated 17.11.2020).

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Authors and Affiliations

  1. Peter the Great St.Petersburg Polytechnic University, Saint Petersburg, Russia

    D. A. Indeitsev, A. V. Lukin & I. A. Popov

  2. Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences, St. Petersburg, Russia

    D. A. Indeitsev

  3. Concern CSRI Elektropribor, Saint Petersburg, Russia

    Ya. V. Belyaev

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  1. D. A. Indeitsev
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  2. Ya. V. Belyaev
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  3. A. V. Lukin
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  4. I. A. Popov
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Correspondence to A. V. Lukin.

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Indeitsev, D.A., Belyaev, Y.V., Lukin, A.V. et al. Nonlinear dynamics of MEMS resonator in PLL-AGC self-oscillation loop. Nonlinear Dyn 104, 3187–3204 (2021). https://doi.org/10.1007/s11071-021-06586-x

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