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Dynamical analysis and chaos control of MEMS resonators by using the analog circuit

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Abstract

This paper investigates the chaos control problem of microelectromechanical system (MEMS) resonators by using the analog circuits. The dynamical analysis, based on bifurcation diagrams, phase diagrams and Lyapunov exponents (LEs), illustrates that transient chaotic behaviors and chaotic behaviors strongly depend on system parameters and the initial conditions of the MEMS resonator. Then, based on the energy flow theory, the circuit differential equation is consistent with its differential equation governing the dynamics, which could mimic the micro-resonator dynamic properties. Accordingly, an analog circuit is designed, and abundant experimental data reveal chaotic behaviors of the MEMS resonator at around 58.791 Hz (1.71 V) and 58.704 Hz (1.68 V). After that, to suppress harmful chaotic oscillation, an adaptive control scheme is proposed and verified by an analog circuit consisting of an error module, a parameter update module and a control input module. Finally, the experimental results of the circuit control system prove the effectiveness of the proposed control scheme.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgements

This project is supported by the National Natural Science Foundation of China (Grant No. 52065008), Science and Technology Planning Project of Guizhou Province (Nos. [2021]5634 and [2020]1Y274), Foundation for Innovative Research Groups of Universities in Chongqing (No. CXQTP20035), and Science and Technology Research Program of Chongqing Municipal Education Commission (Nos. KJZD-K201903001 and KJQN201803004).

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Authors and Affiliations

  1. School of Mechanical Engineering, Guizhou University, Guiyang, 550025, China

    Shaohua Luo, Huanhuan Ma & Fengyun Li

  2. Star Institute of Intelligent Systems (SIIS), Shapingba District, Chongqing, 400030, China

    Shaohua Luo

  3. Department of Mechanical and Industrial Engineering, Sultan Qaboos University, Muscat, 123, Oman

    Hassen M. Ouakad

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  1. Shaohua Luo
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Correspondence to Shaohua Luo.

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Luo, S., Ma, H., Li, F. et al. Dynamical analysis and chaos control of MEMS resonators by using the analog circuit. Nonlinear Dyn 108, 97–112 (2022). https://doi.org/10.1007/s11071-022-07227-7

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