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Dynamical analysis, PCB-based circuit implementation and event-triggered fuzzy neural backstepping control of 3-DOF Duffing-type MEMS resonator

Author

Listed:
  • Xie, Yongzhen
  • Luo, Shaohua
  • Zhang, Fugui
  • Deng, Guangwei
  • Ouakad, Hassen M.

Abstract

This paper presents a comprehensive study on the nonlinear dynamics, circuit-level validation and advanced control of a three-degree-of-freedom (3-DOF) Duffing MEMS resonator. Firstly, the resonator architecture is designed with three coupled masses interconnected via electrostatic springs, forming a chain-like configuration that introduces weakly electrostatic coupling and high-order nonlinearities. The resonator's mathematical model is derived by incorporating both external disturbances and complex coupling effects, which results in a highly nonlinear dynamical system. Secondly, through extensive numerical simulations, the system exhibits rich nonlinear phenomena, including bifurcations and chaotic attractors, under various parameter settings and initial conditions. Meanwhile, a printed circuit board (PCB)-based experimental platform is developed to validate the numerical findings, confirming the presence of chaotic oscillations and defining a safe operational envelope for MEMS chip fabrication. Thirdly, to address intractable issues including state constraints, system uncertainties, chaotic oscillations, and limited communication resources, an event-triggered fuzzy neural backstepping control scheme is constructed. In this scheme, a log-type barrier Lyapunov function (Log-BLF) is designed to ensure the resonator to operate within a safe region by constraining system states, a type-2 fuzzy wavelet neural network (FWNN) and an accelerated exponential integral tracking differentiator (AEITD) are used to approximate unknown terms and avoid “complexity explosion” in the backstepping control, and a switching threshold event triggering (STET) is integrated to relieve communication load without compromising control performance. Finally, extensive experimental results are provided to validate the effectiveness and feasibility of the proposed control scheme, which fully addresses the nonlinear system dynamics and uncertainties via the type-2 FWNN, maintains the tracking error within±0.0025, and reduces the communication bandwidth burden by over 70 % through the designed event-triggering mechanism.

Suggested Citation

  • Xie, Yongzhen & Luo, Shaohua & Zhang, Fugui & Deng, Guangwei & Ouakad, Hassen M., 2025. "Dynamical analysis, PCB-based circuit implementation and event-triggered fuzzy neural backstepping control of 3-DOF Duffing-type MEMS resonator," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925012792
    DOI: 10.1016/j.chaos.2025.117266
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    References listed on IDEAS

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    1. Balamurali, Ramakrishnan & Kamdjeu Kengne, Leandre & Rajagopal, Karthikeyan & Kengne, Jacques, 2022. "Coupled non-oscillatory Duffing oscillators: Multistability, multiscroll chaos generation and circuit realization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    2. Fatoorehchi, Hooman & Zarghami, Reza & Abolghasemi, Hossein & Rach, Randolph, 2015. "Chaos control in the cerium-catalyzed Belousov–Zhabotinsky reaction using recurrence quantification analysis measures," Chaos, Solitons & Fractals, Elsevier, vol. 76(C), pages 121-129.
    3. Ebrahimi, Reza, 2022. "Chaos in coupled lateral-longitudinal vibration of electrostatically actuated microresonators," Chaos, Solitons & Fractals, Elsevier, vol. 156(C).
    4. Xu, Quan & Wang, Yiteng & Chen, Bei & Li, Ze & Wang, Ning, 2023. "Firing pattern in a memristive Hodgkin–Huxley circuit: Numerical simulation and analog circuit validation," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
    5. Alneamy, Ayman M., 2024. "Dynamic snap-through motion and chaotic attractor of electrostatic shallow arch micro-beams," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    6. Luo, Shaohua & Yang, Guanci & Li, Junyang & Ouakad, Hassen M., 2022. "Dynamic analysis, circuit realization and accelerated adaptive backstepping control of the FO MEMS gyroscope," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    7. Li, Zhijun & Chen, Kaijie, 2023. "Neuromorphic behaviors in a neuron circuit based on current-controlled Chua Corsage Memristor," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    8. Abdulaziz, O. & Noor, N.F.M. & Hashim, I. & Noorani, M.S.M., 2008. "Further accuracy tests on Adomian decomposition method for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1405-1411.
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