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

Yongzhen Xie, Shaohua Luo, Fugui Zhang, Guangwei Deng and Hassen M. Ouakad

Chaos, Solitons & Fractals, 2025, vol. 201, issue P2

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.

Keywords: 3-DOF duffing-type MEMS resonator; Chaotic oscillation; PCB experimental platform; Event-triggered fuzzy neural backstepping control; Type-2 FWNN (search for similar items in EconPapers)
Date: 2025
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925012792

DOI: 10.1016/j.chaos.2025.117266

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