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<p>This work investigates the impact of time delay on resonators with nonlinearity introduced via a digital feedback loop. A piezoelectric MEMS cantilever is driven near its fundamental frequency, and an FPGA-based feedback mechanism applies a delayed cubic displacement term. Employing the Krylov–Bogolyubov averaging method, an approximate analytical model is developed to capture the influence of feedback delay on the slow dynamics of amplitude and phase. Experimental results, obtained by incorporating controlled delays ranging from approximately 0.9 to 12 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\upmu \)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="normal">μ</mi> </math></EquationSource> </InlineEquation>s on a device with resonant frequency around 1800 Hz, reveal that even small processing delays significantly alter the frequency response and stability of the closed-loop resonator system. These findings highlight the interplay between feedback-enabled nonlinearity and time delay, while also providing insight for the design and implementation of resonant sensors with feedback-enhanced functionality.</p>

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Time delay effects on a digital feedback-enabled cubic nonlinearity in MEMS resonators

  • 期刊论文

  • 发表日期：

    2026年3月16日

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  • Thomas Hinds,
  • Amro Hesham Abdullah Koshak,
  • Nikhil Bajaj

摘要

This work investigates the impact of time delay on resonators with nonlinearity introduced via a digital feedback loop. A piezoelectric MEMS cantilever is driven near its fundamental frequency, and an FPGA-based feedback mechanism applies a delayed cubic displacement term. Employing the Krylov–Bogolyubov averaging method, an approximate analytical model is developed to capture the influence of feedback delay on the slow dynamics of amplitude and phase. Experimental results, obtained by incorporating controlled delays ranging from approximately 0.9 to 12 \(\upmu \) μ s on a device with resonant frequency around 1800 Hz, reveal that even small processing delays significantly alter the frequency response and stability of the closed-loop resonator system. These findings highlight the interplay between feedback-enabled nonlinearity and time delay, while also providing insight for the design and implementation of resonant sensors with feedback-enhanced functionality.