Abstract

A nonlinear control system that can track the natural frequency of a MEMS resonator was developed in this study. Due to the evolution of fatigue damage, the natural frequency of the resonator decreases. To maintain the device at resonance, a phase-locked loop system is used to track the frequency decay and adjust the driving force accordingly. A model for the control system is introduced and the system behavior is analyzed using an averaging method. A quantitative criterion for selecting the control gain to achieve stability is derived from the analysis. Simulation results are shown to be in good agreement with the prediction of the theoretical analysis.

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