Frequency stabilization control methods for MEMS micro-resonators under multi-physics coupling conditions

Abstract

Abstract

MEMS micro-resonators often operate in a multi-physics coupling environment involving electrostatic fields, molecular force fields, and structural force fields, exhibiting significant nonlinear natural frequency perturbation and frequency drift, which leads to large fluctuations in output frequency. Existing methods struggle to simultaneously characterize the nonlinear coupling effects of Casimir force and electrostatic force, and lack adaptive compensation capability for time-varying disturbances. To overcome this bottleneck, this paper proposes a frequency stabilization control method based on nonlinear coupled dynamics and adaptive compensation using a fuzzy emotional neural network. The main contributions are as follows: a distributed-parameter nonlinear vibration model incorporating dynamic electrostatic force and Casimir force is established, revealing the intrinsic competitive mechanism through which initial gap and beam length affect frequency drift; a fuzzy emotional neural network with dynamic displacement, dynamic electrostatic force, and dynamic Casimir force as multi-field fusion inputs is designed to achieve high-precision real-time estimation of the system's unmodeled dynamics; an error-constrained barrier Lyapunov function is constructed and combined with backstepping control to realize adaptive feedforward-feedback composite compensation of the excitation voltage between the plates. Experimental results show that the proposed method achieves high-precision frequency stabilization control under different micro-resonator lengths (500 μm, 1000 μm, and 1500 μm), with the root mean square error of frequency tracking as low as 0.46×10 4 Hz, which is reduced by approximately one order of magnitude compared with the PID method. The maximum Allan variance is only 4.5×10 -10 , reduced by approximately two orders of magnitude compared with the open-loop state, meeting the accuracy requirements of industrial-grade frequency sources such as 5G base station local oscillators and inertial navigation system clocks. The proposed method does not rely on modifying the device geometry and is insensitive to changes in structural dimensions, providing a feasible and robust intelligent control solution for the engineering application of high-precision MEMS resonators.