Z. Zun, Y. Han, A. Abrol, J. Clark*Auburn University,United States*

Keywords: wideband high-Q, nonlinear resonance

Summary:

We investigate wideband resonance by force feedback. Wideband resonance is achieved by electrostatically increasing the geometric stiffness in MEMS. Geometric stiffness is naturally inherent in MEMS but requires a very large displacement for it to become significant. Nonlinearity is often avoided. However, by characterizing the equation of motion of a MEMS, nonlinearity can be tractable. By feeding back a force that is proportional to displacement-cubed, we are able to achieve a controllable nonlinear stiffening effect at much smaller amplitudes of displacement oscillation. Some issues for high-Q linear resonance that are remedied by nonlinear resonance include: (1) matching the drive frequency with the resonance frequency; (2) matching the resonance frequency of mode-one to that of mode-two; and (3) drifting resonance due to drifting thermal and packaging stresses. However, if the shape of a narrow high-Q frequency response can either bend to the right (spring hardening) or bend to the left (spring softening) then the bandwidth is effectively widened while maintaining high-Q. That is, if the drive frequency is detuned to the right for a spring-hardened system, then high amplitudes are much easier to obtain without needing to match the resonance frequency, and the amplitudes are able to remain high while resonance frequency drifts and while drive frequency remains constant. A couple of reasons for utilizing resonance are to increase the signal to noise ratio and to utilize sinusoidal signal processing methods. Such nonlinearity may also benefit the mode-matching problem in gyros. Some previous studies focused on matching the drive and sense modes of high-Q vibratory gyros [1-3]. Due to process variations and thermal drift, it is difficult for frequencies of the drive and sense modes to match. How well the modes match determines how well the drive mode transfers its Coriolis energy to the sense mode [4]. The higher the Q (i.e. the narrower the bandwidth), the more difficult it is for the two modes to match. In the full paper we will derive the governing model, present our nonlinear feedback circuit, dynamically simulate the wideband high-Q response of MEMS subject to thermal drift, and we will show how a pair of initially unmatched modes of a gyro is able to robustly match by nonlinear resonance. [1] F. Yesil, S. E. Alper, and T Akin, “An Automatic Mode Matching System For A High Q-Factor MEMS Gyroscope Using A Decoupled Perturbation Signal”, Transducers, June, 2015, pp.1148-1151 [2] D. Kim and R. M'Closkey, "A MEM vibratory gyro with mode-matching achieved by resonator mass loading," 2014 IEEE/ION Position, Location and Navigation Symposium - PLANS 2014, Monterey, CA, 2014, pp. 499-503 [3] F. Bu, D. Xu, H. Zhao, B. Fan, M. Cheng, “MEMS Gyroscope Automatic Real-Time Mode-Matching Method Based on Phase-Shifted 45° Additional Force Demodulation”, Sensors (Basel). 2018; 18 (9) : 3001. [4] S. Kumar, B. Hemalatha, "Design and Simulation of MEMS Based Gyroscope,"IOSR Journal of Electrical and Electronics Engineering”, Vol.5, Is.6, pp. 23-30, Jun 2015