MEMS Huygens Clock Based on Synchronized Micromechanical Resonators

With the continuous miniaturization of electronic devices,microelectromechanical system(MEMS)oscillators that can be combined with integrated circuits have attracted increasing attention.This study reports a MEMS Huygens clock based on the synchronization principle,comprising two synchronized MEMS oscillators and a frequency compensation system.The MEMS Huygens clock improved shorttime stability,improving the Allan deviation by a factor of 3.73 from 19.3 to 5.17 ppb at 1 s.A frequency compensation system based on the MEMS oscillator’s temperature-frequency characteristics was developed to compensate for the frequency shift of the MEMS Huygens clock by controlling the resonator current.This effectively improved the long-term stability of the oscillator,with the Allan deviation improving by 1.6343105 times to 30.9 ppt at 6000 s.The power consumption for compensating both oscillators simultaneously is only 2.85 mW·℃^(-1).Our comprehensive solution scheme provides a novel and precise engineering solution for achieving high-precision MEMS oscillators and extends synchronization applications in MEMS.

A feedback control method for phase signal demodulation in fber-optic hydrophones

In the realm of acoustic signal detection,the identification of weak signals,particularly in the presence of negative signal-to-noise ratios,poses a significant challenge.This challenge is further heightened when signals are acquired through fiber-optic hydrophones,as these signals often lack physical significance and resist clear systematic modeling.Conventional processing methods,e.g.,low-pass filter(LPF),require a thorough understanding of the effective signal bandwidth for noise reduction,and may introduce undesirable time lags.This paper introduces an innovative feedback control method with dual Kalman filters for the demodulation of phase signals with noises in fiber-optic hydrophones.A mathematical model of the closed-loop system is established to guide the design of the feedback control,aiming to achieve a balance with the input phase signal.The dual Kalman filters are instrumental in mitigating the effects of signal noise,observation noise,and control execution noise,thereby enabling precise estimation for the input phase signals.The effectiveness of this feedback control method is demonstrated through examples,showcasing the restoration of low-noise signals,negative signal-to-noise ratio signals,and multi-frequency signals.This research contributes to the technical advancement of high-performance devices,including fiber-optic hydrophones and phase-locked amplifiers.

Dynamics and response reshaping of nonlinear predator-prey system undergoing random abrupt disturbances

An actual ecological predator-prey system often undergoes random environmental mutations owing to the impact of natural disasters and man-made destruction, which may destroy the balance between the species. In this paper,the stochastic dynamics of the nonlinear predator-prey system considering random environmental mutations is investigated, and a feedback control strategy is proposed to reshape the response of the predator-prey system against random abrupt environmental mutations. A delayed Markov jump system(MJS) is established to model such a predator-prey system. A novel first integral is constructed which leads to better approximation solutions of the ecosystem. Then, by applying the stochastic averaging method based on this novel first integral, the stochastic response of the predator-prey system is investigated, and an analytical feedback control is designed to reshape the response of the ecosystem from the disturbed state back to the undisturbed one.Numerical simulations finally illustrate the accuracy and effectiveness of the proposed procedure.

STOCHASTIC OPTIMAL VIBRATION CONTROL OF PARTIALLY OBSERVABLE NONLINEAR QUASI HAMILTONIAN SYSTEMS WITH ACTUATOR SATURATION

An optimal vibration control strategy for partially observable nonlinear quasi Hamiltonian systems with actuator saturation is proposed. First,a controlled partially observable non-linear system is converted into a completely observable linear control system of finite dimension based on the theorem due to Charalambous and Elliott. Then the partially averaged It stochastic differential equations and dynamical programming equation associated with the completely observable linear system are derived by using the stochastic averaging method and stochastic dynamical programming principle,respectively. The optimal control law is obtained from solving the final dynamical programming equation. The results show that the proposed control strategy has high control effectiveness and control effciency.

Frequency unlocking-based MEMS bifurcation sensors

MEMS resonators exhibit rich dynamic behaviors under the internal resonance regime. In this work, we present a novel MEMS bifurcation sensor that exploits frequency unlocking due to a 1:3 internal resonance between two electrostatically coupled micro-resonators. The proposed detection mechanism allows the sensor to operate in binary (digital) and analog modes, depending on whether the sensor merely detects a significant jump event in the peak frequency upon unlocking or measures the shift in the peak frequency after unlocking and uses it in conjunction with a calibration curve to estimate the corresponding change in stimulus. We validate the success of this sensor paradigm by experimentally demonstrating charge detection. High charge resolutions are achieved in binary mode, up to 0.137 fC, and in analog mode, up to 0.01 fC. The proposed binary sensor enables extraordinarily high detection resolutions due to the excellent frequency stability under internal resonance and the high signal-to-noise ratio of the shift in peak frequency. Our findings offer new opportunities for high-performance ultrasensitive sensors.

Single-electron detection utilizing coupled nonlinear microresonators

Since the discovery of the electron,the accurate detection of electrical charges has been a dream of the scientific community.Owing to some remarkable advantages,micro/nanoelectromechanical system-based resonators have been used to design electrometers with excellent sensitivity and resolution.Here,we demonstrate a novel ultrasensitive charge detection method utilizing nonlinear coupling in two micromechanical resonators.We achieve single-electron charge detection with a high resolution up to 0.197±0.056 e=/√Hz Hz p at room temperature.Our findings provide a simple strategy for measuring electron charges with extreme accuracy.

Frequency comb in a parametrically modulated micro-resonator

In this paper,we report the frequency comb response experimentally and analytically in a rhombic micro-resonator with parametrical modulation.When the electrostatically actuated rhombic micro-resonator is modulated axially by a low-frequency periodic excitation,a comb-like vibration response with few equidistant positioned fingers in the frequency domain is observed.The finger spacing of frequency comb response is exactly consistent with modulation frequency and the number and amplitude of the fingers can be tuned by modulation strength.A mixed frequency comb with extra comb fingers is further generated when the resonator is modulated simultaneously by two different low-frequency excitation signals.By adjusting the relation of the two modulation frequencies,unequal spacing frequency combs are achieved for the first time,which leads to a more flexible tunability of the comb spacing for different applications.Theoretical analysis based on the dynamic model well explains the corresponding observations.

Synchronization bandwidth enhancement induced by a parametrically excited oscillator

The synchronization phenomenon in nature has been utilized in sensing and timekeeping fields due to its numerous advantages,including amplitude and frequency stabilization,noise reduction,and sensitivity improvement.However,the limited synchronization bandwidth hinders its broader application,and few techniques have been explored to enhance this aspect.In this paper,we conducted theoretical and experimental studies on the unidirectional synchronization characteristics of a resonator with phase lock loop oscillation.A novel enhancement method for the synchronization bandwidth using a parametrically excited MEMS oscillator is proposed,which achieves a remarkably large synchronization bandwidth of 8.85 kHz,covering more than 94%of the hysteresis interval.Importantly,the proposed method exhibits significant potential for high-order synchronization and frequency stabilization compared to the conventional directly excited oscillator.These findings present an effective approach for expanding the synchronization bandwidth,which has promising applications in nonlinear sensing,fully mechanical frequency dividers,and high-precision time references.