The work is devoted to the study of a MEMS resonator dynamics under the action of phase-locked and automatic gain control loops. Particular attention is directed to the study of the nonlinearity factor of the resonator elastic restoring force. It was found that the determination of control system parameters based on the stability analysis of the operating resonant mode, in the general case, does not provide the required phase adjustment and stabilization of the oscillation amplitude. Stable multifrequency modes of oscillations are found, and an analytical study of the mechanisms of their appearance and evolution is carried out under variation of the key parameters of the system. The real regions of the control system stable operation are determined (which do not coincide, as was found, with the regions of stability of the operating resonant mode, due to the presence of hidden attractors in the phase space of the system). A methodology has been developed for identifying such areas of stable operation. A significant complication of the structure of possible motions in the system with an increase in the Q-factor of the resonator is revealed.

Nonlinear dynamics of MEMS resonator in PLL-AGC self-oscillation loop

http://manuscript.elsevier.com/S0888327022004939/pdf/S0888327022004939.pdf

The pendulum adaptive frequency oscillator

This paper presents the results of modeling the nonlinear dynamics of MEMS vibrating wheel gyroscope. Diagrams of possible stationary oscillatory modes are constructed when primary oscillations are excited from an external generator. The influence of geometric design imperfections and perturbations of the physical and mechanical properties of the material on the dynamics and the output characteristic of the sensor is investigated. The factors of the presence of cross components of the elastic and dissipation forces, as well as the asymmetry of the electrode structure of the secondary axis, are considered. The influence of external vibrations on the operation of the gyroscope is studied for cases of translational and rotational vibrations of the base. A number of mechanisms for the transfer of vibration energy to angular vibrations of the sensitive element around the secondary axis are considered, and a quantitative assessment of the value of the false output signal is made depending on the nature of external vibrations, their frequency composition and imperfections in the gyroscope design.

Analysis of imperfections sensitivity and vibration immunity of MEMS vibrating wheel gyroscope

The existing analysis methods for the silicon gyroscope drive loop, such as the perturbation method and period average method, cannot analyze the dynamic characteristics of the system. In this work, a linearized amplitude control model of the silicon gyroscope drive loop was established to analyze the stability and set-up time of the drive loop, and the vibration conditions of the silicon gyro were obtained. According to the above results, a new silicon gyroscope interface circuit was designed, using a 0.35 μm Bipolar-CMOS-DMOS (BCD) process, and the chip area was 4.5 mm × 4.0 mm. The application-specific integrated circuit (ASIC) of the silicon gyroscope was tested in combination with the sensitive structure with a zero stability of 1.14°/hr (Allen). The test results for the ASIC and the whole machine prove the correctness of the theoretical model, which reflects the effectiveness of the stability optimization of the closed-loop controlled drive loop of the silicon gyroscope circuit.

/pdf/research-on-a-silicon-gyroscope-interface-circuit-based-on-ia41o8tu.pdf

Research on a Silicon Gyroscope Interface Circuit Based on Closed-Loop Controlled Drive Loop

&lt;p style='text-indent:20px;'&gt;We present a case study of an active micro-electromechanical system (MEMS). The MEMS cantilever has integrated actuation and sensor mechanisms, which enable the active operation of the system. Our analysis is comprised of numerical continuation of equilibria and periodic orbits, which are briefly compared and discussed with initial experimental observations. In this case study, we consider the dynamic behaviour of two MEMS configurations, one excluding, and the other including a high-pass filter. With that we wish to study any differences between a dynamical system as typically analysed in the literature and the same system when investigated experimentally. We show that the MEMS' dynamic behaviour is significantly influenced by the experimental setup with different dominating dynamics associated with power electronics and filter properties. The dynamics of the MEMS cantilever is characterised by three key effects: the system is an actively operated system; it is a micro-scale system with amplitudes at nano-scale dimensions; and the integrated actuation physics introduces interesting complex dynamics. The MEMS cantilever with its integrated actuation and sensing abilities was developed for a commercial technology, thus, making our findings directly implementable and meaningful.&lt;/p&gt; 

A novel sensing concept utilizing targeted, complex, nonlinear MEMS dynamics

\n In this paper, we present a control strategy for a micro-electro-mechanical gyroscope with a drive mode excited through parametric resonance. The reduced order two degrees-of-freedom model of the device is built, and the drive mode control is implemented using phase-locked loop (PLL) and automatic gain control (AGC) loop. A sense mode vibration control algorithm is developed as well for enhanced sensor performance. The analysis of the drive mode control loops is conducted using the multiple scales method. The robustness of the suggested control loops to parameters perturbation is demonstrated using the model. A simplified linear model of the control loops is shown to predict the device behavior with good accuracy.

T. Perl

Papers

Control of Vibratory MEMS Gyroscope With the Drive Mode Excited Through Parametric Resonance