On controlling the vibrations and energy transfer in MEMS gyroscope system with simultaneous resonance

In this paper, we study the dynamics, transfer of energy and control of the vibrations of micro-electromechanical system (MEMS) gyroscope with linear and nonlinear parametric excitations. This leads to two-degree-of-freedom system. The coupling of the system equations is responsible for energy transfers of the two vibration modes (drive mode and sense mode) and for the resonance in MEMS gyroscope. The resulting governing equation is in the form of a cubic Mathieu equation coupled to a Duffing equation. The averaging method is applied to obtain the frequency response equations near simultaneous sub-harmonic and internal resonance. The stability of the steady-state solution near the worst resonance case is studied and discussed. The effects of the different parameters on the two modes of system behavior are studied numerically. Poincaré maps are used to determine stability and plot bifurcation diagrams. Comparison between optimal linear feedback control and active control via negative nonlinear cubic velocity feedback in the presence of parameter uncertainties and noise measurement are done. The numerical results of stability, phase planes and time history are achieved using MATLAB and MAPLE programs.