Nonlinear Dynamic Vibration Characteristics Of Parametric Excitation MEWS Gyroscope System And The Research Of Time-delay Feedback Control

In this paper, a vibration system of a typical electrostatic driven resonant MEMS gyroscope is studied. We plan to analyze the complex dynamic behaviors (vibration jump and almost periodic function)caused by the nonlinear stiffness and nonlinear forces. Fist of all, Lagrange equation be used to establish the MEMS gyroscope dynamic formulation. Second, the method of multiple scales be used to analysis the characteristic of periodic solution. Third, according to the periodic solution, author study the Hopf bifurcation condition. Fourth, fixed-step length of4th Runge-Kutta method is used to verified theoretical calculation of dynamic behavior. It was found that the variation of the exciting frequency is liable to induces various complex dynamical behaviors of the micro-gyroscope vibrating system such as multi-stability, jump phenomena and quasi-periodic responses under a large angular rate of the carrier and 1:1 internal resonance, and that the control method can avoid this phenomenon is adjusting the driving voltage amplitude and driving frequency. And then, it was explored that improving MEMS gyroscope stability used time-delay position feedback. It found that appropriate parameter of time-delay feedback control come into reduce the vibration amplitude in driving and measurement, and avoid the phenomena of over vibration and multi-stable. Finally, there explored an useful self-adaption method of driving and measuring system. The theory of this system is that automatic adjusting the driving voltage amplitude according the measuring direction amplitude. This self-adaption control method can be used to improving sensitivity and measuring accuracy. In this system, temperature compensation feedback and acceleration correction feedback was used to improve the adaptive capacity to environment of MEMS gyroscope.