Robust optimal design of a vibratory microgyroscope considering fabrication errors

Abstract

A robust optimal design of shape and size is formulated for vibratory microgyroscopes that can reduce the effect of variations from uncertainties in microelectromechanical systems fabrication. The important objective in the design of vibratory microgyroscopes is to reduce the difference between the resonance frequencies of the vertical (detecting) and lateral (driving) modes in order to attain high mechanical detecting sensitivity. The deterministic optimization for this goal results in good performance but is sensitive to fabrication errors. The basic idea of the present formulation is to obtain robustness of the objective function by minimizing the gradient of the objective function with respect to uncertain variables through a proper selection of shapes and sizes. The beam width, length and thickness of vibratory microgyroscopes are adopted as design variables and are simultaneously regarded as uncertain variables in the optimization problems. A robustness check using a newly defined yield through the Monte Carlo simulation has shown that the robust optimal design obtained has generated twice the number of acceptable designs than the deterministic optimum. The important point is that the formulation of minimizing the maximum sensitivity of the objective function requires no statistical information on the uncertainties and yet achieves robustness.