Robust optimal design of a vibratory microgyroscope considering fabrication errors

A robust optimal design of shape and size is formulated for vibratory micro gyroscopes that can reduce the effect of variations from uncertainties in m icroelectromechanical systems fabrication. The important objective in the d esign of vibratory microgyroscopes is to reduce the difference between the resonance frequencies of the vertical (detecting) and lateral (driving) mod es in order to attain high mechanical detecting sensitivity. The determinis tic optimization for this goal results in good performance but is sensitive to fabrication errors. The basic idea of the present formulation is to obt ain robustness of the objective function by minimizing the gradient of the objective function with respect to uncertain variables through a proper sel ection of shapes and sizes. The beam width, length and thickness of vibrato ry microgyroscopes are adopted as design variables and are simultaneously r egarded as uncertain variables in the optimization problems. A robustness c heck using a newly defined yield through the Monte Carlo simulation has sho wn that the robust optimal design obtained has generated twice the number o f acceptable designs than the deterministic optimum. The important point is that the formulation of minimizing the maximum sensitivity of the objectiv e function requires no statistical information on the uncertainties and yet achieves robustness.