불확실 변수에 대한 구배 최소화를 이용한 강건 최적 설계와 마이크로 자이로스코프에의 응용

Abstract

In this paper a formulation of robust optimization is presented and illustrated by a design example of vibratory micro gyroscopes in order to reduce the effect of variations due to uncertainties in MEMS fabrica-tion processes. For the vibratory micro gyroscope considered it is important to match the resonance frequen-cies of the vertical (sensing) and lateral (driving) modes as close as possible to attain a high sensing sensitivity. A deterministic optimization in which the difference of both the sensing and driving natural frequencies is minimized as an objective function results in highly enhanced performance but apt to be very sensitive to fabrication errors. The formulation proposed is to attain robustness of the performance by including the sensitivity ofthe response with respect to uncertain variables as a term of objective function to be minimized. This formulation is simple and proctically applicable since no detail statistical information on fabrication errors is required. The geometric variables, beam width, length and thickness of vibratory micro gyroscopes are adopted as design variables and at the same time considered as uncertain variables because here occur the fabrication errors. A robustness test in terms of a percentage yield by using the Monte Carlo simulation has shown that the robust optimum produces twice more acceptable designs than the deterministic optimum.Improvement of robustness becomes bigger as the amount of fabrication errors is assumed larger. Considering that the magnitude of fabrication errors and uncertainties in a MEMS structure are comparatively large, the present method is illustrated to be a viable approach for a robust MEMS design.