Robust optimal design of a vibratory microgyroscope considering fabrication errors

Abstract

A robust optimal design of shape and size is formulated forvibratory microgyroscopes that can reduce the effect of variationsfrom uncertainties in microelectromechanical systems fabrication. Theimportant objective in the design of vibratory microgyroscopes is toreduce the difference between the resonance frequencies of thevertical (detecting) and lateral (driving) modes in order to attainhigh mechanical detecting sensitivity. The deterministic optimizationfor this goal results in good performance but is sensitive tofabrication errors. The basic idea of the present formulation is toobtain robustness of the objective function by minimizing thegradient of the objective function with respect to uncertainvariables through a proper selection of shapes and sizes. The beamwidth, length and thickness of vibratory microgyroscopes are adoptedas design variables and are simultaneously regarded as uncertainvariables in the optimization problems. A robustness check using anewly defined yield through the Monte Carlo simulation has shown thatthe robust optimal design obtained has generated twice the number ofacceptable designs than the deterministic optimum. The importantpoint is that the formulation of minimizing the maximum sensitivityof the objective function requires no statistical information on theuncertainties and yet achieves robustness.