MEMS tasarımı için performans saptaması ve hassasiyet analizi

Thesis Title : Sensitivity Analysis and Performance Prediction Methodology for MEMS DesignAuthor : Faik Can MeralABSTRACTFuture optical micro systems such as Micro Electro Mechanical Systems (MEMS) scanners andmicro-mirrors will extend the resolution and sensitivity offered by their predecessors. These systemsface the challenge of achieving nanometer precision subjected to various disturbances. Predicting theperformance of such systems early in the design process can significantly impact the design cost andalso improve the quality of the design. Our approach aims to predict the performance of such systemsunder various disturbance sources and develop a generalized design approach for MEMS structuresincluding a sensitivity analysis framework. In this study, we use ANSYS for modeling and analysisof a torsional MEMS scanner mirror. ANSYS modal analysis results, which are eigenvalues (naturalfrequencies) and eigenvectors (mode shapes), are used to obtain the state space representation of themirror. The state space model of the scanner mirror is reduced using various reduction techniques toeliminate the states that are insignificant for the transfer functions of interest. The results of thesetechniques are compared to obtain the best approach for achieving a lower order model that stillcontains all of the relevant dynamics of the original model. After the model size is reducedsignificantly, a disturbance analysis is performed using Lyapunov approach to obtain root-mean-square (RMS) values of the mirror rotation angle under the effect of a disturbance torque. TheLyapunov approach results were validated using a time domain analysis. The sensitivity frameworkdescribed in this study is directly related to the disturbance analysis framework. Analytical formulasare derived for the calculation of the modal parameter sensitivities and the results are verified by thefinite difference method. The analytical formulas for the calculation of physical parametersensitivities are described but they are found to be very inefficient due to the complexity andcomputational expense in calculating the eigenvalue and eigenvector derivatives included in theseequations. Instead, the finite difference method is used to calculate the physical parametersensitivities for the torsional MEMS scanner. Disturbance characteristics of the microscanners aremeasured, using the experimental techniques. The resulting data is utilized in the disturbanceanalysis framework.