Reduced-Order Modeling of Parametrically Excited Micro-Electro-Mechanical Systems (MEMS)

Reduced-order modeling is a systematic way of constructing models with smaller number of states that can capture the “essential dynamics” of the large-scale systems, accurately. In this paper, reduced-order modeling and control techniques for parametrically excited MEMS are presented. The techniques proposed here use the Lyapunov-Floquet (L-F) transformation that makes the linear part of transformed equations time invariant. In this work, three model reduction techniques for MEMS are suggested. First method is simply an application of the well-known Guyan-like reduction method to nonlinear systems. The second technique is based on singular perturbation, where the transformed system dynamics is partitioned as fast and slow dynamics and the system of differential equations is converted into a differential algebraic (DAE) system. In the third technique, the concept of invariant manifold for time-periodic systems is used. The “time periodic invariant manifold” based technique yields “reducibility conditions”. This is an important result because it helps us to understand the various types of resonances present in the system. These resonances indicate a tight coupling between the system