<title>System-level modeling of microsystems using order reduction methods</title>

Abstract

In the development of microsystems, FEM simulators are used to investigate the behavior of system components with high accuracy. Generally, FEM simulations are time consuming. System-level models of all components are needed to allow a fast but sufficiently exact investigation of the system behavior to simulate entire microsystems. Typically, microsystems consist of nonelectrical components and electronic circuits. Providing models for electronic components and languages to describe the behavior of nonelectrical subsystems, simulators like Eldo, Saber, and VHDL-AMS simulators become more and more popular in the development of microsystems. For simple structures such as mechanical beams, models of microsystem components can be derived from analytical descriptions. Another possibility to consider more complex structures is to use FEM descriptions to generate models for system simulation. Some FEM simulators like ANSYS allow to access the numerical values of the system matrices. They are established based on the description of geometry and material data. Usually, these system matrices are very large (10 000 up to 100 000 system variables or more). For system simulation, models with about 10 up to 100 variables are often required. Therefore, methods for order reduction are applied to derive smaller system matrices. An improvement of an order reduction method based on a projection method is introduced in the paper. Using the reduced systems, behavioral models in languages like MAST, HDL-A or VHDL-AMS can be generated automatically. The described method was applied successfully to simulate mechanical microsystem components on system level.

System Level Modeling of the Relevant Physical Effects of Inertial Sensors Using Order Reduction Methods

“…Using an orthogonal projection method [10,11] we transform the above system into a low-dimensional sub-space…”

Sensitivity analysis and adaptive multi-point multi-moment model order reduction in MEMS design

“…For behavior modeling and system level simulation this means that the full order model (FOM) can be seamlessly replaced by the ROM. The transfer functionHðsÞ of the ROM is defined analogously to (4). Additionally, the m a -th order structure of (1) will be preserved, which prevents the costly alternative of reducing an equivalent first order system with increased state space dimension.…”

“…Therefore, these methods have proven as a cost efficient way to reduce the state space dimension of large scale dynamical systems during the last decades [1][2][3][4][5][6]. The lack of a global error bound does not carry weight in our applications, where the signals have a limited bandwidth and local convergence is sufficient.…”

Modeling and finite element analysis of mechanical behavior of flexible MEMS components

“…To obtain more accurate data about the mechanical characteristics of MEMS, modeling and finite element analysis are needed to be developed in additional of theoretical models and experimental tests (Reitz et al 2002;Espinosa et al 2003;Paci et al 2005;Mariani et al 2008). The work developed and presented in this paper combines finite element analysis (FEA) with analytical models and experimental investigations for an accurate estimation of the elastic behavior of flexible MEMS components.…”