Moment‐Matching‐Based Linear Model Order Reduction for Nonparametric and Parametric Electrothermal MEMS Models

Abstract

In this section we present the application of moment-matching-based model order reduction to electro-thermal MEMS models. We use the Block-Arnoldi algorithm, which was described in the section 1.3 (Algorithm 4). Reduced models are easily convertible into hardware description language (HDL) form, and can be directly used for system-level simulation. We further construct parametric reduced-order models with multivariate moment-matching approach, which will be described later in this section. Parametric reduced models are employed within an optimization loop to determine thermal parameters of thin-films. We use the software tool MOR for to automatically create reduced order models directly from ANSYS finite element thermal models. MOR for ANSYS“ is described in more details in section 5.2. Subsection 3.1.1 summarizes the general methodology for applying model order reduction for automatic generation of dynamic compact thermal models for electro-thermal MEMS, presented in [1]. Subsection 3.1.2 describes a silicon based microhotplate, which has been used as a case study in 3.1.3 and 3.1.4. Subsection 3.1.3 demonstrates the application of reduced order model for co-simulation with control circuitry and parameterization of the controller. In subsection 3.1.4 a methodology for the efficient determination of material properties via parametric model order reduction and subsequent automatic parameter fitting is presented. 3.1.5 concludes the chapter and gives an outlook to future developments in the area. 3.1.1 Methodology for Applying Model Order Reduction to Electro-Thermal MEMS Models: Achieved Results and Open Issues In [1] a methodology for applying model order reduction for automatic generation of dynamic compact thermal models for several hotplate-based MEMS devices was presented. Micro-hotplates are essential components in gas sensors, micro filaments and other thermally tunable Microsystems [2]-[4]. Their operation requires the control of the membrane temperature