Temperature parameterized reduced-order modeling method for micro-electromechanical system

Abstract

The invention discloses a temperature parameterized reduced-order modeling method for a micro-electromechanical system, and belongs to the field of micro-electromechanical system design and model order reduction. The method comprises the following steps: extracting quality, rigidity and temperature stress rigidity matrixes, and establishing a two-order dynamical equation related to temperature; constructing an orthogonal mapping matrix V; and projecting the primary two-order dynamical equation to a subspace in which the orthogonal mapping matrix V is positioned so as to acquire a temperature parameterized low-order model. The reduced-order method can greatly reduce the freedom scale of the primary model through an order reduction algorithm so as to improve the system-level modeling and simulating speed based on the reduced-order model. Simultaneously, by adopting the matrix matching principle, transfer functions of the reduced-order model and the primary model can be approximate betterso as to have higher precision. During order reduction, a projection matrix irrelative with parameters can be generated, and finally, a temperature parameter in the primary system is reserved in thelow-order model.

Description

technical field [0001] The invention relates to a temperature parameterized order reduction modeling method of a micro-electro-mechanical system (MEMS), belonging to the field of micro-electro-mechanical system design and model reduction. Background technique [0002] The MEMS device structure is usually made of silicon and processed by semiconductor technology. Since silicon is a heat-sensitive material, its physical properties are greatly affected by temperature. When the temperature changes, the Young's modulus, thermal diffusivity and thermal stress of silicon will change greatly, and the changes of these physical properties It will affect the resonant frequency of the MEMS device, resulting in a large error in the output signal. [0003] In order to shorten the development cycle and reduce product costs, it is necessary to improve the efficiency of design and simulation. Generally, the original model can be processed, and a certain order reduction method can be used t...

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Problems solved by technology

[0004] In the patent application number 200510025270.9, Feng Lihong of Fudan University invented a model reduction method for parameter systems for thermal models, but it is mainly aimed at first-order single-parameter systems. Does not solve the temperature parameterization problem for second-order systems

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