MEMS多域耦合非线性宏建模的轨迹分段线性化方法研究

发布时间：2018-06-24 15:33

  本文选题：微机电系统 + 宏模型　； 参考：《西北工业大学》2015年博士论文

【摘要】：航空、航天等国防科技领域对高端MEMS产品的需求,给MEMS产品的性能指标提出了更高要求,这使得MEMS产品的设计和开发面临新的挑战。而MEMS器件的微型化和多学科交叉的特性,使得MEMS的建模和仿真通常涉及多物理场耦合,相应的动态行为方程具有非线性特性。因此在高端MEMS与IC联合仿真中,如何建立MEMS器件及非线性电路的非线性宏模型,加速高端MEMS系统级设计与优化成为一个重要的研究课题。本文针对MEMS与IC联合仿真对具有高精度、高效率和良好扩展性的非线性宏模型的需求,研究了基于轨迹分段线性化(TPWL)方法的非线性宏建模方法,并利用非线性传输线电路、柔性热敏传感器、微机械开关、柔性微热执行器、平板式微热执行器和静电微泵隔膜对方法的有效性进行了分析验证。主要研究工作如下：1)针对目前非线性热电耦合问题宏建模研究的不足,利用TPWL方法解决了复杂结构的热电耦合MEMS器件的宏建模问题。以MEMS柔性热敏传感器为例,分析了局部降阶阶数和线性化点个数对宏模型精度、阶数和运行时间的影响。研究结果表明,利用TPWL方法生成的热电耦合宏模型在具有很高的仿真效率和近似精度的同时,还具有良好的可扩展性,可用于MEMS热电器件的优化设计和系统级仿真。2)提出了基于全局最大误差控制的改进TPWL方法(TPWL-GMEC方法),解决了TPWL方法难于选取高质量线性化点的问题。通过非线性传输线RC电路、非线性传输线RLC电路和微机械开关验证了TPWL-GMEC方法的有效性。相比于其他线性化点选择算法,本文方法既适用于单轨迹情形又适用于多轨迹情形,所生成的宏模型具有更小的阶数、更少的局部线性模型个数、更高的近似精度和更好的可扩展性。3)为了更好地实现MEMS热电器件的系统级仿真、减少其优化设计过程中的仿真工作量,以两个MEMS热微执行器为例,介绍了TPWL-GMEC方法在MEMS热电器件宏建模中的应用,进一步展示了TPWL-GMEC方法在提取非线性热电耦合宏模型时具有仿真精度高、降阶效果好、加速比高和扩展性好等优点。4)针对TPWL-GMEC方法提取宏模型的计算花费略大于其他方法的不足,通过缩小线性化点选择范围和改变投影矩阵生成方式,提出了结合POD的二次选点TPWL-GMEC方法。该方法在保证精度的前提下,将TPWL-GMEC方法的宏建模效率提高了数倍,从而弥补了其在宏建模效率方面的不足。最后,以平板式热微执行器、微机械开关和静电微泵隔膜三个MEMS器件为例,展示了方法的实用性和有效性。
[Abstract]:The demand for high-end MEMS products in aviation, aerospace and other fields of national defense technology puts forward higher requirements for the performance of MEMS products, which makes the design and development of MEMS products face new challenges. Because of the miniaturization and interdisciplinary characteristics of MEMS devices, the modeling and simulation of MEMS usually involve the coupling of multiple physical fields, and the corresponding dynamic behavior equations are nonlinear. Therefore, how to establish nonlinear macro models of MEMS devices and nonlinear circuits and speed up the design and optimization of high-end MEMS systems has become an important research topic in the joint simulation of high-end MEMS and IC. Aiming at the demand of MEMS and IC joint simulation for nonlinear macro model with high precision, high efficiency and good expansibility, a nonlinear macro modeling method based on trajectory piecewise linearization (TPWL) is studied, and the nonlinear transmission line circuit is used. The effectiveness of the method is analyzed and verified by flexible thermal sensors, micromechanical switches, flexible microthermal actuators, flat microthermal actuators and electrostatic micropump separators. The main work of this paper is as follows: (1) aiming at the deficiency of macro modeling of nonlinear thermoelectric coupling problem, the problem of macromodeling of thermoelectric coupled MEMS devices with complex structures is solved by using TPWL method. Taking MEMS flexible thermal sensor as an example, the effects of local order reduction and the number of linearized points on the accuracy, order and running time of the macro model are analyzed. The results show that the thermoelectric coupling macro model generated by the TPWL method has high simulation efficiency and approximate precision, but also has good scalability. An improved TPWL method based on global maximum error control (TPWL-GMEC method) is proposed to solve the problem that it is difficult for TPWL method to select high quality linearization points. The effectiveness of TPWL-GMEC method is verified by nonlinear transmission line RC circuit, nonlinear transmission line RLC circuit and micromechanical switch. Compared with other linearization point selection algorithms, this method is suitable for both single-locus and multi-locus cases. The resulting macro models have smaller order and fewer local linear models. In order to achieve better system-level simulation of MEMS thermoelectric devices and reduce the simulation workload in the optimization design process, two MEMS thermal microactuators are taken as an example. The application of TPWL-GMEC method in macro modeling of MEMS thermoelectric devices is introduced. It is further demonstrated that TPWL-GMEC method has high simulation accuracy and good order reduction effect in extracting nonlinear thermoelectric coupling macro models. The computation cost of extracting macro model by TPWL-GMEC method is slightly higher than that of other methods. By reducing the selection range of linearization points and changing the method of projection matrix generation, In this paper, a method of quadratic point selection TPWL-GMEC combined with POD is proposed. This method can improve the efficiency of macro modeling of TPWL-GMEC method several times under the premise of ensuring precision, thus making up for the deficiency in macro modeling efficiency of TPWL-GMEC method. Finally, three MEMS devices, such as flat thermal microactuator, micromechanical switch and electrostatic micropump diaphragm, are taken as examples to demonstrate the practicability and effectiveness of the method.
【学位授予单位】：西北工业大学
【学位级别】：博士
【学位授予年份】：2015
【分类号】：TH-39
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本文编号：2062001