Methods And Applications Of Nonlinear Model Order Reduction Based On Trajectory Piecewise Linearization For Mutidomain Coupling MEMS

The demand for high-quality MEMS in aviation, aerospace and other high-tech fields leads to higher performance requirement, and this makes the research and development of MEMS product face great challenges. Meanwhile, because of the microminiaturization and multidisciplinary characteristics of MEMS devices, MEMS modeling and simulation usually need to consider multiphysics coupling effects, and the corresponding equations of the dynamic behaviors are nonlinear. So, in order to speed up system-level design and optimization of MEMS, macromodeling of nonlinear MEMS devices and nonlinear circuits has been a research hotspot in the co-simulation of MEMS and IC.In order to meet the requirements of macromodels with high accuracy, high efficiency and good expandability in the co-simulation of MEMS and IC, nonlinear model order reduction method based on Trajectory Piecewise Linearization (TPWL) is studied. Examples, including nonlinear transmission line circuits, micromachined switch, flexible micromachined thermal sensor, flexible thermal microactuator, in-plane thermal microactuator and micropump diaphragm, are used to verify the feasibility and efficiency of the method. The main contents of this dissertation are summarized as follows: 1) In view of the insufficient research for macromodeling of nonlinear thermoelectric coupled problems, the macromodeling of thermoelectric coupled MEMS devices with complex structures is settled by TPWL method. Taken a flexible micromachined thermal sensor as an example, the effects of local reduced basis order and linearization point number on accuracy, size and time-consuming are analyzed. As demonstrated by numerical results of tests, the thermoelectric marcomodels extracted by the TPWL method have high accuracy, high efficiency and good expandability. Thus, they may be used to the optimization design and system level simulation of thermoelectric MEMS devices.2) A Global Maximum Error Controller-based TPWL (TPWL-GMEC) method is proposed to overcome the difficulty of TPWL method in selecting high quality linearization points. Through a nonlinear transmission line RC circuit, a nonlinear transmission line RLC circuit and a micromachined switch, the effectiveness of the TPWL-GMEC method is verified. Compared with the TPWL methods with other linearization point selection strategies, the TPWL-GMEC method is not only appropriate for single trajectory but also for multiple trajectories, and the obtained macromodels have lower orders, less linearization points, higher accuracy and better expandability.3) To facilitate the system level simulations of thermoelectric MEMS devices and reduce the simulation workload of the corresponding optimization design, macromodeling of thermoelectric MEMS devices using the TPWL-GMEC method is introduced via two MEMS thermal actuators. The simulation results further show the good performances of the TPWL-GMEC method, such as high accuracy, satisfactory reducing effect, high speedup ratio and good expandability.4) Considering relatively high computation cost of the TPWL-GMEC method compared to other methods, the TPWL-GMEC method is coupled with the POD method and a two-stage linearization point selection method. The efficiency of the new method is increased by several times in the premise of precision. Thereby the shortage of the TPWL-GMEC method with respect to the macromodeling efficiency is remedied. Finally, the practicability and efficiency of the improved TPWL-GMEC method is shown by using an in-plate MEMS thermal actuator, a micromachined switch and a micropump diaphragm with electrostatic actuation.