微惯性传感器振动系统的建模、全局动力学分析与时滞控制

项目名称： 微惯性传感器振动系统的建模、全局动力学分析与时滞控制

项目编号： No.11472176

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 尚慧琳

作者单位： 上海应用技术大学

项目金额： 95万元

中文摘要： 本项目定位于应用基础性研究，针对静电微惯性传感器振动系统，通过对(1) 静电微惯性传感器振动系统的建模；(2)静电微惯性传感器振动系统的谐振失稳、发散失稳和全局分岔的机制；(3)静电微惯性传感器振动系统全局动力学行为的时滞反馈控制这三个科学问题的研究，考虑微尺度下多场耦合引起的力、阻尼和刚度等方面的非线性因素，建立几类典型静电微惯性传感器的振动系统模型；研究系统的概周期振动、多倍周期振动、多稳态现象、混沌和动态吸合等行为与设计参数的关系，清晰破坏微惯性传感器振动系统的动完整性的主因，即吸合不稳定和振动跳变(Safe jump)等分形行为的机制；提出利用时滞反馈控制上述全局动力学问题，并研究控制的机理。在本项目中，对动力学的研究是基础，深刻认识微惯性传感器振动系统的复杂动力学行为的机制及其控制机理则有助于提高系统的稳定性，并对基于此的电容式微加速度计和振动式微机械陀螺的设计研制具有指导意义。

中文关键词： 时滞反馈；分岔；全局动力学；控制；微惯性传感器

英文摘要： This project is a fundamental research in both theory and application, which primarily aims at electrostatic micro inertial sensors. The following three scientific problems are mainly studied, 1) modeling of vibrating systems of electrostatic micro inertial sensors; 2) analysis on the anharmonic instability, divergence instability and global bifurcation of vibrating systems of electrostatic micro inertial sensors; 3) delayed feedbacks on controlling global dynamical behaviors in vibrating systems of electrostatic micro inertial sensors. The three major objectives of this project are to consider the factors of the nonlinearity in the electrostatic force, dumping and stiffness induced by the multifield coupling in microscale for constructing vibrating system models of several typical electrostatic micro inertial sensors; to investigate the relationship between the design parameters and the complex behaviors such as quasi-periodic vibrations, periodic-n vibrations, multistibility, chaos and dynamic pull in, and clarify the mechanism of major causes for the loss of dynamical integrity in vibrating systems of electrostatic micro inertial sensors, i.e. the phenomena such as pull-in instability and safe jump; to propose the delayed feedback control to suppressing the above-mentioned global dynamical behaviors and to investigate the control mechanism. In this project, based on the studies on dynamics, having profound knowledge of these complex dynamical behaviors in vibrating systems of electrostatic micro inertial sensors as well as their control mechanism can favor the improvement of the stability of the vibrating systems of electrostatic micro inertial sensors. Meanwhile, the project can give guidence to the design and development of capacitive micro accelerometers and MEMS vibratory gyroscopes based on vibrating systems of electrostatic micro inertial sensors.

英文关键词： delayed feedback;bifurcation;global dynamics;control;micro inertial sensor