时滞位置反馈对一类梳齿型微陀螺振动系统复杂动力学行为的控制  

Control of complex dynamical behaviours of the vibrating system of a type of comb-tooth micro-gyroscope via delayed position feedback

作　　者：尚慧琳 蒋慧敏 秦波 SHANG Huilin;JIANG Huimin;QIN Bo(School of Mechanical Engineering,Shanghai Institute of Technology,Shanghai 201418,China)

机构地区：[1]上海应用技术大学机械工程学院,上海201418

出　　处：《振动与冲击》2022年第20期18-27,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金面上项目(11472176)。

摘　　要：以一类典型的静电驱动梳齿型微机械陀螺动力学模型为研究对象,首先,建立微陀螺结构的二自由度振动模型,并考虑微陀螺结构的实际情况对该模型进行一定的简化;其次,通过多尺度法得到主共振条件下周期解的解析形式及其稳定性,结合数值模拟系统的动力学响应,揭示系统参数影响驱动方向和检测方向的振幅和分岔行为的机制。研究结果表明,激励频率的变化容易引起微陀螺振动系统的多稳态现象及振幅跳跃等复杂动力学行为。此外,通过引入独立参数,将无扰动系统的异宿轨道进行精确的解析表达,进而运用Melnikov方法预测微结构的异宿分岔必要条件,从而获得引起微结构吸合不稳定的驱动电压临界幅值,发现时滞位置反馈控制能够有效抑制该类微陀螺结构的振动跳跃和吸合不稳定等复杂动力学行为。研究结果在微惯性传感器的设计与优化控制有潜在应用价值。A typical electrostatically driven comb-tooth micro-gyroscope was considered.Its 2 DOF vibrating system was established,which was simplified by considering the actual situation of the micro structure.Then,the prediction and stability of the periodic solutions under primary resonance were obtained by applying the multi-scale method.Combining with the numerical simulation for the dynamical responses of this system,the mechanism of the effect of the system parameters on the amplitude and bifurcation behaviors in the driving direction and detecting one were revealed.The results show that it would be easy for variation of excitation frequency to induce the multi-stable attractors and other complex dynamic behaviors such as safe jump.In addition,by introducing new parameters,the heteroclinic orbits of the undisturbed system was expressed analytically;thus the necessary conditions of heteroclinic bifurcation for variation system were predicted via the Melnikov’s method so as to obtain the critical value of the amplitude of AC voltage which could induce pull-in instability of the structure.It was found that the delayed position feedback can be used to suppress the complex dynamic phenomenon of the micro-gyroscope structure,such as safe jump and pull-in instability.The results have potential values in the design and optimal control of Microinertia sensors.

关 键 词：微陀螺 振动跳跃 吸合不稳定 异宿分岔 时滞反馈控制 安全域 

分 类 号：O322[理学—一般力学与力学基础] TH213.1[理学—力学]