参数激励驱动微陀螺振动系统的非线性振动特性和时滞反馈控制研究

发布时间：2019-05-24 04:38

【摘要】：该文考虑一类谐振式静电驱动硅微陀螺的刚度非线性和驱动力非线性,并考虑这些非线性因素引起的复杂动力学行为(如振动跳变和概周期振动)。首先利用Lagrange方程建立微陀螺振动系统的动力学方程,然后利用多尺度法分析系统动力学方程的周期解,进而讨论周期解的Hopf分岔条件,并利用四阶Runge-Kutta法数值模拟时滞受控系统动力学行为随参数的演变,验证理论分析结果的有效性。研究结果表明,在1：1内共振和较大的载体角速度下,激励频率的变化容易引起微陀螺振动系统的多稳态解、跳跃现象和概周期响应等复杂动力学行为；调节交流电压频率和降低交流电压幅值可以有效控制微陀螺振动系统的复杂动力学行为,提高微陀螺振动系统的稳定性和可靠性。根据上述微陀螺振动系统动力学特性,探索应用时滞位移反馈的方式来提高系统稳定性,结果表明时滞反馈控制是一种有效的控制方式,既可以有效的控制系统振幅,防止系统过度振动,又避免了系统多稳态的出现。根究微陀螺振动系统理论研究结果,提出一种有效的自适应驱动与检测控制的工程实现方法,此方法特征在于智能自适应控制和时滞位移反馈控制。自适应控制的原理是根据检测角速度的大小自动控制驱动方向的幅值,以此来控制系统输出,同时引入环境温度和加速度反馈控制,来提高系统抗干扰能力,并利用时滞位移反馈控制的方法来提高系统的稳定性。
[Abstract]:In this paper, the stiffness nonlinear and driving force nonlinear of a class of resonant electrostatic driven silicon microgyroscope are considered, and the complex dynamic behavior (such as vibration jump and almost periodic vibration) caused by these nonlinear factors is considered. Firstly, the dynamic equation of the micro gyro vibration system is established by using the Lagrange equation, and then the periodic solution of the dynamic equation of the system is analyzed by using the multi-scale method, and then the Hopf bifurcation condition of the periodic solution is discussed. The fourth-order Runge-Kutta method is used to simulate the dynamic behavior of time-delay controlled systems with parameters, and the effectiveness of the theoretical analysis results is verified. The results show that the change of excitation frequency can easily lead to the complex dynamic behavior of microgyroscope vibration system, such as multistable solution, jump phenomenon and almost periodic response under 1:1 resonance and large carrier angular velocity. Adjusting the frequency of AC voltage and reducing the amplitude of AC voltage can effectively control the complex dynamic behavior of micro gyro vibration system and improve the stability and reliability of micro gyro vibration system. According to the dynamic characteristics of the vibration system of the micro gyro, the method of applying time delay displacement feedback to improve the stability of the system is explored. The results show that the time delay feedback control is an effective control mode, which can effectively control the amplitude of the system. To prevent the excessive vibration of the system, and to avoid the emergence of multi-steady state of the system. Based on the theoretical research results of micro gyro vibration system, an effective engineering implementation method of adaptive drive and detection control is proposed, which is characterized by intelligent adaptive control and delayed displacement feedback control. The principle of adaptive control is to automatically control the amplitude of driving direction according to the detection angular velocity, so as to control the output of the system. At the same time, the feedback control of ambient temperature and acceleration is introduced to improve the anti-interference ability of the system. The time-delay displacement feedback control method is used to improve the stability of the system.
【学位授予单位】：上海应用技术大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：TH-39;TH113.1

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