Nonlinear Dynamics And Delayed Feedback Control Of Micro-gyroscope System

In this thesis, the nonlinear dynamics behaviors and theirs delayed feedback control of a micro-gyroscope system are investigated, and the following results are given. Firstly, the differential equations of motion of the micro-gyroscope system are obtained based on the Lagrange equation, and then simplified with the actual working condition. For the free vibration of the system, the stability of the trivial solution is discussed.Secondly, the nonlinear dynamics and delayed feedback control of the forced vibration of the micro-gyroscope system is studied. The averaging method is used to solve the motion equations of the forced system and obtain the averaged equations. The influence of system parameters on the amplitude of the vibration is discussed. Then according to the theory of singularity, the bifurcation equation acquired from the averaged equations, is simplified and studied to analysis the bifurcation behavior of the system. In the following, delayed feedback control is applied to the forced micro-gyroscope system, and the effects of feedback parameters on the amplitude of the vibration are discussed.Thirdly, the nonlinear dynamics and delayed feedback control of the parametrically excited vibration of the micro-gyroscope system is investigated. The same as above, the averaging method is used to solve the motion equations and obtain the averaged equations of the system. With the help of Routh-Hurwitz criteria, the stability of the trivial solution is analyzed. The influence of gyroscope forces corresponding to different detuning parameter conditions are examined based on the averaging equations. The singularity theory is employed to study the effects of system parameters on the bifurcation behavior of the system. Then a bifurcation diagram with the increase of detuning parameter is given to investigate the complex dynamical behaviors of the parametrically excited system. The parametrically excited micro-gyroscope system under delayed feedback control is examined. The influence of feedback control parameters on the stability of the trivial solution, the amplitude of the vibration as well as the complex dynamical behaviors is discussed.