Chaotic and Nonlinear Dynamic Analysis of a Rate Gyro With Feedback Control in a Spinning Vehicle

• Main Authors: Chen, Heng-Hui, 陳恆輝
• Other Authors: Ge, Zheng-Ming
• Format: Others
• Language: zh-TW
• Published: 1997
• Online Access: http://ndltd.ncl.edu.tw/handle/41363287132543519477

博士 === 國立交通大學 === 機械工程研究所 === 85 === In this dissertation, a detailed analysis is presented of a single axis rate gyro mounted on a space vehicle. First, the dynamics is analyzed of a single axis rate gyro mounted on a space vehicle undergoing harmonic motion about its input or spin axis and steady angular velocity about output axis. This is a strongly nonlinear damped system subjected to parametric excitation. The harmonic balance method with fast Galerkin procedure and the incremental harmonic balance method with the multivariable Floquet theory are applied to analyze the stability of periodic attractors and the behavior of bifurcation. Besides, phase portraits, Poincare maps, average power spectra, bifurcation diagrams, parametric diagrams, Lyapunov exponents and fractal dimensions are presented to observe Hopf bifurcation, symmetry breaking bifurcation, period doubling bifurcation, interior crisis and chaotic behavior. The modified interpolated cell mapping technique (MICM) is also used to study the basins of attraction of periodic attractors and fractal structure. Further, an analysis is presented for a single axis rate gyro subjected to feedback control mounted on a space vehicle that is spinning with uncertain angular velocity ωz(t) about its spin axis of the gyro. The stability of the nonlinear nonautonomous system is investigated by Lyapunov stability and instability theorems. When ωz is steady, the system is autonomous. The dynamics of the resulting system is examined on the center manifold near the double zero degenerate point by using center manifold and normal form methods. There exist a few kinds of bifurcations such as pitchfork and Hopf bifurcation for local bifurcation analyses, a saddle connection bifurcation for global analyses. The numerical simulations are performed to verify the analytical results. The criteria for the existence of chaos by using the Melnikov technique are given also and chaotic motions are suppressed by a small parameter perturbation of suitable frequency.