| In recent years, inertial sensors have been extensively studied and thoroughly researched to enhance their performance and robustness, overcoming great challenges for better innovations. The complicated fabrication processes of inertial sensors' manufacturing may potentially cause defects and lead to the reduction in their capabilities for detection of signals while environmental factors such as temperature can pose other obstacles and prevent the devices from obtaining the desired strength or stability. Among the many technologies that currently develop micromachined gyroscopes, MEMS (Microelectromechanical Systems) have been one of the fastest growing technologies used for gyroscope manufacturing due to their low-cost. However, one of the greatest challenges of the MEMS technology for micromachined gyroscopes is that it does not meet the requirements for inertial guidance systems. In this work, an approach is proposed to improve the robustness of a Coupled Inertial Navigation Sensor (CINS) System, which consists of a ring of vibratory gyroscopes coupled along their driving axes, bi-directionally, uni-directionary, and directly. While the sum response of synchronized states gains a larger output than an individual one, the purpose of the coupling in the drive-mode is to enhance the sensitivity and minimize the negative effects of the drift rate in a CINS device. Intensive numerical simulations are performed to investigate the behavior of this high dimensional system and its response to changes in parameters, mainly the number of gyroscopes, Coriolis force, and coupling strength. Bifurcation diagrams outlining the response of the system are obtained numerically with the aid of the continuation software AUTO 2000 and XPP. Individual behaviors, including synchronization, are further analyzed using analytical methods based on perturbation theory. The Lyapunov-Schmidt reduction is applied to determine the stability properties of the synchronized solution, which emerges through a pitchfork bifurcation that can be either supercritical or subcritical, depending on the coefficients of the nonlinear terms in the governing equations of motion. Abstract group theory is also used to predict the different patterns of motion for different ring sizes. The study of stochastic noise, assumed to be Gaussian band-limited, is explored extensively to investigate the benefits of the coupling systems over the uncoupled ones. Results show that coupling can reduce phase drift and even lead to a new concept of a drive-free gyroscope system. |
