Equations of Motion Extraction for a Three Axes Gimbal System

Inertial stabilization of a sensor mounted on non-stationary platforms is an important task in many applications such as image processing, astronomical telescopes, and tracking systems. For this purpose, some type of gimbaling arrangements is typically used. For implementing the LOS stabilization, usually a two-axes gimbal system is used which the sensor is mounted in the inner gimbal. The dynamic modeling and designing the control system for two axes gimbal system have been studied extensively, but there is a few works on three axes gimbal system. In this paper, the equation of motion for a three axes gimbal system is derived by the moment equation. The effect of angular velocities of the base into the gimbaled dynamic system and cross-coupling between gimbals are presented. In addition, some critical notes are presented for constructing the gimbal assembly. Moreover, a model based control strategy is proposed for controlling the gimbal dynamics.